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Intei-nationai Sympos/Radiation physics ; QC100 .U57 n6.461, 1977 C.2 NBS-PUB-C 19

V) J

NBS SPECIAL PUBLICATION 461

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1 7 »77 ^^'^ Radiation Physics

^-7- ___ _________________ ^ ^ ^

Proceedings of the

(^^1 International Symposium on Radiation Physics,

held at Bose Institute, Calcutta, India

November 30-December 4, 1974

Edited by: . .

A. M. Ghose

Nuclear Physics Laboratory

Bose Institute, Calcutta—700 009, India

D. V. Gopinath

Safety Research Laboratory

Reactor Research Center

Kalpakkam 603 102, India

J. H. Hubbell

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

S. C. Roy

Nuclear Physics Laboratory

Bose Institute, Calcutta—700 009, India

Organized by. Bose Institute, Calcutta, India

Co-sponsored by: Department of Atomic Energy, India

Assistance from:

International Atomic Energy Agency

,

National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

U.^NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued January 1977
Library of Congress Cataloging in Publication Data

International Symposium on Radiation Physics, Bose Institute, 1974. Radiation physics. (NBS special publication ; 461) "CODEN: XNBSAV."

Supt. of Docs. No.; C 13.10:461

1. Ionizing radiation-Congresses. 2. Radiation- Congresses. 3. Radia- tion-Measurement-Congresses. 4. Cross sections (Nuclear physics)

Congresses. I. Chose, A. M. II. Bose Research Institute, Calcutta. III. India (Republic) . Dept. of Atomic Energy. IV. Title. V. Series; United

States. National Bureau of Standards. Special publication ; 461. QC100U.S7 no. 461 (QC474] 602Ms [539.7"2) 76-608379

National Bureau of Standards Special Publication 461

Nat. Bur. Stand. (U.S.), Spec Publ. 461, 268 pages (Jan. 1977) CODEN: XNBSAV

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PREFACE

Radiation Physics is an interdisciplinary science and in the past different

aspects of the subject such as nuclear and

atomic cross section measurements and

analysis, shielding of accelerators, dosimetry, nuclear electronics, radiation

biophysics, etc., have been discussed in

specialized symposia and seminars. It has

been increasingly felt that a symposium

presenting the subject matter in an integrated manner would be useful to specialists working in isolated areas of radiation

physics as well as to those interested in

the global view of the entire subject.

The International Symposium on Radiation

Physics held in Bose Institute, Calcutta

from November 30 to December 4, 1974, with

these ends in view provided a forum for

exchange of experiences and ideas among

different vjorkers in Radiation Physics

from different countries.

The symposium was organized by Bose

Institute, Calcutta. Moral and financial

support was received from the Departments

of Atomic Energy and Science and Technology, Govt, of India; National Bureau of

Standards, U.S.A. and International Atomic

Energy Agency, Vienna. Vie express our appreciation to those organizations.

Apart from a few minor changes, the

papers published in these proceedings

essentially represent wha.t the authors

submitted as the "final versions of their

presentations in the symposium. The

editorial board apologizes for any mistake

that might have crept in inadvertently.

All papers were retyped at Bose

Institute, Calcutta, on composition (25%

reduction) guide sheets supplied by the

National Bureau of Standards for direct

photo-reproduction. In some cases the

inserted figures and tables, although the

best available to the editors, suffer in

legibility, particularly after the sizereduction. In these cases we suggest that

interested readers write to the authors

for more detailed versions of these papers

which in most cases have been published

elsewhere

When commercial equipment, instruments and materials are mentioned or identified in these proceedings it is

intended only to adequately specify

experimental procedure. In no case does

such identification imply recommendation

or endorsement by the National Bureau of

Standards, nor does it Imply that the

material or equipment identified Is necessarily the best available for the

purpose

We regret the inordinate delay in

publishing the proceedings, the reasons

of which are beyond our control.

The editorial board gratefully

acknowledges the assistance of the U.S.

National Bureau of Standards Office of

Technical Information and Publications

received for printing and publishing

these proceedings.

A. M. Ghose

D. V. Goplnath

J. H. Hubbell

S. C. Roy

ill
I

ABSTRACT

These proceedings contain Invited and contributed papers presented at the International Symposium on Radiation Physics organized by and held

at the Bose Institute, Calcutta, India Nov. 30-Dec. ^, 197^. The purpose

of this symposium, recognizing radiation physics as the thread held in common by a variety of medical, engineering and scientific disciplines,

was to bring together specialists from these disciplines to report on, exchange, and make available through these proceedings, information and

experiences of common Interest to workers in these diverse disciplines.

Topics thus brought together in this symposium Include new measurements,

theoretical developments, compilations and applications of basic cross section and transport data for photon, electron, neutron and heavy Ion

beams Interacting with matter.

Key words: Cross sections; dosimetry; electrons; neutrons; photons;

radiation physics; symposium.

iv
TABLE OF CONTENTS

Contents Page

Preface Ill

Inaugural Address, by R. Ramanna 1 SESSION A : BASIC INTERACTION CROSS SECTIONS

CHAIRMAN: W. S. Snyder (USA)

Al. Present Status of Photon Cross Section Data 100 eV to 100 GeV

(Invited Talk), by J. H. Hubbell 3

A2. Semiemplrical Formulation of Coherent Scattering of Gamma Rays,

by S. C. Roy and A. M. Ghose 17

A3. Experimental Photoionization Cross Section of Gamma Ray Photons

for Low, Medium and High Z Atoms, by B. Slnha (Goswaml) and

N. Chaudhuri 20

7 SI A4. Inner Bremsstrahlung Accomipanying Electron Capture in Be and Cr,

by H. Sanjeevaiah and B. Sanjeevaiah 23

A5. Inelastic Scattering of 279 keV Gamma Rays by Bound Electrons In

Heavy Atoms, by D. S. R. Murty, V. Govlnda Reddy, E. Narasimhacharyulu

and S.T.P.V.J. Swamy 26

A6. Gamma Ray Attenuation Coefficient Measurements at 1115, 1173 and

1332 keV, by S. Gopal and B. Sanjeevaiah 29 SESSION B : BASIC INTERACTION CROSS SECTION

CHAIRMAN: A. K. Ganguly (India)

31. Radiation Physics and Nuclear Technology (Invited Talk),

by P. K. Iyengar 32

B2. Variation of Total to K-Shell Photoelectric Cross Section Ratios

with Atomic Number and Photon Energy, by R. Gowda and

B. Sanjeevaiah ^1

83- Optical Model Analysis of Non-elastic Interaction of 1^1.2 MeV Neutrons,

by B. Pal, A. Chatterjee and A. M. Ghose 44 SESSION C : BASIC INTERACTION CROSS SECTIONS

CHAIRMAN: J. H. Hubbell (USA)

CI. Geometric Factors in Radiation Physics Measurements (Invited Talk),

by A. M. Ghose 47

C2. Measurement of Angular Distribution of Incoherently Scattered

Gamjna Rays from Atoms , by B. Sinha (Gosvfami) and N. Chaudhuri 55

C3. Measurement and Analysis of a Few 14 MeV Neutron Capture Cross Sections,

by M. Majum.dar and B. Mltra 57

C5. Intermediate Energy Approximation of B-H Formula for the Bremsstrahlung

Cross Sections, by K. Gopala and B. Sanjeevaiah 60

V
Page

SESSION C (Continued)

C6. A New Method for the Measurement of Differential Elastic Scattering

Cross Sections of Past Neutrons, by S. Nath, A. Chatterjee

and A. M. Ghose 64

C8. Compton Scattering of 1.12 MeV Gamma Rays by K-Shell Electrons,

by P. N. Baba Prasad, G. Basavaraju and P. P. Kane . 6?

C9. Nuclear Theory Based Cross Sections of Th-232, Th-233 and U-233

and Their Applications in Reactor Technology, by S. B. Garg

and Ashok Kumar 70 SESSION D : RADIATION TRANSPORT: THEORY AND APPLICATIONS

CHAIRMAN: L. S. Kothari (India)

Dl. Development of Radiation Shielding Standards in USA (Invited Talk),

by D. K. Trubey 7^

D2. Integral Equation Methods in Radiation Transport,

by D. V. Gopinath 79

D3. Neutron Transport Problems in Spherical Geometry, by D. C. Sahnl 87

D4. Transport of Neutrons During Reactor Transients, by S. K. Kapil 91

D5. Criticality Calculations by Source-Collision Iteration Technique

for Cylindrical Systems, by V. K. Sundaram and D. V . Gopinath 9^

D6. Stochastic Method of Calculations for Fast Systems,

by B. K. Godwal and M. P. Navalkar 97

D7 . A Random Sampling Technique for Choosing Scattering Angles

from Arbitrary Angular Distributions in Dosimetric and

Shielding Computations, by P. S. Nagarajan, C. P. Raghavendran,

P. Sethulakshmi and D. P. Bhatia 100

D8. Monte Carlo Calculations on Dose Distributions from Plane Infinite

Oblique Electron Sources, by C. R. Gopalakrlshnan

and V. Sundararaman 106

SESSION E : RADIATION SCATTERING IN BULK MEDIA

CHAIRMAN: D. K. Trubey (USA)

El. Backscattering of Gamma Rays (Invited Talk), by T. Hyodo 110

E2. Transmission of Cf Fission Neutrons Through Various Shields,

by Y. T. Song 119

E3. Back-scattering (Sky Shine) of Gamma Rays from a 65O Curie ^'^Co Source by Infinite Air, by J. Swarup and A. K. Ganguly 12H

Eh. Backscattering of Gamma Rays by Barriers from Various Media,

by D. B. Pozdneyev 129

E5. Gamma Ray Streaming Through Annular Cylindrical Duct,

by K. P. N. Murty, R. Vaidyanathan and R. Shankar Singh 132

E7 . Multiple Scattering of 12-40 MeV Heavy Ions Through Small Angles,

by B. W. Hoot on, J. M. Freeman and P. P. Kane 136

vl
Page

SESSION E (Continued)

E8. Charged Particle Transport In One-Dimensional Finite Systems,

by G. Muthukrlshnan, K. Santhanam and D. V. Gopinath 140 E9. Passage of Heavy Charged Particles Through Matter,

by Shankar MukherJ i and B. K. Srlvastava

SESSION F : RADIATION SHIELDING

CHAIRMAN: P. K. Iyengar (India) .... ,

Fl. Neutron Thermallzatlon in Hydrogenous Moderators (Invited Talk),

by L. S. Kothari II49

F2. Neutron Transport Studies In Fast Reactor Shields,

by R. Valdyanathan, K. P. N. Murty and R. Shankar Singh I63

F3 . Shielding for the Variable Energy Cyclotron at Calcutta,

by G. Muthukrlshnan, Hari Singh and R. Mukherjee I66

F5. Computer Codes and Data Available from the Radiation Shielding

Information Center, by D. K. Trubey, Betty F. Maskewitz

and R. W. Roussin I7I F6. Gamma Ray Build-up Factors for Finite Media, by K. John

and D. V. Gopinath lyil SESSION G : RADIATION DOSIMETRY AND INSTRUMENTATION

CHAIRMAN: V. G. Bhlde (India) -.

Gl. Physical Principles of Photon Dosimetry (Invited Talk),

by W. S. Snyder 177 G2. Track Theory Applied to Physical, Chemical and Biological Systems,

by S. C. Sharma and Robert Katz I83

G3. Spectrum Shapes of Low-Energy Photon Sources, by R. C. Sharma,

S. Somasundaram, K. Unnikrishnan and Shlv Datta I88

G5. Dose Function for Beta Dosimetry, by S. J. Supe and Shlv Datta 193

G6. Actual Problems in Photon Dosimetry (Invited Talk), ' ....

by D. F. Regulla and G. Drexler 197

SESSION H : RADIATION DOSIMETRY AND INSTRUMENTATION

CHAIRMAN: S. Makra (Hungary) - .. ,

HI. Neutron Dosimetry by Thermoluminescence Dosimeter (Invited Talk),

by Y. Furuta and Shun-lchi Tanaka 209

H2 . Effect of Heat Treatments on Thermoluminescence of Pure AlpO.,,

by A. S. Basu and A. K. Ganguly 219

H3a. Thermoluminescence Mechanisms in Lithium Fluoride, by S. P. Kathuria,

V. N. Bapat, C. M. Sunta and V. K. Jain . . 222

H3b. Thermoluminescence Response of LiF to Gamma Rays,

by V. K. Jain and S. P. Kathuria • • • 227

vii
Page

SESSION H (Continued)

H4. Change in TL Sensitivity of Quartz due to Stress,

by M. David and A. K. Ganguly 231

H5. ESR-TL Correlation Studies in CaSO|,(RE) Phosphors, ' • by K. S. V. Nambi 23H

SESSION I : RADIATION DOSIMETRY AND INSTRUMENTATION

11. Neutron Dose Evaluation Using Calculated Neutron Spectra

(Invited Talk), by S. Makra 238

12. Utilization of Plastic Scintillator in the Measurement of

Uncharged Radiations, by P. K. Sarkar and K. N. Kirthl 2H7

13. Neutron Spectrometry by Sandwich Surface Barrier Technique,

by 0. P. Joneja 252

15. Role of High Resolution Ge(Li) Detector in Trace Element Study in

Water Activated with Thermal Neutrons, by J. M. Chatterjee (Das),

E. Peeters and M. A. Castiaux 255 CONCLUDING SESSION

Summing up of the Deliberations of the International Symposium on Radiation Physics, by A. K. Ganguly 257

viii
INAUGURAL ADDRESS

R . Ramanna

Director, Bhabha Atomic Research Centre

Trombay, Bombay-400085 , India

Prof. Sircar, Prof. D.U. Rose, Prof,

jhose, Ladies and Gentlemen:

I feel deeply honoured in being

asked to inaugurate this International

Symposi\im on Radiation Physics. It is

gratifying to note the magnitude of the

participation in this symposium from

various countries and India. I hope all

of you will have a pleasant and useful

time at Calcutta.

At this function, I v^ould like to

share some of my thoughts with you who

represent a very wide cross section in

nuclear physics on the future of nuclear

research in countries like India. V/hile we are classified as a developing

country, we happen to have a very large

number of nuclear physicists of ability

and some facilities for the study of

nuclear reactions and nuclear structure

and at least one big facility for

nuclear physics, the Variable Energy

Cyclotron which v/e are fabricating

entirely ourselves. I would therefore

like to ask myself the question before

all of you - what should be our future

programme especially considering that

providing facilities for Huclear Physics

takes both time and money ?

In the past, a greater part of the

-luclear Physics research in India has so far been closely connected with the

expansion of the atomic energy programme.

At the beginning of the programme, a

1 IleV cascade generator was installed at

TIFR, in the early fifties. This

together with radioactivity studies

constituted the nuclear physics research

facilities in the country till the

reactors in Trombay, were commissioned.

.Vith the commissioning of the reactors,

fission physics and reactor-based

nuclear and solid state physics research

started. In the early sixties the 5.5

.leV van de graaff accelerator at Trombay

'.fas installed. >/hile the nuclear

physics activity of BARC and TIPR

centred around these facilities, several

universities and DAE assisted institutes

like the Saha Institute also started

nuclear physics research using mainly

radioactivity and low energy accelerators. Since these came into existence,

there has been no further expansion of

nuclear physics research facilities

except for the forthcoming VEC project.

The performance of the nuclear

physicists during this time can be rated

very good considering the facilities

available. Notable contributions were made in the fields of nuclear structure,

fission and theoretical physics, apart

from the contribution of the nuclear

physicists to the atomic energy programme,

development of electronics and in the

field of technical physics.

It should be to the credit of the

nuclear physicists in the country that

the VEC facility is being built entirely

with local effort. The commissioning

of the VEC project is being eagerly

awaited by the nuclear physics community

of the country. In the first phase,

experiments are planned with particles

of energy up to 60 HeV. The enthusiasm

of the physicists is evident from the

experimental proposals submitted to the

seminar on VEC utilisation to be held at

the annual i'iuclear Physics and Solid

State Physics Symposium to be held in

December this year in Trombay. Experiments are being made to study (a) the few

particle nucleus interactions through

elastic and inelastic scattering

studies (b) nuclear structure studies

through their electromagnetic and strong

interactions and (c) fission phenomenon.

Further proposals to enhance the

utility of the Cyclotron is also under

consideration for the second phase of the

operation of the machine. For instance

it is planned to have heavy ion

facilities with Variable Energy

Cyclotron. Looking even more further

ahead we must ask ourselves whether we

should have a versatile heavy ion

facility at the VEC, by combining it

with a straight accelerator like a tandem machine which I believe can also

be made in the country. Is it

worthwhile ? Can we afford it ? This is as far as the immediate

future is concerned. But what of the

more distant future ? Should we expand

our nuclear physics activity further or have we reached a stage where we cannot

afford any further expansion ? In

discussing this question, we should

consider, forgetting for the time being

our economic situation, the performance

of the people so far, the experience

they have gained during the past and

the trend which nuclear physics

1
activity is taking in general in the rest

of the world. It is true, unfortunately

that days when small groups of people

working on a simple problem and can achieve useful result have gone. To achieve tangible results, it is necessary

to concentrate our efforts in major

national facilities. Granting that the

credibility of our nuclear physicists is

established and that we should not let

their past experience go to waste, we could think of the ways in which nuclear

physics activity can grow in the country.

The two major areas in v/hich

nuclear physics may grow in the future are

1. Phenomena involving the whole

nucleus or a large number of particles

in the nucleus : viz.

a) Production and study of exotic

nuclei like super heavy nuclei

and nuclei far off the stability

line,

b) physics of nucleus at low nuclear

densities like at the nuclear

surface

,

c) new phenomena involving various

collective degrees of freedom

like the giant resonances, high

spin states leading to nuclear

Heissner effect.

d) study of features like viscosity

of the nuclear matter, through

heavy ion studies.

These experiments require a heavy

ion accelerator with upgrading of the

VEC facility as envisaged above.

2 . Phenomena involving a few

nucleons and their correlations in nuclei

are

a) nuclear radius and surface

studies using n, K and p absorption in nuclei,

b) importance of baryon resonances

in nuclear systems, which should

connect up the elementary particle physics and nuclear

physics,

c) Mesic and hyperonic atoms giving

rise to a wealth of information

about the charge, mass and

current distribution in nuclei,

d) investigation of unstable elementary particles themselves by

secondary process, when they are produced in nuclei.

These studies require a machine with

an energy of 4-6 GeV_which is capable of

giving K, n, ji , and p beams.

The listing of possible experiments

under the circumstances can only be vague

and very restricted. But I have made

such a listing only for the purpose of

discussion as to what should be done for

the future. It is seen that the set of

experiments involving the whole nucleus

or a large number of particles can be

undertaken in a upgraded VEC facility, we should therefore give it serious consideration and try to provide funds for it.

However, in the case of phenomena of a few nucleons and their correlations in

nuclei, the need for a large machine is

beset by many question marks especially

from the point of view of the cost, time

of construction and the need for various

maintenance facilities. But I do not

see why the nuclear physicists in the

country cannot start making feasibility

studies just as we did when we planned

the VEC project. Feasibility studies

should not stop just because big

machines are entirely out of our range

financially though not technically as things stand.

I have great pleasure in inaugurating the conference and wish all of you

a very successful meeting.

2
PRESENT STATUS OF PHOTON CROSS SECTION DATA 100 eV TO 100 GeV*

J. H. Hubbel±

National Bureau of Standards

Washington, D.C. 20234

Recent developments in theoreticaJ. and experimental cross sections for the basic photon interactions with atoms (photoeff ect

,

coherent and incoherent scattering, and electron-positron pair

production) are reviewed. Emphasis is on the extensive total and

subshell photoeffeet calculations by J. Scofield, and on atomic

form factor and incoherent scattering function data calculated by

D. Cromer and by R. Brown. Some comparisons of these theoretical

results with available explicit cross section and total attenuation

coefficient measurements are presented.

(Atomic form factor, attenuation coefficients, cross sections, gamma rays, incoherent scattering function,

photoelectric effect, pair production, photons,

x-rays

)

Introduction

Dr. Ghose, Dr. Ramanna, Chairman

Dr. Snyder, fellow Symposium participants it is my pleasure to revisit on this occasion the city of Nobel

laureate (literature, 1913), Rabindranath

Tagore who in his G-itanjali wrote:

"'ifhere the mind is without fear and

the head is held high}

Where knowledge is free}

Where the world has not been

broken up into fragments by narrow domestic walls

}

Where words come out from the depth

of truth}

Where tireless striving stretches

its arms towards perfection;

Where the clear stream of reason

has not lost its way into the

dreary desert sand of dead habit;

Where the mind is led forward by

thee into ever-widening thought

and action —

Into that heaven of freedom, my

Father, let my country [or, my

world] awake."

30 appropriate to the spirit of this

Symposium.

In this talk I will (1) touch briefly on some topics in photon cross sections and dosimetry which will be

explored in much more depth and detail

by other speakers in this and other

-'sessions, (2) show some comparisons of

present theoretical cross sections with

available total and partial measurements

(3) look a little at Z-smoothness with

its implications for Z-interpolation,

and finally (4) make some estimates of

how well we are converging toward

"underlying reality" or the unique

photon cross section set we would all

like to have.

General Background

Any review of x-ray cross section

data should start with Rbntgen, whom we

call to mind with figure 1. This

picture, assumed to be of Frau R<3ntgen's

hand, is reproduced from Rontgen's 1895

discovery paper^ , and should have a "familiar ring" to it.

Fig. 1.

*Work supported by the NBS Office of Standard Reference Data.

3
As well as taking pictures of bones

and other hidden objects, x-rays deposit

energy, or "dose", in the media through

which they pass, as illustrated in

figure 2 by a radiation-sensitive dye

^ solution developed by McLaughlin et al. . The s-ray dose range 0-100 kilorads

illustrated in figure 2 is important in

a variety of practical applications

including, as shown in figure 3» insect

popiilation control ard food storage-life

;ension.

KILORADS 0 5 10/5 25 50 75 100

Fig. 2.

100 -r 1-

Codlmj Mcih

1

Snoil, Grain Mo?hGrain M.1e_

Fruit Leof Roller- Sugo'Cdne LeafhcpperFruit FlyBeon Weevil, Screw Worm Fly_

Tse' ".e Fly_ Pea V/eevil,l*(lowfever N'.asqjiro_ Boll Weevil, Block Blow Fly ^ Rice Weevil -

CocKchorer Peefle

*• House Fly

i J

Sit

' In figure 4 we indicate the principal photon interaction processes (see,

e.g. ref.4 ); (a) K , creation of electron-positron pairs, (b) t, atomic

photoeffect and (c) a incoherent

(Compton) scattering, contributing to

the above "energy deposition", and the

types of secondary radiations (annihilation radiation, bremsstrahlung, fluores- cence and Compton scattered photons)

which subtract from the energy deposited

at a photon interaction site. Sums over various combinations of these cross sections, corrected for the escape of

secondary radiation appropriate to a given problem, are the so-called "true

absorption coefficient" \^Q_/p, the "mass

energy transfer coefficienl? • \i-g/p, and

the "mass attenuation coefficient' t^gj^/p

(see ref . 5 for a review of this nomenclatiire) as schematically shown in

figure 4.

lyp H-a/p P-^/P l^en/P

Fig. 4. The "mass attenuation coefficient

(x/p which should include, in addition to

the processes shown in figure 4» a con- tribution from coherent (Rayleigh) seaTM

ttering a

coh. is usuall.y defined for

purposes of tabulations as (see, e„g.re£

4,6,7):

ABSORBED DOSE

(kilorods

)

'tot (1)

Fig. 5.

4:
in which N, = Avogadro's number

(6.022045 X 10 atoms/g-atom) , M i3 the

atomic weight (g/g-atom) and

tot

= -X+ T coh. (2)

The mass attenuation coefficient ii/f is

obtained from narrow-beam measiirements

of monoenergetic photon beams transmitted

by samples using the relations

or

- ln(l/lQ)/t

(3)

(4)

where I and I are the beam intensities

o with and without the interposed sample,

respectively, and t is the sample thick- ness in mass per unit area. The relative magnitudes of the

above interaction processes as a function of photon energy are shown in

figure 5 for the case of copper, with

the further addition of the photonuclear cross section a which has ph. n. a broad peak, or "giant resonance"

feature, centered at about 24 MeV for

light nuclei, decreasing in energy with

increasing mass number to about 12 MeV

for the heaviest nuclei^ . Experimental

total cross sections o^q^ for copper,

derived from existing n/f measurements^

using the above relations in equations

(4) and (1), are shown in figure 5 as

the small circles.

COPPER (Z=29)

10 eV IkeV IGeV lOOGeV

The coverage of total cross section

measurements for other elements is shown

in figiire 6 in which the solid black

bars indicate that we know a. . or u/p" tot '^'^

to within a ± 2'/. uncertainty. A fea

ture of interest in figure 6 is the

in existing measurements in the neigh

borhood of 1 keV.

ESTIMATED UNCERTAINTY

v1 .1 IMeV ISeV PHOTON ENERGY Fig. 6. Comparisons of Theoretical with Experi- mental Total Cross Section Data

In the next series of figures we will compare some of the total cross section measurements indicated in

figure 6 with some existing compilations

of theoretical or smoothed data.

In figure 7 for hydrogen we see

that the Henke et al. (67 He 01)-^°

PHOTON ENERGY, keV Fig. 7.

5
total cross section measurements and

the Crasemann et al. photoeffect

measurements suggest, as discussed by

Cooper-'-^ that the photoeffect cross section for molecular Hp is roughly AO'/. higher than for atomic H for photon

energies 0.5 to 10 keV. An even larger

enhancement (as much as a factor of two)

in the coherent scattering cross section for Hp vs. H^is predicted by

Bentley and Stewart"*--^ (see also

integral data in ref. 14). Hence,

although cross section compilations

(see, e.g. ref. 4,6,7) customarily

present data only for the exactlycalciilable isolated H-atom, for practical applications a table of molecular H- cross section data should perhaps also ' be included in subsequent compilations.

Figure 8 for lithium shows the gap

in our experimental information around

1 keV mentioned earlier also the status

of some of the calculated and fitted

results. No significant difference is seen here between the Sandia (Biggs and

^^SANDIA (1971) 3*-' a 62 Bo 01 —

68 Ko 01 — ~ V

o 69 De 01 —

60 Go 01 V 57 OJ 0!

— \

\

N(I971) * 65 Pf 01 —

0 21 He 01 —

O 59 Ro 02 ~

• JO Ma 01 —

lo" \ ~ \ Z \

• 65 We 01 « 35 Mo 01 35 Ge 02 ^

o« 10 z<

1 \L SCOFIELD (1973)

^ j-HARTREE - SLATER YyHARTREE - FOCK \ 10

V

10°

(O'' 1 1 i/inl 1 1 1 mill Wiiiiiil 1 1

mil i 1 Mini

O' 10° lO' 10^ PHOTON ENERGY, keV Fig. 8 .

lO' 10

lighthill parametric fit and the

Kaman (Veigele et al.^° ) calculated

values. In Scofield 's-"-' recent photoeffect calculation, covering the range

1 keV to 1.5 MeV for all elements Z = 1

to 101, he has suggested that his

Hartree-Slater results could be improved

by renormalizing to the Hartree-Fock

model. Lithium happens to be the

element most affected in the K-shell by

this renormalizacion, here shown to

decrease by ?/• .

In figure 9, moving up through the

periodic table to nitrogen, we see the

I keV region reasonably well measured,

as gas targets lend themselves well to

studies in this region. Above 100 keV

we must still rely on either theory or interpolation across Z, although some data (not shown On this figure) for

nitrogen in the range 0.66 - 1.35 MeV,

deduced from measurements on carbon (in

II hydrocarbons), boron carbide and

boron nitride, were recently published

by Goswami and Chaudhuri-^" .

lO"' 10° lo' 10^ 10* lo'' PHOTON ENERGY. keV Fig. 9.

lo"' 10° io' 10^ id' id" PHOTON ENERGY, keV Fig. 10.

6
In figure 10 we see that silicon, an important detector material, again

shows a wide gap in the ezperimental

information in the vicinity of 1 keV

and in this case the K absorption edge.

Further measurements filling in the

region around 1 keV woiild be usefiil.

In the region around 1 MeV the recent

silicon measurements by Goswami and

Chaudhuri^" (not shown in this

figure) are in much better agreement

with the theoretical curve than the

indicated measurements by Mavroyannakis

and Antoniades (70 Ma 01)19 and by

Boltaks et al. [5B Bo Olj^O . In figure 11 we have germanium,

another popular detector material. The

region of interest to crystallographers

from 4 to 30 keV and extending up to

100 keV is rather well mapped out,

but down around the 1 edges (1.22, 1.25

and 1.41 keV) there are disagreements

of the order of 10'/. The (not shown)

recent Goswami-ChaudhurilS .0.66 - 1.35

MeV measurements are in good agreement

with the theoretical curve shown.

PHOTON ENERGY, keV Fig. 11.

Figure 12 shows tin taken down on additional decade to 10 eV. Low-energy

data reported by NBS (Codling et al.

[66 Co 01] 21 and DESY [Haensel et al.

68 Ha 01]^^ synchrotron-light groups

and by the Leningrad group (Lukirski

et al. (66 Lu 02)^5 ) reasonably

consistent, and can be compared with the

Mc6uire24 and Kamanlo calculations,

and with the parametric fit by the

Sandial5 group. Above 1 keV the LLLNBS (McMaster et al.25,26) tabiilation

follows the. 1936 data by Biermann

(36 Bi 01^ 'K which is 30/. higher than

the Scofieldl'7 or Kamanl6 calculations

at 1 keV. Hence for tin, as for some elements previously mentioned, new measurements in the neighborhood of

1 keV would be useful.

PHOTON ENERGY. keV Fig. 12.

In figure 13 gadolinium is seen

to have a good distribution of measurements, all of them more recent than

1967, all reasonably consistent. Below,

1 keV the Kaman photoeffect calculation

is seen to agree within 20'/. with the

measured points except for the absorption peak at 150 eV observed by

Zimkina et al. (67 Zi 01)28 .

-II' iiin| I I 1

1 Mii| I I i iimi'—I I

I —I I 1 1 nil

PHOTON ENERGY. keV Fig. 13.

7
In figure 14 uranium measurements

are gradually filling in toward lower

-I r energies. Where the Kaman and

Scofield-'-'^ photoeffect calculations

overlap in the range 1.0 - 2.5 keV,

and disagree by 10% , the recent 1-10

keV measurements by Del Grande and

Oliver (75 De 01)29 favor the Kaman

results. However at lower energies the new 130 - 450 eV uranium measurements

by Cukier et al.^O (not shown), although

PHOTON ENERGY. keV Fig. 14.

exhibiting a shape similar to that predicted by Veigele et al.^^ , are closer

in magnitude to the Sandia (Biggs and

Lighthilll5) extrapolation down through

this region. Further uranium measurements at and below 1 keV are in .,-| progress at the University of Hawaii-^

A More Explicit Look at Photoeffect

A more sensitive graphical com- parison of measured total attenuation

coefficients with calculated photoeffect cross sections can be achieved

by subtracting cal ciliated coherent and

incoherent scattering cross sections

from the measured totals, then multiplying these "photoeffect" differences

by an appropriate power of photon

energy. In figures 15 and 16 we see that the power is a convenient

compromise for application to all

elements Z = 1 to 100. Veigele and

Briggs52 have constructed these and

similar plots for all elements having

measured data in the Kaman file, for

purposes of evaluating theoretical

photoeffect cross sections shown as

solid curves in figures 15 and 16

(Kaman-l-^ below ~1 keVj Scofield^'

above 1 keV)

ENERGY (KEVt Fig. 15.

The principal features in figure

15 for carbon are (a) the slight systematic divergence of the "difference"

photoeffect data points from Scofield^^ '. theory in range 10 to 30 keY, and (b)

the complete breakdown above 30 keV of

this method for experimentally determining the carbon photoeffect cross section.

In figure 16 for uraniiijn we can now see more clearly the relation of the

Del Grande and Oliver^S measured points

(open circles) to the Veigele et al.^^

calculation (0.1 to 2.5 keV for uranium)

and to the Scofield-^' calculation ( 1 to

1500 keV)

Fig. 16.
Scattering Data

This section of the talk is a brief summary of a recent extended-range

tabulation and discussion of the atomic

form factor F(x,Z) and the incoherent

scattering function 8(2, Z), to which

reference can be made for further

detailsl4 . The atomic form factor for hydrogen

is shown in figure 17 for (a) a neutral

isolated hydrogen atom (solid curve)

calculated using the simple closed-form

"exact* formula given by Pirenne53 , (b) the "floated sphere" (0.07 2. off the

proton into the bond) Stewart et al. res- ult34 (circles useful for approximating

terminally-bonded hydrogen, and (c) H in

molecular H2 as calculated by Bentley

and Stewartl3 (triangles) using Kolosfioothaan35 wavefunctions

F(x. [Hi)

16'

FU.H), PIRENNE

• FU,H-FS.). STEWART, ET AL,. AND rC^ EXTRAPOLATION

- Fl«, jHj), BENTLEY-STEWART, AND X"* EXTRAPOLATION

0.1 1.0 X, sin(9/2j/x il) Fig. 17.

In figure 18 the ratios of the

above Stewart et al.34 and BentleyStewartl5 molecular-hydrogen results

to the Pirenne atomic-hydrogen results

suggest that H2 molecule, at least for

x<1.0 i""^, strongly resembles the He

atom. That is, the effective BentleyStewart -J- H2 form factor (~V2 for x =

0) as used in calculating the coherent

scattering cross section for H2 would

be of the form

2(h^H2)|,^0^' = 2{.J2 ']=^4 (5)

[) which can be compared with

(6)

u 1.0 \

\

\

\ I

Fix, H- F S.l/FIx, H 1

F(x,-|H2)/FIx, H)

2.0 3.0 4.0

X, sin(8/2)/x(A)

Fig. 18.

For elements other than hydrogen,

the atomic fQrm factor in the present

tabulations^^ was pieced together from

available numerical calculations by

Brown^" and by Cromer and Mann 37 , additional extended-range results -.g supplied by Cromer to Veigele et al. ,

F(x,Z)

-o-ooo-co -oO CROMER

BROWN

BETHE-LEVIN6ER PRESENT TABLES 8R0WN ( } , K < 2 fl"' B - L , NORM TO BROWN AT 2A"'. ( 1, . , 2I''

0.1 1.0 X, Sin (9/2 )/x(A) Fig. 19.

13—0__p 000 00 o CD c

10'

2

10'

F(x,Z)

id'

O CROMER

BETHE-LEVINGER IK-SHELL) PRESENT TABLES

CROMER, K < 10 X"' B.-L , , > 10 J-' \

I \.X

01 10

X, sin (e/2)/x(A) Fig. 20.

9
and from the Bethe-Levinger58 closedform expression for the asymptotic

high-x region. The composition of the

present tables from the above datasoiirces is indicated in figures 19, 20

and 21 for helium, aluminum and lead.

Fix, Z)

-o-ooo oo oaooococ

PRESENT TABLES CROMER. X 10 A"' 10 l~'

0.01 0 1 1.0 10 100

K, sin (e/2)/x(A) Fig. 21.

In figure 22 through 26 we compare

the above theoretical form factor tabulation with available measurements for

MEAS^

• 8.04 keVl O 17.5 kev' CALC : PRESENT (BROWN)

} [69 Ha Ol]

1.0 o 2.0

X, sin (e/2)X(A) Pig. 22.

1.0 ^ 2.0

X, sln(e/2)/'x(A)

Pig. 23.

F{x,Z)

1 I 1 I 1 1 1 1 1 1

MEAS. : —\* V 8 04 keV [36 Br 01] '

= A 17.5 keV [55 Be Oil — \ o 175 keV [6 1 Ba 01 ] -

0 430 kcV [68 Wa Oil — ^\ 145 keV [69 Gh Ol] —

': • 17.5 keV [69 Jo Olj

•<V 8.04 keV [69 Ro 01] -

. 8.04 keV [71 Li 01] CALC.: — —~— PRESENT (CROMER) TP _

1 1 1 1 I 1 1 1 ! \~ I \ 1.0 ^ 2.0

X, sin (9/2 A) Fig. 24.

3.0

1.0 10

X, 5in(9/2)/'x(A) Pig. 25.

F(x,Z) Z

r~DLQi 1 M 1 1

1

[

1 III 1 lll 1 1 1 1 I

, 1 l| ;

-

_ MEflS:

. 1330 keV |157Be OIJ O 1330 keV [SSBe Ol] y 2620 keV [58 Eb 01] — O 5 II keV [66 Ha Ol]

Vv

^\ J

- & 1330 keV [71 Ho Ol]

Z CALC

_ PRESENT ( CROMER

T F

' CROMER - VEIGELE

1 1 1 Mil! 1 1 1 1 1

B -L 1

,1,1 , 1 1 1 1 11 i[ \

1.0 X, sin(9/Z)/X( Pig. 26.

10
the elements beryllium, neon, aluminum,

tin and uranium, also with, form factors

calculated using the Thomas-Fermi (TP)

statistical model of the atom. In the

measurement-reference symbols in

figures 22-29, the first two digits

refer to the year of publication and

are followed by the first two letters

of the first-author's last name and am additional number for uniqueness. For

example, "[58 Sb 01]" stands for "Eberhard, F., G-oldzahl, L. and Hara, E., J.

Phys. Radium i^, 658-667 (1958)". A

complete listing of measurement references for these and other elements is

given in reference of this paper.

Figures 27 to 29 show similar com- parisons of the present theoretical tabulations-^^ of the incoherent scattering function S(x,Z) with available

measurements for carbon, aluminum and

lead. For the elements helium through

carbon we have used the configurationinteraction results of Brown35 in

preference to those of Cromer and

Mann39 for S(2,Z) [also for F(z,Z)].

As can be seen in figure 27 for carbon,

the differences in S(z,Z) for Be, B

and C between Brown and Cromer-I*Iann in

the range z=0to0.5^ are substan-

"1—

9.13 HV [42 La 0 Ij CALC: PRESENT (BROWN ) CROMER

5 1.0 X, sin(e/2)/x( A) Fig. 27.2.0

MEAS,280 ktV (64 An 01] O 662 ttV (66 Qu Oil

PRESENT ( CROMER )

20 40 60 80

X, sin(S/2)/X(A) Fig. 29.

tial, resulting in 20'/. to 30*/. differences in the integrated incoherent

scattering cross section at 1 keV.

Pair Production

Recent total attenuation coefficient measurements by Ahrens et al.40

suggest that calculated pair production

cross sections in present tabulations^ , 6 ,7 ,15 may be too low by amounts

shown in figure 30 of 0.8'/., 2*/ and 4/. for the elements copper, tin and lead at

photon energies 10 to 11 MeV.

Since no theoretical treatment is

yet available for this intermediate

energy region, various semi-empirical

schemes, as shown in figure 31, have

been employed4 ,41 ,42 , to join the

^ (I). c«lculff;»d Or Mu96e\.L (Ahren % ^ ei (.)

Cu

S(», Z) z

1

1 1

,

MEAS

0 17.5 li«V [42 Lo 01 1 » i.05 keV [56 Wo 01

i 280 keV [S4 An Oil V 17.5 ktV (6 e Ph 01]

CALC.

/ ,

1

1 PRESENT (CROMER)

1. .J_ J

1 , 1 1.2 sm(8/2)/x(A) Fig. 28.

Sn

Pb

lO-o laz 10* fO s lae n.o PHOTON EH£ROT / M.Y

Fig. 30.

11
T 1 I

1 r—~i r

10 20 30 i.0 =0 &0 70 90 '^0 100 110 PHOTON ENERGf / MeV Fig. 31.

threshold-region (1.022 to 5 MeV) re- sults to the high-energy asymptotic

region. In these schemes the highenergy Davies-Bethe-Mazimon43 Coulomb

correction is usually modified to

prevent the cross section from going

negative and, within the spread of

available data-points, to smoothly join

the threshold region. In subsequent

tabulations, unless this gap in o\ir

theoretical iinderstanding is bridged

in the meantime, the empirical corre- ction-function suggested by Ahrens et aL

should be used in calculating pairproduction cross section values.

Z-Smoothness

Rau and Fano44 have suggested

looking for breaks in Z-smoothness in

the various interaction cross sections

not only in crossing the rare gases

but also in the vicinity of the "noble

metals" copper, palladixim and gold

which mark the completion of the L, M

and W d-electron shells.

o.oiL__i__J i L I !

\ I \ I 0 20 40 60 80 100 Z Fig. 32.

In figure 32 the ratios of various

bound-electron incoherent (Compton) sca- ttering On^^ models to the free-electron

EW Zlein-Nishina model are plotted vs.

Z. Here we see that although the

Thomas-Fermi (TF) statistical model

predicts a smooth Z-dependence, the

Cromer-Mann39 Hartree-Fock and Brown36

configuration-interaction models at

1 keV indeed display breaks where predicted by Rau and Fano44 . On the other hand the coherent

scattering cross section, plotted

against Z in figure 33 for several cons- tant energies, is seen to be insensitive

not only to Z-discontinuities in atomic

structure, but also to the choice of

atomic model except for the lowest-Z

elements

= 1

1 keV l^^, '

y

Ml ""i^ 10 hev

K Y

^^^0^0f''^~^ 100 hev

THOMAS-FERMI

• GROMtR-VEIGELE

A BROWN, BETHE - LEVINGER

^^fc.grt""*"'*'^! MeV

• 1

1 1 1 1 1 1 1

Fig. 33.

With the systematic all-Z photo-.g

effect calculations by Veigele et al.

and ScofieldlV now available, it is

also possible to look similarly at the

photoeffect cross section i for theoretical predictions of departures from Zsmoothness. In figure 34 > based on the

Scofield-^'7 results at 1 keV, the major

Z-dependence between absorption edges is

removed by dividing the cross section in

barns/atom by Z^, and here various multiples-of-ten factors have been applied

to examine these regions side-by side.

Although argon, krypton, palladium

and gold fall well-between edge-regions

for 1 keV, the pronounced structure

seen for incoherent scattering is not

present. The Veigele et al.lo calculated photoeffect results at 1 keV are qualitatively the same as in figure 34.

Thus present theory, at least, would

suggest that the photoeffect and total

12
o

S20

E = 1.0 KEV

Fig. 54.

attenuation coefficient can be interpolated across Z (except across absorption edges) to 1 or 2'/, although for

the heavier elements larger errors could result if a gap between measured

elements is too large.

Convergence in Time

In figure 35 one final means of

examining and evaluating photon cross sections is shown. The attenuation

coefficient for the 8.04 - keV copper

emission line in various materials

has been remeasured over the years,

following the 1909 measurements by Barkla

and Sadler45 . In this figure the

measured values have been divided by the

ENDF/b"? [McMaster et al.25 ,26 ] com- pilation values, represented by the

unit-value solid horizontal lines.

In addition to the experimental

points and the MDP/B library arbitrary

baseline in figure 35 the dash-dot

line represents the LASL [Storm and

Israel^ ] theoretical compilation and

the dotted line is the Kaman [Veigele

et al.-^° ] compilation which was fitted

to experimental values. Such graphs

indicate the rate of convergence (if

any) of measurements and theory toward

determining "underlying reality" in

which the data-points and compilationlines should coalesce to a single horizontal asymptote for each element as we proceed off to the right. . . In figure 35 copper is interesting

in that the experimentally-based Kaman

compilation appears 5"/ higher than the

bulk of the data points, even though

the two high points. Dyer46 and

Ehrenfried and Dodds47 were not given

excessive weight in the fitting. This

compilation assumed Z-smoothness, with

five iterations fitting alternatively

energy and on Z. Hence it is still

possible that the "real world" is not

as smooth in Z as suggested by the

Scofield and Kaman calculated results.

Moving down to tin and lead we see that the LASL° values, which are here

the Brysk-Zerby48 theoretical photoeffect , are 3 - 4X lower than the

measured values. The Scofield-'-' values

for \iranium, as we have noted, are also

a few percent lower than the recent Del

Grande and 01iver29 measurements in

this region.

Conclusion

In summary, uncertainties in the

available photon cross section information appear to be of the order of 20'/. or greater below 1 keV, 3 to lOX in the

region 1 to 10 keV and 1 to 4*/ above

10 keV.

Fig. 35.

13
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14
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27. Biermann, H.H., Die Massenschwachungskoeffizienten monochromatischer

Rontgenstrahlen ftir Cellophan, Al,

Se, Ag, Cd, Sn, Sb und Te bis

lois, Ann. Phys. 26, 740-760 (1936).

28. Zimkina, T.M., Fomichev, V.A.,

Gribovski, S.A., and ZhTikova, I.I.,

Some Peculiarities in X-Ray Absorption by Lanthanum Group Rare Earth

Metals, Fiz. Tver. Tela ^, 1447-

1450 (1967). See also: Izv. Akad.

Nauk SSSR Ser. Fiz. ^k* 874-882

(1967). Also Zimkina, T.M.

,

personal comm.

29. Del Grande, N.K., and Oliver, A.J.,

Soft X-Ray Cross Section Measurements for Uraniiim (Abstract), Bull.

Am. Phys. Soc. 18, 635 (1973).

Also Del Grande, N.K., personal

comm

30. Cukier, M. , Dhez, P., Wuilleumier,

F., and Jaegle, P., Photoionization

Cross Section of Uranium in the

Soft X-P^y Region, Phys. Lett.

A 48, 307-308 (1974)

31. Henke, B.L., personal comm.

32. Veigele, Wm. J., and Briggs, E.

,

personal comm. Also: Hubbell, J.H.,

and Veigele, Vftn. J., Comparison of

Theoretical and Experimental Photoeffect Data 0.1 keV to 1,5 MeV, NBS

Tech- Note 901 (1976), 43 p.

33. Pirenne, M.H., The Diffraction of

I-Rays and Electrons by Free

Molecules , (Cambridge Univ. Press,

London 1946), page 9.

34. Stewart, R.F., Davidson, E.R., and

Simpson, W.T., Coherent X-Ray Scattering for the Hydrogen Atom in

the Hydrogen Molecule, J.Chem.Phys.

il, 3175-3187 (1965).

35. Eolos, W., and Roothaan, C.C.J.

,

Accurate Electronic Wave Functions

for the Hp Molecule, Rev. Mod. Phys.

22, 219-232 (I960).

36. Brown, R.T., Atomic Form Factor for

Neutral Carbon, J.Chem.Phys. 55 . 353-355 (1971)? See also: Phys. Rev.

A 1, 1342-1347 (1970) 2, 614-620

(1970), 5, 2141-2144 (1972) and 10,

438-439 (1974).

37. Cromer, D.T., and Mann, J.B., X-Ray

Scattering Factors Computed from

Numerical Hartree-Fock Wave Functions, Acta Crystallogr. A 24, Part 2,

321-324 (1968).

38. Levinger, J.S., Small Angle Scattering of Gammas by Boimd Electrons,

Phys. Rev. SJ, 656-662 (1952).

39. Cromer, D.T., and Mann, J.B.,

Compton Scattering Factors for

Spherically Symmetric Free Atoms,

J. Chem. Phys. £1, 1892-1893 (1967).

Also: Cromer, D.T., Compton Scattering Factors for Aspherical Free

Atoms, J. Chem. Phys. 4857-

4859 (1969).

40. Ahrens, J., Borchert, H., Eppler,

H.B., Gimm, H., Gundrum, H., Riehn,

P., Ram, G.S., Zieger, A., and

Ziegler, B., Photo-Nuclear CrossSections and Pair-Production CrossSections in the Range of 10-150

MeV, Proc . Electron Accel. Working

Group Conf., Giessen, Germany (Sept.

1971), pp. 359-370.

41. Grodstein, G.W., X-Ray Attenuation

Coefficients from 10 keV to 100 MeV,

Natl. Bur. Stand, Circ. 583 (1957),

54 p.

42. Koch, H.W., Electromagnetic Cross

Sections for Electron and Nuclear

Research, Nucl. Instrum. Methods

28, 199-204 (1964).

43. Davies, H., Bethe, H.A. , and

Maximon, L.C., Theory of Bremsstrahliing and Pair Production. II. Integral Cross Section for Pair

Production, Phys, Rev. 788-

795 (1954).

44. Rau, A.R.P., and Fano, U., Atomic

Potential Wells and the Periodic

Table, Phys. Rev. 162, 7-10 (1968).

45. Barkla, C.G., and Sadler, C.A.,

The Absorption of Rbntgen Rays,

Philos. Mag. 17, 739-760 (1909).

15
46. Dyer, G.R., The Determination of

Low-Energy X-Ray Mass Absorption

Coefficients for Copper, M.S.

Thesis, Emory Univ. (1962), 80 p.

47. Ehrenfried, C.E., and Dodds, D.E.,

X-Ray Mass Attenuation Coefficients

in the 1.49 to 11.9 keV Range,

AFSWC-TN-59-33 (I960), 56 p. 48. Brysk, H., and Zerby, C.D.,

Photoelectric Cross Sections in

the keV Range. Phys, Rev. 171

292-298 (1968).

Discussion

W.S.

I refer to the fi^re showing the

early calculated results of Jaeger and

Hulme published in 1936. There were

only three other calculations shown

in the later years. Is it likely that more calculations would improve our knowledge of the photoelectric effect ? J.H. Hubbell

J.H. Hubbell

In my opinion, one of the most

urgent areas of need is the measurement

of whole-atom incoherent scattering

differential cross sections, from which

one can derive values to check present

theoretical incoherent scattering

functions. Although the K-shell and some L-shell measurements are very

valuable, we need the whole atom data

for compilation purposes. Dr. J.W.

Motz at N.B.S. plans to make some measurements, but more would also be

useful.

Snyder

The Jaeger-Hulme ( 1936 ) points were

for pair production rather than atomic

photoeffect. There are still some

1 5p/5t>orn

o Jaeger-, Hulme (1936)

D Davis, Bethe,MaxinRon (195A) — 0verb0 (197o) --expected energy dependence

1o loo looo Photon Energy /MeV

40 Additional figure from Ahrens et al.

unresolved differences between experiment

and present theory in the case of both '

'

photoeffect and pair production. Hence

in either case further calculations based

on improved atomic models would Indeed be

desirable,

A.M. Ghose '

What would you consider to be the \ most useful areas to which experimental

investigation should now be directed ?

' • -

i

16
SEMIEI-IPIRICAL FCRI-IULATION OF COHERENT

SCATTERING OF GAi'RiA RAYS

S.C. Roy and A.M. Ghose

Nuclear Physics Laboratory

Bose Institute, Calcutta-700009

India

An empirical formula to estimate Rayleigh scattering cross- section of gamma rays depending on photon energy and momentum

transfer involved was first developed by Nath and Ghose by considering the available theoretical and experimental cross-section

values. V/ith availability of much accurate cross section values

in recent times by using lar^e volume Ge(Li) detectors [M.Schumacher

et al, Hucl.Phys. A206, 531 (1973)4 Nucl.Phys. A213, 306 (1973) J it

becomes necessary to recheck the existing formula. V/e observe

reasonable difference in cross-section values in the region where

theoretical calculations are not available due to the uncertainties

in earlier measurements. In the present paper an analytical

formula of coherent scattering cross-sections of photons valid for

photon energy below 1.5 I'leV and upto momentum transfer 2.0 in units

of mc has been developed. The calculated values for different

photon energies have been compared with experimental results and is

in good agreement within experimental uncertainty.

(Analytical formulaj coherent scattering; cross section;

gamma rays; photons; Rayleigh scattering.)

Introduction

For photons of energy less than

about 1.5 I-leV and momentum transfer

during collision below about 2.0 mc units

[m is the mass of the electron, c the

velocity of light] Rayleigh scattering

is the most dominant of the processes

constituting coherent scattering of

gamma rays. Also, Rayleigh scattering,

being one of the fundamental modes of

interaction of radiation with matter, not

only requires careful investigations on

its ov7n right but careful estimation of

riayleigh scattering is important in

various radiation physics measurements

and calculations. Unfortunately,

theoretical computation of Rayleigh

scattering is a complex problem and it is

not practicable to compute the Rayleigh

scattering intensity for all photon

energy and for all scatterers.

Therefore, a simple analytical formula,

even if it is obtained semi-empirically

,

vrhich can reproduce Rayleigh scattering

cross section reasonably v/ell is useful

to radiation physicists. An attempt v/as

made by liath and Ghose-'- to develop such

a formula on the basis of the then

available theoretical and experimental

cross section values. Recently more accurate cross section values have been

reported^''* and it has become necessary

to modify the above formula. In the

present paper the development of an

analytical formula of coherent cross section valid for photon energies below

1.5 i'leV and up to momentum transfer 2.0

mc units will be described.

Derivation of the Empirical Formula

The empirical formula was proposed

on the basis of the form factor approximation in the low energy limit. If the

coherent scattering cross section a(e,Z)

is expressed in the follov-ring form:

a(e,Z) - i(l+cos2e)r2 znf(q) ... (1)

where, 6 is the angle of scattering

Z is the atomic number of

scatterer

f(q) is a function of momentum

transfer q rQ is the classical electron

radius

,

then a(e, Z)/i(l+cos2e) is a f^onction of

only and has no explicit dependence

either on the angle of scattering or on the energy of the photon. Such depend en ce is implicit through momentum transfer

q. Nath and Ghose plotted 0(q,Z) = a(e, Z)/T(l+cos2e) as a function of q and

observed it to be a smooth function of

q for energies of the photon below 0.4

MeV, but above 0.4 HeV to be a family of curves falling systematically below one another as energy increases. Nath and

17
Ghose ascribed this trend to relativistic

effects and proposed empirical corrections

to make the above expression a smooth

function of q for all values of photon

energy. This was done by introducing a factor 9(E,q) whose values is 1 for

0 <E ^0.4 MeV and (15-5 S - 4.4)"'^"35q.

for E>0.4 HeV. Using recent experimental

value of cross sections measured by

Schumacher et al, and by Roy, Nath and

Ghose4 we have now detected an explicit

energy dependence of a(q,Z) for photon

energies as small as 0.145 MeV for large

angles of scattering. The plot of log

a(q,Z) against q for different photon

energies is shown in Figure 1. In

general, it can be said that within the

experimental uncertainty coherent

scattering cross section is independent

of energy for q<!0.15 nic

'

1 III ui i:'.-. 01 mc

Fig. 1. Experimental a(q) data of lead

for different photon energies

plotted as a function of q.

In the present paper we shall derive

the modified semi-empirical formula for

a standard absorber which is taken as lead for obvious reasons and the estimation of cross section values for other

elements will be taken up later. The

equation (1) for a standard absorber of

atomic number Zq will be

a{e,Zo) = i(l+cos2e)r2(ZQ)^('l^f(q)

By plotting log a(q,ZQ) for standard

absorber lead against l/E for different

values of momentum transfer involved we observe that it can be approximated by a straight line with varying slope and

intercepts. Therefore the equation (1)

a(e,Zo) = i(l+cos2e) exp[a(q)+b(q)/Ej

The curves were fitted by least

square fitting and values of 'a' and 'b' were thus derived. As expected 'a' varies very rapidly with q for smaller

values of q and varies linearly with q for q>0.7 mc . It has been observed

that values of a for q)> 0.7 mc can be

fitted by a polynomial in q. Similarly

values of b obtained for different

values of q was plotted against q and

an expression for the sane has been

obtained. The expressions for 'a' and

'b' are given below

a = 15. 3395-44. 4843q+127.56l7q2

-197.0323q5+343.6817q4

b = 0.2532q for O^q^O.7 mc

a = 3.965 4-3.9848q

b = 0. 0769+0. 2731q2*^'^^^' for q>0.7mc

The general formula for the coheroit

scattering cross section of any element

Z can be written as : a(e,Z)=T(l+cos2e) ( Z/Zq)^^^'!^ exp[a+

(b/E) Jxl0-28cm2,

where index n(q) obtained by l^ath and

Ghose is given by

n(q)=2. 90+0. 08q+l. 27^-0. 36q^ q>0.1 mc.

for q below 0.1 mc an additional term

-0.90 exp(-500q2) was found necessary.

Discus sion

The coherent scattering cross section calculated on the basis of the

present formula for lead was compared

with the experimentally obtained values

in Figure 2. Except for photon

energies 1.17 and 1.33 HeV the cross section values for angles greater than

30° were taken from the measurements

18
1^

L^*«. »o'(Ref.2,3)

section values for photon energy .1.33 HeV

and angles 30° onwards were compared with

tiie measured data of Dixon, Storey and

Kardie et al; whereas for angles less

than 30° were co:npared with measured

values of i<ath and jhose5, Hoy and Ghose°

and standing and Jovan.ovich" . The

comparison shows that agreement is quite

satisfactory within the experimental

uncertainties. SchumacherlO studied Zdependence of coherent scattering cross sections in the intermediate to high

Z region for a few elements and more accurate measurements covering wider

range of elements are necessary to

recheck the values of n as obtained by

i>Iath and Ghose. The present formula will

be utilised to study electronic charge

density distributions of various elements

and to recheck the earlier calculations

by Roy and G-hose-^-^ for lead.

Our thanks are due to Prof. 3.M.

Sircar, Director, Bose Institute for his

kind interest in the work.

Refer enc e s

1. Nath, A. and Ghose, A.ii. , NBS

Technical l^ote 442 (1968).

2. Schumacher, K., Phys . Rev. 132, 7 (1969)

3. ochumacher, M, Smend, P. and Borchert,

I., JJucl. Phys. A206 . 531 (1973).

4. Roy, S.C., Ilath, A. and G-hose, A.!-!., Nuclr. Instr. and Methods (accepted for

publication

5. I'lath, A. and Ghose, A.r-'I., Wucl. Phys.

^, 547 (1964).

6. Dixon, W.R. and Storey, R.S., Can. J. Phys. 46, 1153 (1968)

7. Hardie, G., Merrow, v/.J. and Schwandt

,

D.R., Phys. Rev. CI, 714 (1970).

8. Roy, S.C, and Ghose, A.ii., Ph.D.

thesis of Roy (C.U'. 1971).

g. Standing, K.G. and Jovanovich, J.V.

,

Can. J. Phys. (1962) . 10. Smend, P., Schumacher, i-i. and Borchert,

I., Nucl. Phys. A21'j . 309 (1973).

11. Roy, S.C. and Ghose, A.k., Phys. Rev.

8A, 2298 (1973).

6 55 10 So w 85 i25 rtS" SCATTERING ANGL£ W DEGREES

-rtr

2. Comparison of the empirical

formuJLa ^/ith the experimental

data for different photon

energies

made by Schumacner. For angles loss than

3C°, except for 1.33 1-ieV, the cross section values are taken from the

measurements made by Roy, iiath and

Ghose^ and i>Iath and Ghose^. The cross section values of 1.17 ileV for angles

30° onv/ards v;ere taken frpm the measurements of Dixon and Storey*^. The cross
EXPSRIM^:i;NTAL PHOTOIONIZATION CROSS

Si:;CTI0N3 OF GMOTA RAY PHOTONS FOR LO\I, MBDITTM AND HIGH Z ATOMS

B. Sinha (G-oswami) and N. Chaudhuri

North Bengal TJniversity, Darjeeling

India

Direct measurements of subshell and total photoionization

cross sections reported so far are relatively few. Total photoionization cross sections have been determined previously from

the measured total photon attenuation cross sections using the

available theoretical estimates of incoherent and coherent

scattering cross sections and above 1.02 MeV the electron-positron

pair production cross section. This method is suitable at an energy region for such atoms for which photo absorption contribution is larger than or at least comparable to other individual

contributions to the total photon attenuation coefficient. Theoretical investigations have been continued to improve the accuracy

of individual cross sections. J.H. Scofield has calculated

screened relativistic photoionization cross sections for all 100

atoms (Z = 1 - 100) in the energy range from 1 keV to 1.5 MeV.

Refined incoherent and coherent scattering calculations for all

100 elements over a wide energy range using SOP Hartree-Pock wave functions have been reported recently. Improved pair production

cross sections are also available. In view of these accurate

theoretical results and inadequacy of experimental information

on photoionization in the energy from 10 to 100 keV and above,

v/e have evaluated experimental total photoionization cross sections

for lov7, medium and high Z elements in the range Z = 12 to 92, from

the very accurately measured total cross sections using the accurate

theoretical estimates of partial cross sections. An analysis of

the experimental results has been made and interpreted in a comparison of the theoretical photoionization results recently published.

The Z dependence and photon energy dependence of total cross sections have also been studied.

(Coherent scattering, cross sections, gamma ray, incoherent

scattering, pair-production, photoionization.)

Introducti on Highly accurate relativistic treatment of the photoionization process in

the Hartree-Slater screened potential , model has recently been made by Scofiela

for all atoms with Z from 1 to 101 in

the photon energy range from 1 to 1500

keV. In this energy range the only

other high-accuracy cross section calculations are those for 14 atoms in the

range of Z from 13 to 92 by Schmickley

and Pratt 2 . In view of these highly accurate

theoretical results, we feel a need for

reanalysis of the earlier measurements

and to carry out accurate measurements

of photoionization cross sections for

low, medium and high Z atoms over a wide

range of photon energies. The direct

measurements of phot oab sorption cross

sections so far reported are relatively

few, because of experimental difficulty

in separating the photoelectric process

from other processes involved. The other

method is to measure the total attenuation of photons, from which photoionization cross sections can be obtained by

subtraction of theoretical values for

the scattering (coherent and incoherent) cross sections and pair production cross sections for photon energy above 1,02

MeV. This method gives sufficiently

accurate resialts for such photon energies

and atoms for which photoionization con- tribution is larger than or comparable

to the scattering and pair production

contributions. Further, these cross section values must be very accurately

known. Highly accurate theoretical

values of coherent scattering cross section and incoherent scattering cross section are now available from the com- pilations of Veigele et al^ and of

Hubbell et al^. These cross section data

are based on Hartree-Fock atomic formfact or and incoherent scattering fu^^-c- tion calculated by Cromer and Mann^ and

Cromer°. In the compilation of

20
Hubbell 9t al, Bethe-Levinger relativistic K-shell form factor was used for

the atomic form factor above a momentum

transfer of 0.5 mc. New theoretical

results for pair production cross sec- tions in the energy range from 1.02 - 5 MeV have been given by ^verb^jS ^ Since

the individual photon cross sections are very accurately known theoretically at

present, the total attenuation method is

well suited in the present energy range

where available experimental data are found to be inadequate.

Method

The total attenuation method has

been used to obtain photoionization

cross sections for 34 elements from our

own measurements and the recent measure- ments of Conner et al^*-* . The measurements of total attenuation were made at a level of accuracy of about 1% . All

total attenuation data for each element were converted to attenuation cross sections usin^ the recent data of physical constant s-^^. Theoretical scattering

(coherent and incoherent) and pair production cross sections at our photon

energies were derived through interpolation of published cross section data

mentioned in the section 1.

The total attenuation data analysed

here have been obtained by excluding or minimizing a number of systematic errors which were present in many of the earlier attenuation measurements. The error in the final photoionization

cross sections for each element and

energy is a combination of errors of

(i) the measured attenuation cross

sections, (ii) theoretical scattering

and pair production cross sections and

(iii) interpolation of theoretical

cross sections.

The measiarement of transmission

of photons through a spherical or a cylindrical absorber totally enclosing

a point source of photons yields absorption cross sections of photons for

absorber atoms. Owing to the circular

symmetry of the source-absorber assembly, there is no preferred direction of

photon scattering to a suitable photon

detector and the transmission measurements by a uniform spectral sensitivity

photon counter under the required geometric conditions give total absorption

cross sections directly. Ghose-^^ developed the sphere transmission method and

measured photoelectric cross sections

by employing a uniform spectral sensitivity photon coijinter. V/e have determined absorption cross section by measuring photon transmission through

cylindrical lead absorbers in a. procedure the same as that adopted by G-hose . Results amd Discussion

Accurate theoretical whole atom

cross sections for photoionization process were not available in early sixties

and the earlier experimental values of

total atomic photo-absorption cross sec- tions were compared with the calculated

K-shell cross sections using the available values of total-to-K-shell cross

section ratio. V/e have given in Table 1

the present experimental results and the new whole atom theoretical cross sections

only for some atoms representing low,

medium and high Z elements. The theoretical results are those obtained from

tabulations giveg by Scofield and

Schmickley-Pratt . The cross sections

of Scofield are found to agree within

about iX with those of Schmickley - Pratt for the common elements in these

two calculations. For a given element

these cross sections were plotted against

photon energy to obtain a smooth curve. The cross sections were read from these curves at energies for which cross sec- tions were not directly calculated by

Scofieldl and Schmickley-Pratt 2 . it is seen from the table that the new whole

atom photoionization cross sections are in fair agreement with the measured data

except for the cross section for lead

(Z = 82) at 88.1 keV which is almost the

same as K-shell threshold energy of this

element. By the method of least-squares,

the Z^ variation of the experimental

cross sections in the range of Z from

12 to 92 has been studied at fixed photon energies. The value of the exponent

n has been found to increase from 4.2 to

4.6 in the energy range from 88 keV to

1.33 MeV. An analysis has also been

made for the variation at fixed Z in

the energy range above K-shell threshold

energy of the element. The exponent m is found to decrease slowly from 2.8 to

2.5 in the range of Z between 16 and 30

and again from 2.5 to 2.3 in the range

Z = 57 to 82.

The results of our cylindrically

symmetric transmission method are in

agreement with those obtained in the„

sphere transmission method by G-hose

This indicates that perhaps there is not

much practical distinction between two

experimental arrangements.

21
Table 1

Total phot oionizat ion croas sections

for some representative elements in the

low, medium and high Z ranges. (The final

error to the experimental cross section is

shown in parentheses).

Photon Z Experimental

energy photoionization

(keV) cross section

(barns/atom)

13

26

50

88.1 74

82

92

22

145.4 40

57

79

26

208.4 50

74

92

26

50

74

92

50

74

92

57

64

82

92

279

412

662

57

1115.5 64

82

1173

1252

(mean

value

for

Co-60

photons)

1332

57

64

82

1, 28,

423^

1783

2141

868,

2 38,

167

584,

1

33,

174.

399.

0,

14.

80,

187,

4, 29. 73.

2,5. al4.

14. 23.

,06(0.20

,46(0.46

.8 3.50)

.1 (9.40)

.9 (9.70)

.9 (5.60)

.95(0.10)

.35(0.23

.90(0.53)

.63(3.90)

.88(0.31)

,80(0.64)

.1 1.50)

,2 (2.00)

,66(0.28

,6 (0.50

.1 (0.80)

,8 (1.40)

.87(0.50)

.4 (0.70)

.4 (0.2)

.94(0.53)

,06(0.60)

.8 (0.40)

,40(0.63)

,60(0.70)

Theoretical

values from

calculat ions

of Scofieldl,

Schmickley and

Pratt 2 (barns/

at om)

0.815(0.35)

1.50(0.40)

5.02(0.50)

0.67(0.34)

1.51(0.38)

4.61(0.48)

82 a3. 85(0. 50;

57

64

82

0.663(0.32)

1.23(0.36)

3.54(0.45)

1.21

28.8

424.0

1800.0

2500.0

895.0

2.9

3.7

165.0

580.0

1.8

35.5

179.0

407.0

0.82

15.4

80.3

192.0

5.30

29.2

73.6

2.92

4.92

14.9

23.9

0.952

1.6

4.97

0.87

1.50

4.52

4.10

0.685

1.22

3.56

3. Veigele et al.,Kaman Sci.Rep.,

KN-71-43l(a) (1971).

4. Hubbell et al. , J.Phys.and Chem.Ref.

Data 4, 471 (1975).

5. Cromer, D.T. and Mann, J., Chem.Phys.

42,1892 (1967).

6. Cromer, D.T., J. Chem.Phys. ^,4857

(1969) . 7. Levinger, J. S. , Phys. Rev. 87, 656

(1952).

8. 0verb0,I., Thesis Univ. of Trondheim

(1970) . 9. GoswamijB. and Chaudhuri, J. , Phys.

Rev. A2, 1912 (1973).

10. Conner, A. L. , At water, H. F. , Plassmann,

3.H. and McCrary , J.H. , Phys.Rev.Al,

3 (1970).

11. Hubbell, J. H., Nat. Stand .Ref. Data,

Ser.NSRDS-NBS 29 (1969).

12. Ghose,A.M.,rTucl.Phys.2i, 539(1966),

Nucl. Inst, and Methods li, 45 ( 1965).

a - Results by the direct method.

References

1. Scofield, J.H. UCRL-51326(1973)

2. Schmickley, R.D. and Pratt , R.H. , Phys.

Rev. 164. 104 (1967).

22
INNER BREMSSTRAHLUNG ACCOMPANYING- ELECTRON CAPTURE

IN '^Be Al^D 5-^Cr

H. Sanjeevaiah and B. Sanjeevaiah

Department of Physics, University of Mysore

Manasagangotri, Mysore-570006 , India

The inner bremsstrahlung spectra accompanying electron capture

7Be and 51Cr are studied in coincidence with the 477 and 325 keV ; • gamma rays respectively. The random coincidence counts are

subtracted from the true plus random coincidence counts to get the

inner bremsstrahlung spectra. The disintegration energies of "^Be and Cr leading to the first excited states of and V respectively are determined from the Jauch plots. Using these values the

total disintegration energies of 7Be ^Li and ^Icr ^ly decay processes

are calculated. The total disintegration energies are also measured

directly by studying the inner bremsstrahlung spectra emitted in the

gro-und- to-ground transitions. The results obtained by these methods

will be presented and discussed.

(Coincidence; electron capture; excited state; gamma ray,- ground

state; inner bremsstrahlung; Jauch plot; spectrum; transition.)

Introduction

When a nucleus captures an orbital

electron there is a small probability

that this process is accompanied by the

emission of electromagnetic radiation.

This effect, known alternatively as radiative capture or inner bremsstrahlung

(henceforth denoted as IB) was predicted

by Morrison and Schiff-'-. The energy

spectrum of the electromagnetic radiation

was calculated to be continuous upto some maximum energy, the end-point, and to

have a characteristic shape.

Most of the early experiments^"^

performed to verify Morrison-Schif

theory showed an excess of low energy

photons. This was explained in allowed

captures by an improvement of the theory

presented by Martin and Glauber5»w which

included relativistic effects and the

possibility of radiative capture from

both S and P orbital states. However,

the predictions of both the theories

become nearly equal over a wide range of

energy below the end point. Therefore

it may be assumed that the shape of the

IB spectrum in the higher energy region

is essentially given by Morrison-Schiff

theory. Then by constructing the

Jauch-plot of the IB spectrum one can

get the end-point energy. If the

K-shell binding energy of the daughter

nuclide is added to the IB end-point

energy, one gets the disintegration

energy of the process. The present

experiments are performed to measure the

disintegration energies of electron

capture processes in 7Be and 51cr.

Experiment

The IB spectra accompanying electron

capture in 7Be and„ 51Cr to the first

excited states in 'Li and 51v are measured

in coincidence with the nuclear y-i'ays

from the de-excitation of these states.

Two Nal(Tl) crystals I'x li " and li " x 2"

in size are used in a face-to-face geometry. The resolving time (2t) of the

coincidence circuit used in the measurement is 40 ns. The bigger crystal

detects the IB photons and the signals

from it are scanned in a single channel

analyser. The smaller crystal detects

the nuclear Y-i"ays and the single channel

analyser which receives the signals from

this crystal is set on the required

photopeak. The IB detection assembly is

housed in a lead chamber of 3" wall

thickness. A lead plate of thickness

1.7 mm is placed in between the source

and the smaller crystal. This is done

with a view to reduce the spurious

coincidences due to escape X-rays and

cosmic rays.

The IB emitted in the ground-toground transitions is measured in each

case in the energy region beyond the

photopeak using the shielded Nal(Tl)

crystal and the single channel analyser

associated with it. The intensity of the sources used in these measui'ements are

somewhat higher than those of the sources used in the coincidence measurements.

The purity of the sources used in the

present investigation is checked by

recording the single spectrum over two

half-lives in each case. No significant

23
impurity peaks are detected. 51cr was obtained from Bhabha Atomic Research

Centre, Bombay, India in the form of

CrCl2 obtained from the

Radio Chemical Centre, Amersham, UK in

the form of 3eCl2.

Results and Discussion

The IB spectrum emitted in coincidence with the nuclear y-rays is obtained

by subtracting the random coincidence

counts at each channel from the corres- ponding true-plus-random coincidence

counts. Corrections for Compton

continuum, detection efficiency, energy

resolution and K X-ray escape are considered following the method of Liden and

Starfelt'''. Correction for energy reso- lution and K X-ray escape are found to

be insignificant in the energy range of

present interest. A large contribution

to the error comes from counting statistics. Jauch-plots of the corrected

spectra are constructed to get the endpoint energies. A typical Jauch plot

for the IB from electron capture decay

of '^Be is shown in Fig. 1.

Fig. 1. Jauch plot V'N(E)/E in arbitrary units versus E in keV

for the IB from electron

capture decay of '^Be to the

first excited state in 7Li.

The IB spectrum emitted in the

ground-to-ground transition is obtained

by subtracting the background co^mts at

each channel from the corresponding

total counts in each case. After

considering the corrections as before

the Jauch-plots are constructed. A typical Jauch plot for the IB from

ground-to-ground transition ^Be 7jjj_ is

shovm in Fig. 2. [The results of the

present measurements are given in

Table 1 along with those of other

workers in the fieldj

60p

Fig. 2. Jauch plot VN(E)/E in arbitrary

units versus E in keV for the IB

from ground- to=ground transsition 'Be —> 'Li.

The end-point energy of the IB

spectrum in '^Be emitted in coincidence

with 477 keV nuclear y-^^ys is found to

be 394 + 16 keV. This is in good agreement with previously measured values^* 9. The K- shell binding energy in'^Li is very

small. Therefore the disintegration

energy of the process may be considered

to be 394 + 16 keV. The end-point energy

of the IB emitted in the ground-to-ground

transition is found to be 867 + 10 keV.

This agrees fairly well with that

computed from the first measurement

(394 + 16 + 477 = 871 + 16 keV)

Table-1

End-point energies of IB spectra

Transition End-point Referenergy (keV) ence

„ E.C

'Be (First

excited

395+25

388+ 8

8

9 state) 394+16 Present

7 E.G

'Be -\± (ground-to 867+10 Present

ground)

51 ^'^

^-^Cr .51y* (First 424+16 10

excited 427+14 Present

state)

E.C

51cr— (ground-to 725+20 11

ground

)

794+60 12

748+16 Present

The end-point energy of the IB

spectrum in 51cr e-iitted in coincidence

with 325 keV nuclear y-Tays is found to

be 427 + 14 keV. This is in good

agreement with previously measured

24
value . The disintegration energy

corresponding to this transition is

433 + 14 keV. The end-point energy of 1,

the IB emitted in the ground-to-ground

transition is found to be 748 + 16 keV. 2, This is in good agreement with the value 3' computed from the coincidence measurement

(427 + 14 + 325 = 752 + 14 keV) . 4.

The results of the present experi- 5^ :nents clearly show that the predictions

of Morrison-Schiff and Martin-Glauber 5. theories become nearly indentical with

regard to the spectral distribution of 7. the IB photons in the higher energy region.

This is indicative of the fact that the S. major contribution to the IB spectrum in

the higher energy region comes from 9. radiative capture from L3 orbital state.

The deviation of the Jauch-plot from 10,

linearity in the low energy region,

however, shows the contribution from the 11.

P orbital state as well. This is

explained by I'lartin-G-lauber theory. In 12.

addition, one might observe an interesting deviation in the energy interval

40-140 keV in Fig. 1. This may be

attributed to the inadequacy of even the

relativistic theory to account for the

shape of the IB spectrum from 'Be where

it is expected to be quite accurate.

References

Morrison, P. and Schiff, L., Phys.

Rev. 24 (1940) . Saraf, B., Phys. Rev. 642 (1954).

Hadansky, L. and Rasetti, F. , Phys.

Rev. 2Ay 407 (1954).

Lindquist, T. and Wu, C.S., Phys.

Rev. 100, 145 (1955) • Glauber, R.J. and Martin, P.O., Phys,

Rev. 10^, 158 (1956) . Martin, P.O. and Glauber, R.J., Phys,

Rev. 102, 1307 (1958)

Liden, K. and Starfelt, N., Ark. f.

I^s. 7, 427 (1954).

Lancman, H. and Lebowitz, J., Phys.

Rev. C2, 465 (1971) . Borje, I, Persson and Steven, E. Koonin, Phys. Rev. C^, 1443 (1972).

Koonin, Steven E. and Persson, Broje

I., Phys. Rev. C6, 1713 (1972).

Offer, S. and Wiener, R., Phys. Rev.

107 . 1639 (1957).

Narsimha Murthy, K. and Jnanananda,

Swami, Ind. J. PureeAppl. Phys. 12,

557 (1967).

25
INELASTIC SCATTERING OF 279-KEV GAMMA RAYS

BY BOUND ELECTRONS IN HEAVY ATOMS

D.S.R. Murty, V. Govinde. Reddy, E. Narasln±iacharyulu, and S.T.P.V.J. Swaray

Department of Physics, Osmania University

Hyderabad, India

The differential cross section for the inelastic scattering

of 279-KeV photons by K-shell electrons of thorium was experimentally determined and expressed in terms of free electron scattering

cross section at scattering angles of 30°, 50"^, 70°, 105°, 125° and

150°. Two scintillation spectrometers and a fast-slow coincidence

circuit were used. The differential cross section for the inelastic

scattering vanishes as the scattering angle approaches zero and

becomes larger than the free electron scattering cross-section at

very large angles. The experimental results were compared with

those computed on the basis of different theories. Total cross section for the bound electron scattering was also obtained by

graphical method.

(Bound electrons} cross section^ gamma rays; inelastic

scattering; K-shell electron; photon; x-ray.)

Introduction

Among various types of interactions

of gamma rays with matter, Compton effect

is of considerable importance in the

energy region of few hundreds of KeV.

To study the effect of electron binding

on Compton scattering especially at lower

photon energy is of considerable interest

and has-been studied by several workers

' . In this present investigation

the differential cross section of 279

KeV gamma rays scattered by the K-shell

electrons of thorium was measured in the

angular range of 30°-150° in terms of

free electron scattering cross section.

The total cross section was also obtained

from the differential cross section by

graphical method.

Method

In the present investigation the

number of gamma rays scattered inelastically by the K-shell electrons were measured in coincidence with the corres- ponding fluorescent x-rays. Both the

scattered gamma rays, and the x-rays were detected using Wal(Tl) scintillation

spectrometer. A fast-slow coincidence

circuit with an effective resolution of

30 ns along with 20-channel pulse height

analyser was employed. The false coincidence contribution was determined by

using an equivalent aluminium foil and

subtracted from the total coincidence

counting rate. The thickness of the

thorium scatterer used throughout

observed angular range was 11.59 mg/cm"^.

Another observation was made for

scattering angle of 125° with a thinner

thorium target of thickness 4.89 mg/cm^.

A 0.9Ci radioactive Hg source was used

as the source of 279 KeV gamma rays.

Results and Discussion

The differential cross section of

279 KeV gamma rays scattered by K-shell

electrons of thorium was calculated in

terms of free electron scattering. The

ratio dav-/da-p (da-^ represents differential scattering cross section for K-shell

electrons dap represents the corresponding cross section considering the

electrons as free) was presented in

Fig. 1. The errors shown are standard

deviations. The observation that the

scattering ratio da-^/dap at 125° with

two different thicknesses (11.59 and

4.89 mg/cm^) of scatterers remained

unaffected confirmed the findings of

Krishna Reddy et al^ that the effect of

scatterer thickness is negligible on the

bound electron scattering below 20 mg/cnr

for photon energy of 662 KeV. The ex- perimental values of dax/da-p increases

from 0.264 at © = 30° to 1.191 at 9 = 150°. The increase of the ratio with

increasing scattering angle can be

easily understood from the fact that

higher and higher momentum is transferred

to the electrons at those angles and

thereby increases the probability for the

ejection of bound electrons. The ratio

reaches unity beyond 6 = 125° with 279

KeV gamma rays whereas the same ratio

reaches iinity belo^J 70° for the same scatterer with photon energy, of 662 KeV

as observed by Krishna Reddy". The

general trend of the experimental curve

as presented in Fig. 1 is that the ratio

doj^/dap approaches zero as the scattering angle approaches zero. It may i

26
sa

atTHORIUM (Z.90)

30 60 90 I20 150 SCATTEHINS C^^^v) J

tuere is no agreement between the experimental and calculated values.

Jauch and Rohrlich9 developed the

idea that in Compton scatterin^j the

initial electron is free but not stationary especially at large scattering

angles when the momentum transfer is more than the momentum of the initial electron.

Based on this idea they obtained an expression for the scattering of gamma

rays by free electrons with non-zero

velocity, i'rom this the average cross- section doiyd-Q- which is a good approximation is given for any value of

by the following expression

,da;,, J } dIL ?')d(cos a)

1

"d(cos (p)d(cos a)

Fig. 1. Comparison of present values of

dayr/da^ with the values obtained

from Eq. (1), Eq. (2) and Eq

(3).

however be pointed out in this connection that the exact relativistic calculation of V/hittingham'^ for the

incoherent scattering of 662 KeV photons

from K-shell electrons of lead gave a non zero value even at zero angle. Wo

relativistic calculations are available

for direct comparison with the present

experimental results.

The effect of electron binding on Compton scattering was usually taken

into account by introducing a scattering

function 3 as a correction to free

electron cross section and may be

expressed as:

where 9 is the angle between the planes

formed by K, P and K,K- where K, K- are

the three momentum vectors of the photon

and P is that of the initial electron,

a is the angle between the incident

photon and initial electron; is the

differential cross section for a given

value of 9 and a. The average differential cross- section using the above equation was obtained by computing da-j^/dnfor

different values of 9 ana a using IBM

1620 computer and the mean value is

determined for each scattering angle.

The values thus obtained are shown in

Figure 1 and are not in agreement with

the experimental results even at large

scattering angles. If one ignores the

variation in 9 and considers the variation in a alone as was pointed out by

I-Iotz and Missoni^C' the average cross section can be given , ., -1

da^(kQ,e,Z)

k is the incident photon energy, 6 the

angle of scattering, Z the atomic

number of the element and Sv is the

probability that the K-shell electrons

receive a momentum k from the incident

photon. Jeglecting transitions to

excited discrete states Shimizu et al°

obtained an equation for 3^^. The values

of Sjj. obtained on the basis of this

calculation was presented in Fig. 1. It is clear from the figure that excepting

the general trend of the two cixrves

< dJl/'

d(cos a)

-1 .. (3)

d(cos a)

The mean scattering cross section values

for different scattering angles calculated on the basis of this equation was shown in Figure 1 for comparison with

the experimentally obtained values. In

this case also the calculated values are

not in agreement with the experimental

values. However the values obtained by

the equation (2) and (3) agree fairly

27
well for scattering angles upto 50° and

diverges violently beyond 50°.

From the above information we may

conclude that tne experimental results

do not agree with any of the existing

theories throughout the angular range of

observation.

By multiplying the ratios dov/dop

with free electron (Klein-Wisnina j cross sections the bound electron scattering

cross sections were obtained and these were plotted in figure 2. The curve was extended to 0° on the lower angle side

and to 180° on the higher angle side.

The free electron cross section was also

shown by dotted line in the same figure.

The area under the bound electron curve represented the total cross section a-^ due to bound electron scattering while

the area countered by the Klein Nishina

values represented the total cross section due to free electron scattering and the ratio Oy/a^^ came out as about 0.5. Parthasaradhi reported this

ratio as 0.81 for lead.

The differential incoherent scattering cross sections have been computed

on the basis of Thomas-Permi bound

electron model by Donaldson et al-"- for

different elements and energies and the

interpolated values pertinent to the

present case are shown by dashed curve

(Kaman iMUClear) in figure 2. These

values pertain to all the bound electrons but not to k-shell electrons alone.

Acknowledgements

The authors express their grateful

thanks to the Department of Atomic

Energy for generous financial assistance.

The thorium foils were kindly supplied

by the Atomic o.'^aels Division of the

Bhabha Atomic 1-tesearch Centre. Thanks

are also due to the Head of the Physics

Department for the facilities given.

References

1. Hamalinga Reddy, A., Lakshminarayana

,

V. and Jnanananda, S., Proc. Phys

Soc. 91, 71 (1967).

2. Pingot, 0., iJucl. Phys. A 123 , 334

(1969)

3. Pingot, 0., Le Journal De Physique

33, 189 (1972) . 4. I'lurty, D.S.R., G-ovinda Reddy, . and

Narasimhacharyulu, E., J. Phys. A

(Gen. Phys.)6, 265 (1973).

5. Krishna Reddy, D.V., Narasimhacharyulu, E. and Murty, D.a.R., Proc.

Ind. Acad. Sci L XX 11, Sec. A, 185

(1971)

"0

10.

11.

12,

/ X

•. ^

/

Fig.

60

60

40

20

0 ^ 60 90 120 150 33o

SCATTEP'^i''- iNGLF (DEC.)

2. Comparison of experimental

differential incoherent scattering cross sections with calculated values from Klein-Nishina

formula and Thomas-Fermi bound

electron model.

Krishna Reddy, D.V., Ph.D. Thesis,

Osmania University, 1971.

V/hittingham, I.B., J. Phys. A (Gen.

Phys.) 4, 21 (1971) . Shimizu, S., Rakayama, Y. and

Mukoyama, T.,Phys. Rev. 140, A 806

(1965)

Jauch, J.M. and Rohrlich, F.,The

theory of photons and electrons

Cambridge, Mass. Addison-Wesley 1955-

Motz, J.W. and Missoni, G., Phys.

(1961) . K. , J. Phys. A 1,

Rev. 124, 1458

Parthasaradhi

,

171 (1968).

Donaldson, M.E

Veigele, V/m.J.

Henry, E.i-i. and

Ray transport, Vol.

5, Kaman Nuclear, Colorado springs,

Colorado, 1965.

28
GAMT'IA RAY ATTSITUATION COSFPICI.^NT W jJASUxHSBTSNTS

AT 1115, 1173 AND 1332 KB7

3. Gopal and B. Sanjeevaiah

Department of Physics, University of Mysore

Manasagangotri, Mysore-570006, India

(lar^ma ray attenuation coefficients in C, Al, Cu, Zr, Sn

and Pb v/ere measured for ^gamma ray energies 1115, 1173 and 1330

keV using the technique employed earlier by the authors for

similar measurements at lower energies. The results will be

presented here and discussed.

(Attenuation cpefficient; counting sequence; cross

section} gamma rayj photon.)

Introduction

Studies on the interaction of gamma

radiation with matter yield useful information for designing experimental arrangements for handling the isotopes decaying

by gannna emission. The most important

quantity characterising the penetration

and diffusion of garaTfia radiation in extended media is the attenuation coefficient

'J.. This quantity depends on the photon

energy S and the nature of the medium.

3ramna ray attenuation coefficient meas^areraents have been made from time to

time using narrow-beam-collimated geometry-'-"-'-^. In these experiments it is tacitly assumed that the energy-degraded

photons due to multiple scattering in the

sample do not reach the detector and hence

the good geometry condition is preserved.

But it may be expected that the number of

m.ultiple scattered photons reaching the

detector would increase as the sample

thickness increa.ses. The recent investigations^!' 12 indicated that the gamma ray

attenuation coefficients i'fould improve if

one follows the counting sequence of

;onner et al8 toget her x-iith the criterion

at <^1, V7here u is the gamma ray attenuation coefficient and t is the thickness

of the sample. In this paper we report

the gamma ray attenuation coefficients

measured in carbon, aluminum, copper,

zirconium, tin and lead at gamma ray

energies of 1115, 1173 and 1332 keV using

the above criterion.

Experimental Method

The experimental set-up and the

-3hape and size of the samples used in the

present investigation are the same as

those described bv the authors earlier^W^.

65 The gamma ray sources of 10 mCi Zn

flll5 keVT and 10 mCi o<JGo (1173 keV and

1332 keV) in the form of radiographic

capsules (supplied by the Isotope Division, Bhabha Atomic Research Centre, Bombay,

India) have been used. The gamma ray lines

of 1173 and 1332 keV are resolved by the

scintillation spectrometer.

The gamma ray attenuation coefficients are determined by following the

counting sequence of Conner et al° choosing the sample thicknesses such that

(at = 0.2 to 0.4 for 1115, 1173 and 1332

keV gamma ray energies in carbon, aluminum, copper, zirconium and lead. A sufficient number of counts was recorded so that counting statistics contributed less

than O.3X error. The background counts

were taken by placing a 15 cm long lead

cylinder of 1.5 cm diameter in the sample

position. The errors associated with

measured gamma ray attenuation coefficients have been calculated by the method

described earlierll» 12.

Results and Discussion

The values of attenuation coefficients measured in this experiment are given in Table 1. Also the attenuationg

coefficients determined by Conner et al , Henry and Kennett^ and Ooswami and ChaudhurilO which are common to our measurements are given for comparison.

It can be seen from Table 1 that the

present values are in general agreement

with the results of Conner et al°, Henry

and Kennett9 and Ooswami and Ghaudhuril^

suggesting that the sample thicknesses

used by them satisfy our criterion Lit<^l.

Also it can be observed that in some cases our values fill the gaps in the improved

gamma ray attenuation coefficient measurements.

29
Table 1

Comparison of measured total attenuation coefficients (cm /m).

(In parentheses is given the uncertainty in the last one or two

places )

31eraent Snergy Present work Conner et al Henry and ' G-oswami and

(keV) Kennett9 ChaudhurilO

(error 1'/.)

J—I—L J 0.060251(26) 0.06043(27) 0 .06017 0 - 0601 C 1

)

Garb on 1173 0.058261[24;) 0.0585( 1)

1332 0.05524<[24;) 0.0551(1)

1115 0.05842(31) 0.05807(45) 0 . 05781 O.C583( 2)

A T TiTTi "i Ti inm 0.05655(29;

1332 0.05347(28) - 0.0531(2)

XXJ. J 0.05586(28;] 0 • ^ J J i J

0.vV oW ^nnPT ^^ X n 73 0. 054341

1332 0.050961

1115 0.05407(27;) Zirco- 1173 0.05295(26;) nium 1332 0.04965(28;

1115 0.053671 ) Tin 1173 0.05227(

1332 0.04944(27;]

1115 0.06384(28;) 0.06324(32) 0 .06413 0.0640(1)

Lead 1173 0.06167(32)1 0.0615(1)

1332 0.05556(31) 0.0557(1)

References

1. Davisson, Q.¥. and Evans, R.D., Phys.

Rev. 8.1, 404 (1951).

2. ColTatc', 3.A., Phys, Rev. 82, 592

(1952).

3. V.'iedenbeck,M. , Phys. Rev. 126. 1009

(1962).

4. Ramana Rao, P. V., Rama Rao, J. and

Lakshminarayana, V,, Proc . Phys. 3oc

82, 1081 (1965).

5. Perkin, J.L. and Douglas, A.C . , Proc.

Phys. 3oc. 22, 618 (1967).

6. McCrary, J.H., Plassmann, 3.H.,

Puckett, Conner, A.L. and

Zimraermann, (T.V/., Phys. Rev. 153 . 307 (1967).

7. Carter, R.W., Rohrer, R.H. , Carlton,

V.'.R. and Dyer, ^.R., Health Phys.

11, 593 (1967).

8. Conner, A.L., Atwater, H. F. , Plassman,

3.H. and McCrary, J.H. , Phys. Rev. Al,

539 (1970).

9. Henry, L.G. and Kennett, T.J., Can. J. Phys. 41, 1167 (1971).

10. Coswarai, B. and Chaudhuri, F., Phys.

Rev. A7, 1912 (1973).

11. Copal, S. and Sanjeevaiah, B., Nucl.

Instr. and Meth. 1P2, 221 (1973).

12. Copal, S. and Sanjeevaiah, B., Phys.

Rev. A8, 2814 (1973).

Discussion

A.M. Chose

I would like to know what

special cares have been taken by you to

improve the accuracy of your measurements?

S. Copal

We have adopted the geometry of

Davisson and Evans but the distance between the source and the detector is doubled and the diameters of the slits are halved. This makes the maximum angle for

scattered photons {'^^^y^ to rnach the

detector equal to IS'-' and therefore the

contribution of coherently scattered photons on the measured attenuation coefficients is less than 0.05X • Also in our

30
geometry the sample position becomes

insensitive to garama ray attenuation

coefficient measurements. Our investigationsH'^2 indicate that the multiple

scattered photons reaching the detector

can be largely minimized by selecting

the sample thicknesses less than nt= 1

where |i is the attenuation coefficient

and t is the thickness of the material

and thereby improving the measurements.

D. V. Gopinath

Has it not been recognized much

earlier that the foil thickness should

be much smaller than a mean-feeei)ath for

attenuation coefficient measurements ?

^3. ?opal

I do not knov.' why it was not recognized earlier in the measurements of

gamma ray attenuation coefficients.
RADIATION PHYSICS AND SIUCLEAR TECHITOLOGY

P.K. Iyengar

Bhabha Atomic Kesearch Centre

Trombay, Bombay-400085

India

Understanding of basic interaction processes of radiations V7ith atoms, nuclei and bulk matter contributes a lot

towards the advances in nuclear technology. Yet it seems

that moi-e accurate and wide ranging measurements are required

to make accurate predictions for the design of reactors,

accelerators etc. The present article is a birds-eye viev;

of the problems which need solution in new technologies - problems due to radiation effects, study and solution of

which can arise from use of accelerators.

(Cross section; energy transfer,- gamma rays,- moderator; neutron; radiation damage; reactor;

scattering; spectrometer).

Introduction The subject of radiation physics is

a very general one. Long before man understood the structure of matter and

atoms and started theorising interaction

of radiation vjith matter, nature has been

using it in various ways. Por example,

plants nave been using optical radiation

In photosynthesis, met erological pheno- mena are a result of interaction of

radiation v/ith bulk matter.

Confining our attention to nuclear

technology, the radiations we are concerned with here are m.ainly y-vays, neutrons

and charged particles, that too in a small energy region. Parameters which

govern tiieir interaction with atoms,

nuclei and bulk matter have been measirred

for several decades now, yet it seems

that more accurate and v;ide ranging

measurements are required to make

accurate predictions for design of

reactors, accelerators, in many of the

applications. It is not my intention to cover all these, for there are several

papers in this conference dealing with

basic theories, experimental measurements and computer codes. I shall

restrict myself to a fev/ examples which

to my mind have contributed significantly

to nuclear technology. This also helps

to remind us that research in understanding the basic interactions of radiations

with both individual nuclei and collective systems can contribute a lot

towards advances in nuclear technology.

Uniq ue Mo derating Propertie s of

Zirconium hydride

An interesting example of how a systematic study of interaction of slow

neutrons v/ith matter lei to the development of a powerful, nev; moderating

material for use in nuclear research

reactors, is the discovery of the unique

tnermalising properties of zirconium

hydride. During the late fifties

physicists were interested in understanding the effects of chemical binding on the scattering and thermalising properties of various hydrogen bearing

compounds. The object of the studies v;as the difference in behaviour of the

hydrogen atom when it is free and when

it is bound in various chemical compounds

such as water polyethylene, zirconium and

other metallic nydrides. The emergence

of pov/erful research reactors having high

neutron fluxes and the concurrent development of sensitive nev/ experimental

techniques enabled the observation of

phonons - by the inelastic energy

transfers betv/een incident neutrons and

crystal lattices.

The tetrahedral structure of

zirconium hydride wnerein the hydrogen

atom sits at the centre of a tetrahedron

of zirconium atoms, performing nearly

harmonic oscillations bestows this

material with very interesting neutron

scattering properties. The tightly

bound proton is found to have quantized

optical vibration levels spaced at equal

intervals of '^'0.14 eV. Although Fermi

had predicted as early as 1936, while

discussing neutron slowing down by

hyurogenous moderators, that the boimd

proton would act as a simple harmonic

oscillator bound to an infinitely heavy

atom and have energy levels of nh-J , the first experimental evidence of such

a system was obtained only in 1957 in

simple total transm.ission experiments

with zirconium hydride^. Pig. 1 shows

the total neutron cross section of the

hydrogen in zirconium hydride obtained

with a crystal spectrometer. The arrows indicate the excitation levels for

32
°C 05 .'0 .15 .20 .25 .30 .33 ^"55 ^0 i;> INCi.-JEM NrjTRO.N £r..ESGY(»v) -ig. 1. xOtal neutron cross section of

hydrogen in Zr H2 as a function

of neutron energy.

hydrogen vibration in zirconium lattice.

Fig. 2 shows the energy distribution of

neutrons scattered from zirconium

hydride as measured^ at 296°K. The peak

at ~C.14eV corresponding to the first

optical vibrational level is clearly

visible. (Below .02 eV there is some indication of the acoustic modes and at

.28 eV a double phonon scattering peak is

just visible). Since these levels would

be excited or de-excited by collisions

with neutrons, energy transfers betv/een

slow neutrons and zirconium hydride can occur on_ly in multiples of h-i ~ 0.14eV,

vrhich is verjf large compared to kT

(~C.25 eV) , the thermal energy of the

moderator

CO 0 20 C30 ENERGY TRANSFER, Tiu (eV)

Jig. 2. Energy distribution of scattered

neutrons from Zr H2 at 296°K.

Because of the above characteristics

low temperature zirconium hydride

- oderator exhibits an unusual neutron

spectrum, significantly different from a

MaxTx-ellian distribution. During the

blowing dovm process once the neutron

energy becomes less than 0.14 eV it

cannot transfer any more energy to the

lattice. However collisions down to

ibout 1 eV is as if it v/ere with free

- jdrogerii hence the slowing down source

into the 0-0.14 eV region is xmiform

(independent of energy) and is unaffected

by molecular binding effects or moderator

temperature. When the zirconium hydride

moderator is heated, neutrons pick up

energy from the vibrating protons in

quanta of 0.14 eV; as at higher moderator

temperatures, more number of vibrating

protons are found in an excited state.

The fraction of neutrons speeded up to the

region hi) "tOu? ^^'{^^^ therefore proportional to e~ . This phenomenon has been very

effectively exploited in the design of a research reactor possessing a strong

prompt negative temperature coefficient

of reactivity. The TRIGA research

reactor as it is called, uses enriched

uranium mixed intimately with zirconium

hydride and fabricated into fuel rods.

V/hen this solid homogeneous fuel moderator rod gets heated following an accidental power excursion the average

energy of the neutron spectrum quickly

increases resulting in significant loss

of reactivity, "instantly" shutting down

the reactor. The prompt temperature

coefficient of such reactor has been

shov;n to be given by

dk _ _d -h-i /kT

dT " ^dT ®

- a_(^)2 -To/T

0 , ; where = h /k ~ 1500°K

and T ~ 300°K

a is a constant measuring the relative

loss of importance of the speeded up

neutron. The TRIGA class of reactors are very safe and have been operated successfully as Pulsed reactors producing strong

pulses of thermal neutrons.

Slowing Down Time Lead Spectrometer

The Slowing Down Time (SDT) Lead

Spectrometer^ represents another example

wherein certain special features of

neutron interaction with matter have been

exploited. Unlike zirconium hydride

which is an efficient moderator by

virtue of the presence of hydrogen, lead

has a high mass number of 207 because of

which the neutron loses on an average

only 1/. of its energy per collision.

This, coupled vrith the fact that

scattering cross section of lead is

independent of energy, leads to a type

of focussing with time during the

slowing down of monoenergetic neutrons

injected into a large lead assembly.

33
Neutrons undergoing elastic collisions

thus gather into a comparatively narrow velocity group which as a whole gradually

shifts towards lower velocities with

increasing slowing down time. Fig. 3 depicts this behaviour schematically.

By injecting short bursts of fast

neutrons periodically into a large block

of lead and by looking at events for a short interval of time -^t, delayed by

time t with respect to the initial burst,

approximately monoenergetic neutrons

could be selected. The basic equations

governing SDT spectrometer are given

below

;i)

where t : time after neutron pulse

M : Mass Number

scattering mean free path

Va,1^ • neutron velocities at to, t 2

:t) 4- e-S^

abc

• Tp-t/i (2)

^0

Q

abc

r2

Slowing dovfn density at centre source intensity

dimensions of the block

geometrical buckling

neutron age

neutron lifetime

D =

Dispersion D is given by

2_ kT

3M + 4E (3;

Equation 1 in this figure defines

the relationship between the slowing

down time t and the energy of neutrons

corresponding to this time. Equation 2 give the slowing down density of

neutrons at time t. The velocity distribution of

neutrons at any instant during slowing

down is found to be a gaussian with a dispersion given by equation 3» where E is the neutron energy corresponding to

time t

The second term, represents the

additional spectral broadening caused by

the thermal motion of the lead nucleiThese characteristics enable a large block of lead together with a pulsed neutron soujrce to be used as a neutron spectrometer having several

useful applications. The main advantage

of the slowing down time (SDT) lead

spectrometer is the large gain in

intensity by 3-4 orders of magnitude

compared to conventional time-of-flight

methods. It has been used in a wide

energy range from 0.1 eV to ~1 keV for

the measurement of capture cross Sections of a variety of nucleit • BOO/* sees

^ 3M ^ 4B

0-2 0-4 OS

.3. Slowing down spectrum in lead as

a function of energy for various

slovring down times.

Fig. 4 gives the capture cross-section

oflOS^ measured as a function of

neutron energy, using an SDT spectrometer.

A second application is for the determination of resonance parameters^. By

measuring the capture gamraa rays and

using an area method of analysis, the resonance parameters of -'- Ag, -^-'°Au,

.L3lri>a^ iDPjjg etc., have been obtained.

SOOfOO 20 fO

sooj ^see

S 4 S ^

Fig. 4. Variation of neutron capture

cross section of Ag-'-'-'" as a function of neutron energy.

34
An important application of the SDT

spectrometer is in the non-destructive

assay of Pu in irradiated fuel rods.

In the energy regign belov? 1 eV fission

cross section of^-^^ij- and -^^Pu are

similar except at 0.3 eV where ^^^pu. has

a large resonance. This difference has

been exploited to determine the 239pu

content of irradiated fuel elements by

measuring the fission yield as a function of neutron energy in the energy

range 0.1 eV - 1 eV. Fig. 5 shows

different behaviour of 259pu and 235u

samples obtained during a calibration

experiment carried out at Trombay.

Var/aiioH of // ^/g x t as a fu/icfion tf l:'r't

_

' ror Pu AND l^r

lit

%

s5

ti* rtt r(C tfi' time //}.<• sfc.f

Fig. 5. Variation of fission yield in U

-^^ and Pu239 as a function of

neutron energy.

Radiation Effects in Kuclear Technology

In the next few minutes, I v;ould now like to deal with the effects of

radiation bombardment on the physical

and mechanical properties of materials.

In the field of nuclear technology, one

is concerned with these effects since

they turn out to be major problems in

the design and development of nuclear

reactor systems. The nuclear reactor,

as everyone knows, is a high intensity

source of fast neutrons, heavy high

energy fission fragments, charged

particles and gami.-ia rays. The energy

contained in these various radiations

gets deiosited in various components of

the reactor system like the fuel

cladding and structural materials and

ultimately we are interested in extracting this energy content in one form or another to produce electrical energy.

Here I am not concerned about the

extraction of energy but about the

radiation effects that take place (in

the process of energy deposition in the

components and consequent behaviour of

the components) over long periods of -, time (of the order of a few years).

On the microscopic scale, it is

well-known that an energetic radiation

bombarding a solid can impart sufficient

kinetic energy to a lattice atom,

resulting in the lattice atom being

displaced from its normal position.

This was suggested by Wigner about

thirty years ago. Since then a large

number of physicists have been studying

phenomenon of radiation bombardment of

solids. In particular the stiidy of

formation, combination and annealing of

point defects in solids has been

pursued in a number of laboratories.

This forms a part of defect solid state

studies. For example, materials like

copper have been irradiated in nuclear

reactors at very low temperatures of the

order of 4°K and the resistivity of the

samples has been measured, after bombardment, as a function of temperature.

The recovery spectrum was studied to

understand the kinetics of recovery and

thereby the underlying atomic mechanisms.

This kind of v^ork is being pursued even after two decades; the recovery spectrum

is rather complex particularly in alloys

and there la a wealth of information to

be unravelled. Similarly interest in

optical properties of defects and other

studies are well known. These studies are essentially of basic interest to

understand the defect solid state and can be pursued only when the defect

concentration is sufficiently low. When

the defect concentration increases,

although the radiation effects increase

in their magnitude and importance

theoretical understanding become

difficult due to the complexity involved

in taking account of the mutual interactions between various kinds of defects

in the high concentration limit. On the

otherhand, during the lifetime of a reactor, various components of the

reactor get exposed to such large doses

of radiation that they come to contain a large concentration of defects within a few years and consequently radiation

effects begin changing certain physical

properties that they become technologically important. It is in this region

that physicists have begun taking interest in the last few years and my

purpose in the rest of the talk is to

high light this aspect of defect solid

state. I shall review briefly the

nature of radiation effects and how

these studies are conducted.

35
Radiation Damage

(a) Fast Neutron Bombardment

To begin with let us consider the

effect of fast neutron bombardment of a solid, in Fig. 6. Here the neutron ox energy let us say 0.1 MeV enters the

solid on the left side and collides with

an atom of the lattice. The atom is

knocked out of its 'official' position

and moves in some direction. The neutron

follows a different path. The atom

knocked out by the neutron is called the

Primary Knock-on Atom (PEA). The

kinetics of the collision like the mass

of the atom, angle of scattering

determine the energy of the PKA. It can, in its turn, have elastic and 'inelastic

collisions with other atoms in the

lattice. There can be excitation or ionisation of atoms in addition to other

atoms in the lattice being knocked out

of their sites. Hence the PKA produces

secondaries in its path and secondaries

tertiaries in their turn and so on. The

net result is a cascade of collisions

and atoms displaced from, their lattice

sites. This process goes on till the

energy transfer in a collision falls

belovr say 25 eV. This is the order of

energy required to displace atoms from

their sites. Below 25 eV, atoms cannot

be removed from their sites but this

energy gets transferred to a large

number of atoms in the form of thermal

energy - kind of 'hot-spot ' in the

material. In the literature these

regions are known as 'thermal spikes',

locally in such regions, the effective

temperatures can exceed the melting

point of the solid for short times and

recr3'-stallisation can take place. So,

therefore a single PKA can create a lot

of havoc as it ploughs through the

lattice. Sites from where atoms are removed can lie vacant-vacancies - and

dislodged atoms can come to rest at

irregular points in the lattice - interstitials. Such PKA cascades occur in

large numbers in a fast neutron bombardment till the neutron loses all its

energy and comes to thermal equilibrium

with the solid. Unless the neutron

escapes from the lattice, it is

absorbed by one of the atoms of the

lattice resulting in formation of an 'impurity' atom. The net result of all

this is that the order present in the

lattice changes to disorder and the solid

is said to be damaged due to radiation.

V/hat we have discussed so far applies to

all materials be they elemental metals

or alloys. In the case of fissile

materials, in addition to 'radiation

damage' as discussed above, vje have the

process of fission taking place, a source of fission fragments, Y"^^-^^' more neutrons etc. The fission fragments

carry enormous energies resulting in

large scale localised damage. Secondly

the fission fragments decay ending up in

gaseous products like Kryton and Xenon.

Another effect common to fissile and nonfissile materials is the formation of

hydrogen and helium due to (n,p) and

(n,a) reactions in the material.

' NEUTROH PATH WH I I I PRIMARY PATH SECONDARY PATH .....o> TERTIARY PATH

• Vacancy

O Impurity ^ St>ik»

Fig. 5. Typical damage pattern in fast

neutron irradiation.

(b) Charged Particle Bombardment

In the case of a charged particle

bombardment, shown schematically in

Fig. 7, the nature of radiation damage

is qualitatively and quantitatively

different from that in neutron bombardment. In addition to phenomena like

back-scattering sputtering etc., the

essential characteristic is that the

damage is rather dense and is confined

to a thin surface layer because of the

couJLombic nature of the interaction. One

does find however displaced atoms at

larger distances because of focussed

collisions. Impinging atoms can penetrate deeper if they are 'channelled'.

Certain components in nuclear

reactors, controlled thermonuclear fusion

reactors and space-vehicles are exposed

to a high flux of radiations - neutrons,

Y-rays, fission fragments and charged

particles. Several radiation effects occur as a result of the materials being

in this hostile environment.

36
- iHitmiitiAL

fACANCT

ir.APVtO ATOM

VACANCr

I

i—

I 5IM^7t) '•OCU53IH0 0 o c^ oo .o; o_^o

o o o

0.^0 o o

Q'lCmo o o

_ o o

O.Q O O

IW)

«U»fArf ^

VjAf.ANCy

Fig. 7. Typical damage pattern in charged

particle irradiation.

Radiation Effects (Mechanical)

A few radiation effects part iciilarly

those that affect the mechanical properties of materials are: a) radiation

growth in fissile materials like

uranium, for example, at room temperature,

when 1/. atoms have undergone fission in

monocrystal, the specimen increases in

length by AOO'/. .

(b) a similar effect on a reduced

scale occurs in anisotropic, non- fissionable materials also when they are bombarded by fission products.

(c) radiation hardening - increases

of the flow stress or yield stress of a crystal normally at low temperatures.

(d) change in the ductile-brittle

transition temperature - I shall refer

to this in greater detail in a few

minutes

(e) swelling due to gases - accumu- lation of fission products like Kr or Xe

can, for example, cause swelling of the

fuel when these gases are formed in

sufficiently large concentrations. This

phenomenon in uraniim is known to result

in 'frothing' of uranium.

(f) radiation creep - neutron

irradiation produces a weaker material

when the material is under load.

(g) swelling due to 'void' formation:

o Recently Cawthorne and Pulton of

Harwell observed that certain fast

reactor structural materials like stainless steel irradiated by neutrons

exhibited nearly 6/. increases in volume

due to 'voids'. Void-swelling is

believed to arise from nucleation and

growth of three dimensional vacancy

agglomerates, possibly originating and

stabilised in the beginning by a few gas

atoms particularly that of He. Void

formation is an important radiation

effect usually in the temperature range

of 0.3 Tm to 0.5 Tjjj.

(h) loss of ductility at high temperatures above 0.5 Tj^ due to formation

of gas bubbles when voids anneal out.

(i) blistering formation on surfaces

due to gases inside materials.

Technological Consequences

I shall now pick up a few of the

effects mentioned above and illustrate

how these effects play an important role

in the economy and technology of reactor

systems.

(a) Change in NDT

I have already referred to the effect

resulting in the change in ductile to

brittle transition temperatures. The

pressure vessels used to contain reactors are made of some kind of steel let us say. Steel as we all know is ductile above

a certain temperature but brittle below

this temperature. This characteristic

temperature at which the materials goes

over from ductile to brittle condition

is referred to as NDT in literature

(Nil-Ductility Transition). The important

point to note is that a small flow like

a hair-line crack can propagate at great

velocities below the ED'S. Above the NDT

this does not happen. A very large

number of cases in shipping are known

wherein huge ships have just broken

apart as a result of their temperature

coming down below NDT in cold waters.

Hence to remedy the situation the NDT

must be as low as possible (much below

normal operating temperatures) which can be achieved by suitable change in carbon

content of steel or by alloying the steel

with various elements. The pressure - vessels used in reactors also should

therefore be made of such materials that

its NDT must be below the operating

t emp eratur e

More than a decade earlier it was

observed that due to radiation damage

the NDT was found to shift to higher

temperatures as a function of dosage.

Fig. 8 shows this behaviour qualitatively.

In other words, a pressure vessel

designed properly out of a material

having a low NDT was no longer suitable

after operation of the reactor for a few

years since its NDT could move into the

37
operating temperat\are range of the

reactor or can even move up beyond this

range. Technologically, therefore, a new situation arose wherein there can be

a catastrophic failure of the pressure

vessel itself. Several nuclear and

non-nuclear solutions to this problem

have been proposed from time to time.

Suffice to say that a new element,

namely change in NJjT, has to be taken into

account in the design and fabrication of

reactor pressure vessels.

IRRADIATION INDUCED NDT SI-! ""

Y t Y

ORIGII-iAL INCHCM'^O NDT viELO i>iPi:;>:i._,

5: ol _J 1 L

, .IIMT5GRATEU NEUTRON EXPOSURE

'y,

f ^ n/cm^>0.1 MeV)

Fig. 8. Qualitative features of change in

NDT as a function of irradiation

dose.

(b) Void Swelling

The fast breeder reactors which are currently under design are expected to

provide fluences of order 10^3 to 10'^'^ to various reactor components like fuel

cladding etc. during the life of the

fuel. The void swelling in such cases could be 10/. or more. Such swelling is

expected to result in two important

effects. It will decrease the breeding

ratio (atoms of fissionable material

generated per atom, of fissionable

material consumed) because additional

free space must be provided in the core

to accommodate the swelling. (Secondly

other problems can arise from fuel pin

buckling, core warping etc. due to non uniform temperature and flux distributions and consequent non-uniform void

density distribution) . Hence in fast

reactor technology, void swelling has come to be looked upon as a greater bane

compared to other problems such as low

temperatiire hardening, high temperature

embrittlement and the acceleration of

diffusion controlled processes known

earlier. Material assessment has become

important. However in order to obtain

this data through fast neutron irradiation one has to go through tedious and

time consuming irradiations over ten or twenty years in fast neutron environment

if one were to use the materials for such

periods of time in the reactor. This is

clearly an unsatisfactory situation. It is here a new breakthrough has been

achieved by charged particle irradiation

using accelerators. Charged particles,

though limited in their range, interact

through atomic interactions which have

cross sections four to six orders of

magnitude larger than the nuclear cross- sections of the neutron. The damage

rate is several orders greater than the

neutron damage rate. So in principle

the damage density produced during many

years irradiation within a reactor can

be 'simulated' in a few hours using ion

beams. Experimental studies involve

irradiation of materials by light or medium heavy charged, particles like G,

Al, Ni etc. accelerated to energies of

order of a few tens of MeV. These

irradiated materials are then examined

using transmission electron microscopes

and parameters like void density and

void diameter are measixred. It is

observed that when specimens are irradiated for comparable damage doses as with fast neutrons, the micrographs

reveal almost similar void patterns.

Fig. 9 shows comparison of 316

stainless steel which has been irradiated

by neutrons and charged particles". The

figure on left corresponds to irradiation

by fast neutrons ( > Q.l MeV) at EBR-II

to a fluence of 3x10^2 n/cm^ for a duration of one year and that on the

right hand side, the same material bombarded by 5 MeV nickel ions to a fluence of 3xlOl6 ions/cm^ over a duration of 30 minutes. You can see the

similarity in voidage. In this context

I wish to point out that the Variable

Energy Cyclotron that is being constructed by Bhabha Atomic Research Centre at

Calcutta could prove to be a very

powerful instrument for such studies.

Physicists who are conversant with

acceleration techniques and solid state

physics can play a very important role

in this effort of materials assessment

38
for fast reactors. Physics of void

formation, void morphology, inter com- parison of accelerator samples and

reactor samples (to take into account

accelerated damage rate in case of

simulation experiments) are areas wherein physicists can contribute to our understanding

n 5X rO rt/c^'

(A) Neutron irradiated at 585 °C (1 year exposure)

for sufficiently long time. The vacuum wall of the chamber containing the plasma

is expected to operate at temperatures

of order of 700° to 1000°G and is

exposed to bombardment of neutral atoms,

neutrons, photons and charged particles.

As a result of bombardment by these it is

expected that the wall can undergo large

scale erosion.

Typical parameters'^ of a chamber

are given in Table-I and assuming very

small sputtering coefficients of the

order of less than l/. even, it is seen

that the life time of such vessels could

be very small indeed. In addition to

this recently a new problem is expected

to play a major role. The plasma is

expected to contain H"*", He"*", T"*" etc. and

these can bombard the wall. If radiation

damage is caused by gaseous projectiles

such as thege, the impurity concentration

due to these atoms builds up in the

material as a function of dose. Secondly

such products can accumulate due to (n,p)

and (n,d) reactions also. Due to low

solubility of the gases in the metal, the

gaseous atoms can precipitate out of the

metallic solution and create 'bubbles' in

the interior or 'blisters' on the surfaca

Depending on the size of the blisters

and metallic strength, the blisters can

get rupt\ired and skin defoliation can take place. Fig. 10 shows the kind of

blisters observed by Das and Kaminsky-^^

is vanadium as a result of charged

particle bombardment. Low energy

accelerators (2-3 MeV) can be used for

irradiating materials v;ith protons,

particles etc. and one can examine the

surface using scanning electron

microscopes. This figure shows a sample

of one such study in which 0.5 MeV

particles were used to bombard the

surface of polycrystalline vanadium film

at 600°C. Interesting results are

obtained as a function of irradiation

temperature, projectile energy, preirradiation treatment, micro-structure

etc. on other metals and alloys also.

Table-I

Fig. 9.

(B) Ni ion irradiated at 5«5 'C (30 njinutes exposure) Voids in 316 stainless steel due

to neutron and Hi bombardment.

(c) Blist ering

Tremendous efforts are underway all

over the world to make the controlled

thermonuclear fusion a reality for

meeting power needs of the future. One

of the problems in this area has been

containment of the plasma in a vessel

500 MW(t) Fusion Reactor Parameters

.2 V/all area Radial loss

Particle flux

Average Sputtering Coefficient

Erosion rate

Wall thickness

Permitted loss

Life-time

400 m' 10^5 IONS/SEC

2.6 X 10^^

lONS/Cm^/sec

0.008 ATOM

low

1.2 mm/Year

1 cm

20/. 2 Years

39
Fig. 10. Blisters in polycrystalline

vanadium produced by charged

particle bombardment.

Conclusion

I have tried to give a birds-eye

view of new problems that need solution

in new technologies - problems due to

radiation effects, study and solution

of which can arise from use of accelerators. Radiation Physics, in the broad

sense of the word, has large scale

implications in these new technologies.

10.

References

He Reynolds, A.W., Nelkin, M.S.,

Rosenbluth, M.N. and Whittemore, W.L.

PICG, 297 (1958).

Woods, A.D.B., Brockhouse, B.N.,

Sakamoto, M. and Sinclair, R.N.

,

Inelastic Scattering of Neutrons in

Solids and Liquids - (IAEA) p. 487

(1961)

Bergmanm, A. A., Isacoff, A.I., Murin,

I.D., Shapiro, F.L., Shtranikh, I.V.

and Kazarnovsky, M.7., PICG, 135

(1956)

Chandramoleshwar, K., Navalkar, M.P.,

Ramakrishna, D.V.S., Nuc I.Inst, and

Methods 60, 113 (1968).

Chandramoleshwar, K., Navalkar, M.P.,

Ramakrishna, D.V.S., Ramanna, R. and

Subramu, E.R., PICG (1964).

Radiation Damage in Reactor Materials,

Proceedings of an IAEA meeting Vol.1

and Vol. II (1969)

Proceedings of the BNES Nuclear Fusion

reactor Conference (1970)

Gawthorne, C. and Fulton, E.O., AERER 5269 (1966), p 446 and Nature 216,

575 (1967).

Kulcinski, G-.L., Nucl.Inst. and

Methods 365 (1971).

Das, S.K. and Eaminsky, M. , J.Appd.

Phys. ^, 25 (1973).

40
VARIATION OF TOTAL TO K-SHELL PHOTOELECTRIC CROSS

SECTION RATIOS WITH ATOMIC NUMBER AND PHOTON ENERGY

Ramakrisiina G-owda and B. Sanjeevaiah

Department of Physics, University of Mysore

Manasagangotri, Mysore-570006, India

The total to Z-shell photoelectric cross" section ratios are

calculated from the measiired total and K-shell photoelectric cross

sections (using a well type plastic scintillation spectrometer) in

copper, zirconium, silver, tin, tantalum, gold, and lead for 145 '4,

279.1, 411.8 and 661.6 keV gamma rays. The ratios are plotted

against the atomic number and also the photon energy. The theoretical ratios obtained form the cross sections of Scofield [UCRl

Report No. 51326] are also plotted and a comparison is made. The

dependence of these ratios on the atomic niunber of the element and

the photon energy is discussed.

(Atomic nixmber; cross section; K-shell; measurement;

photoelectric effect; photon)

Introduction

Until the 1960's the relativistic

calculations gave only the cross sections for the K-shell. It was the practice to estimate the contribution of

all other higher shells by using the

ratio o^/a-p,} where a-j; and are the

total and K-shell photoelectric cross sections respectively. The law of

"five fourths" simply claimed that

a^/ag; = 5/4. This value holds good only

for high Z materials above Hulme energy

limit G.35 MeV-^. Davisson and Evans , Grodstein' and Davisson^ tabulated the

absolute photoelectric cross sections

together with cross sections for the

various gamma ray intexaction processes

contributing to the total. In the

tabulation of Davisson and Evans'^ the

total atomic cross section was obtained

by applying the 5/4 law to the K-shell

cross sections. Grodstein^ also

followed a similar method, but instead

of using the 5/4 law she used the ratios

ag^_i_T jj/ag; as calculated with Stobbe's

formura5 and similar formula of Hall , which corrects the overestimation of cross sections for the low Z values. In

the later table of Davisson^ she used

Kirchner's experimental ratios' measured

at the K-shell thresholds in which the

Z-dependence of this ratio was found to

vary monotonically from 1.09 for

aluminium to 1.235 for uranium.

Hubbell gives an empirical fit to

calculate the ratios ot/^K ^ function

of Z with an accuracy of +2 to 3 percent

with Kirchner values. This fit does not

take into consideration any possible

energy dependences^ Later calculations

of Rakavy and Ron-^ showed that the

ratio is slightly energy dependent es- pecially at low energies. So the

calculations using Kirchner 's values are

found to be xinder- estimated above

K-shell threshold.

The total to K-shell photoelectric

cross section ratios are measvired by

Hultberg^^ using magnetic beta ray

spectrometer at the energies 1332, 662

and 412 keV gamma rays in uranium.

Latyshev-'--'- gives the ratios for Z = 73

and Z = 82 at 2.62 MeV. Experimentally

measured K-shell and L sub-shell ratios

are tabulated in the recent review

article of Pratt et al . Results and Discussion

The total and K-shell photoelectric

cross sections are measured using a well

type plastic scintillation spectrometer^

previously described by the authors^-^"^

'. Using these measured total and K-shell

photoelectric cross sections, the ratios

are calci^lated in copper, zirconium,

silver, tin, tantalum, gold, and lead

for 145.4, 279.1, 411.8 and 661. 6 keV

gamma rays. The ratios are plotted

against the atomic number (Z) in Pig. 1.

and against the photon energy in Fig. 2.

The theoretical ratios obtained from the

cross sections of Scofield-*-® are also

plotted in the ssune figure for comparison. In the plot of total to K-shell

ratios against the photon energy, one can observe the energy dependence at

lower energies. Especially for high Z materials the dependence is found to be

prominent. As the energy increases the

dependence decreases. The total to

ill
i>25| 1 i

<

1

1 1 r

uiol 1 1 1 I L_ ,_ » 20 30 40 50 60 7C •ATOMIC NUVBER Fig. 1. Variation of total to K-shell

Photoelectric cross section

ratios with atomic number.

K-shell ratios obtained using the measured cross sections are found to be

consistantly higher than those obtained

from Scofield values at 145.4 keV, and

as the energy increases the agreement

becomes fair. These ratios are found

to vary monotonically as Z increases.

The errors on these ratios are found to

be about 97. in the case of photon

energy 145.4 keV and 6'/. at all other

photon energies.

References

1. Hxilme, H.R., McDougall, J.,

Buckingham, R.A. and Fowler, R.H.,

Proc. Roy Soc. (London) A149 . 131

(1935).

2. Davisson, CM. and Evans, R.D., Rev.

Mod. Phys. 2±, 79 (1952).

3. Grrodstein, G-. White, N.B.S. Circiilar

No. 583 (1957).

4. Davisson, CM., Alpha-Beta-G-amma Ray

Spectroscopy, Ed. K. Siegbahn, Vol.1,

Chap. 2 (1965) (North Holland,

Amsterdam)

100 300 BOO TOO 900

Fig. 2. Variation of total to K-shell

Photoelectric cross section

ratios with photon energy.

5. Stobbe, M. Ann. Physik 7, 661 (1930).

6. Hall, H. Rev. Mod. Phys. 8, 358

(1936).

7. Kirchner, F. 1930, Handbuch der

Experimental Physik, Ed. W. Wien

and F. Harms ( Akademische,

Verlagsgesllschaft , Leipzig).

8. Hubbell, J.H., Nat. Stand. Ref. Data.

Ser. NSRDS-NBS 29, (1969).

9 . Rakavy , G- . and Ron , A . Phys . Rev

159 . 50 (1967).

10. Hultberg, S. Arkiv fiir Fysik 1^, 307

(1959)

11. Latyshev, G.D., Rev. Mod. Phys. l^,

132 (1947).

12. Pratt, R.H., Ron, A. and Tseng, H.K.

Rev. Mod. Phys. 273 (1973).

13. Gowda, Ramakrishna and Sanieevaiah,

B. J. Phys. (GB) A6, IO4I U973).

14. Phys. Rev. A8, 2425 (1973).

15. J. Phys. B TgB) 2, 1772 (1974).

16. Phys. Rev. A6, 2569 (1974).

17. Can. J. Phys. 846 (1974).

18. Scofield, J.H., UCRL Report No. 51326

(1973) (unpublished).

42
Discussion

Roy. 3.C .

1. Have you measured tj^ or

"^^Q^g^l or both, of them ? 2. Well, in case of measuring t^,

how are you sure that you are considering

K-eleetrons only ? 3. Next, is there anything new in

the technique from the conventional

measurements ? 4. Can you assign any reason for the

large observed discrepancy for some of

the elements ? Gowda. R.

1. We have measured both total and

K-shell cross sections.

2. For monoenergetic electrons the

pulse height amplitude spectrum in the

scintillators is mainly a Gaussian. The

main peak in the photoelectron spectrum

is attributed to the K-shell electrons

and using the left portion of the peaks

Gaussians were fit. The areas under these

Gaussians TjKJuld then give the number of

K-shell ph(t>toelectrons . Also the plot of

observed K-shell photoelectron peak

energy against the pulse height amplitude

gives a straight line.

5. Although the experimental technique is similar to the conventional

methods we have introduced some modifications in the geometry and the detector

size. We also observe the peak due to

photoelectrons in aluminium at 145.4 keV,

which was not observed in earlier experiments. This shows that our experimental

set up is much better than the previous

ones

4. If we draw the error bars on the

ratios there is agreement in the case of

all the elements within the errors. The errors are about 6X at 279-1, 411.8

and 661.6 keV and 9X in the case of 145.4

keV.

^3
OPTICAL MODEL .liiALTS IS OF NOimASTIC

INTERAGTIOl^" OF 14-2 I-IEV REUTH.OiiS E. Pal, Arun Ghatterjee and A. II. G-liose Nuclear Physics Laboratory, Lose Institute

Calcutta-700009, INDIA

I'Jon- elastic cross sections of several nuclei for 14.2

MeV neutrons have been measured using sphere transmission

technique. The measured data together v/ith the results of

others have been analysed with optical model using a least

square criteria over a wide range of mass number (l2^A-^207).

(Gross section; multiple bias; neutron; non-elastic;

optical model-, param.eter; polynomial extrapolation;

sphere transmission.)

Introduction Optical I-Iodel Analysis

In the present work, the experimental

and theoretical studies on neutron non- elastic interactions have been undertaken

in the 14 lieV region. Efforts have been

made here to find out an average set of

mass-independent optical model parameters,

utilizing essentially the non-elastic

scattering cross section data measured

by us. References 1 to 9 contain the

works already carried out in this field.

Measurement of Hon- el as

t

ic Cross

Section for Different Nuclei

Non-elastic cross sections of seven nuclei for 14.2 MeV neutrons have been

measured by using reciprocal sphere

transmission teciinique. Two important

correction factors arising from (a) the

recoil energy loss suffered by elastically scattered neutrons and (b) the

multiple scattering in the finite

scatter er thickness have been estimated

by raul/tiple bias and polyno.mial extrapolation methods^*-' respectively. The

results obtained are presented in

Table 1.

Table 1

IJon-elastic Cross Sections

(barns) for 14.2 MeY Neutrons

Element a^g in barns

0 0.82 + .02

Al 0.94 ± .02

Cu 1.49 ± .03

Cd 1.90 + .04

Sn 1.90 + .03

W 2.40 + .06

Pb 2.57 ± .05

ilnalysis of non-elastic data obtained

from present measurement as well as from

data obtained by others-^^ »-'--'- '^2 ^g^g

performed using the widely used nine

parameter local optical potential given

by the following form: ^ j

where the symbols have their usual significance.- Volume absorption term in the

imaginary part of the potential has not

been considered because of its negligible

contribution^^ on the absorption of 14

MeV neutrons. The spin-orbit part of the

potential has practically no effect on non-elastic cross section. Therefore,

throughout our present analysis we have

fixed the param.eters Vs, Vq and as at

their reasonably expected values, namely,

V3:=7.0 MeV, Tq^1.25 fm, aa=0.65 fm

In the 14 MeV region the compound elastic cross section is negligibly small-^^ and

so we have disregarded this effect and

co:iip8,red the measured cross sections vrith

the computed values directly.

The experimental cross sections Og^-p

may be compared with those predicted by

optical model, Ofa^ simply by examining

the sensitivity of cr's on parameters. The

difference between tiiese two cross sections denoted by Oerror '^^^y ^® then ex- pressed as a summation of variation of cross section with each free parameter aj

of the model about a fixed initially

chosen value a? i.e.

*V.'ork carried out under a PL-480 Project sponsored

by the National Bureau of Standards, U.S.A.

44
a = a -cj,,=y ;

) . 6a -; error exra th / 6ai o J

... (2)

We have started v/ith an initial set of

parameters chosen from the works of

Perey and Buck-'- and V/ilmore and Hodgson^,

ilon-elastic cross section data for

several elements (seventeen) have been

taken from different soiirceslO'H»12

,

Each of the six pararaeters was varied

arbitrarily by 2'/. from its initial

value keeping others fixed. Thus partial

6ath.\ derivative , corresponding to eacn parameter was obtained. Least square

criteria v^as applied to eqn. 2. A nass- independent set of parameters which, in

principle, should give optimiim fit to the

experimental data was then obtained. The

parameter set thus obtained has been

presented in Table 2. Table 2 Optical Potential Parameters

from llon-elastic Cross Sections

Pitting .

Table 3 Comparison of the 14 MeV A-lndependent

Average Parameters Obtained in the

Present Investigation with those

Reported by Other Authors .

Paranet er Bj orklund

and

Pernbach

(14 MeV)

Rosen^;^ et al^

(14.5

MeV

Cassola

and

ICoshel

(14.0

HeV)

Present

work

(14.2

MeV

^^o 44.0 44.5 43.4 40.24

^0 1.25 1.25 1.25 1.26

^0 0.65 0.65 0.63 0.62

11.0 5.75 8.20 9.8

1.25 * 1.25 1.24 1.48

0.98* 0.70 0.47 0.45

( * indicates parameters pertaining to

surface absorption potential of Gaussian form)

3.0

(MeV) (fm) (M^V) (fm) (fS)

40.225 1.261 0.618 9-795 1.477 0.452

A comparison of theoretically calculated

values of cross section crth.» with the new parameter set against the measured

'"'-lues of present investigation has been

".le in fig. 1. In table 3 we have corn- ered the potential parameters with the

. /erage parameters obtained by Bjorklund

and Fernbach^, Rosen et a35 and Cassola

I and Koshel7.

Discussion

The amount of variations from set to

, set noted in the values of a particular

i parameter is not surprising; that diffeJ rent approaches of analysis would lead to

*,j sets of slightly varying values, is

I expected normally. The value of rj)

/ obtained in our analysis is notably

ly.rge compared to that of each set.

^owe'ver, this value though large, is not

unrealistic . Optimum parameter searches

' for individual elements ha've quite often

1 lead to values which vary over a wide

, range from element to element. For

; example7, maxira-um and minimum values of

' rj) are foimd to be 1.49 (for K) and 1.04

'for ill) respectively.

It will be seen from fig. 1, that

except for too low mass number elements.

1 " 1 1 1 I 1.0 2.0 3.0 4.0 5.C 6.0

Fig.l. Experimental and theoretical

nonelastic cross section of 14.5,

MeV neutrons as a function of A

the cross sections calculated with the new set of mass independent parameters

agree well with the experimental results

over a wide range of mass numbers. The

variations for low A nuclei are not

surprising since the optical model is not

expected to be valid for low mass number

elements. The parameters given in

Table 2, thus represent, in the mass independent approximation, a set of

reliable parameters for describing non- elastic scattering of 14 MeV neutrons

from nuclei of mass number lying in

the range 12 4207.

^5
Since our next endeavouir will be to

make another approach to fit the nonelastic as well as elastic scattering

data simultaneously, with a single set

of parameters, we have not attempted

multiple iterations for obtaining more accurate values of the parameters.

References

1. Perey, P.G. and Buck, B., Nucl . Phys

12, 353 (1967).

2. Bjorklund, F.J. and Fernbach, S.,

Phys. Rev. lO^, 1295 (1958).

3. Bngelbrecht, C.A. and Fiedeldey, H.,

Ann. Phys. 262 (1967).

4. Aver'Yanov, I.K. and Purtseladze, Z.Z.,

Sov. J. Nucl. Phys. 1, 193 (1968).

5. Rosen, L., Beery, J.G-., Goldhaber,

A.S. and Auerbach, E.H., Ann. Phys.

M. 96 (1965).

6. Becchetti, F.D. and Greenlees, G.V/.,

Phys. Rev. 182, 1190 (1969).

7. Cassola, R.L. and Zoshel, R.D., Uuovo

Cim. 363, 1968.

8. Korzh, I. A., Kashuba, I.F., Kozin,

B.D. and Pasechnik, i-i.V., Sov. J. Wucl. Phys. 7, 190 (1968).

9. Wilmore, D. and Hdgson, P.E., DjucI . Phys. ^, 673 (1964).

10. Chatterjee, A. and Ghose, A.M., Phys.

Rev. 161, 1181 (1967)

11. I'lacGregor, H.fl., Ball, W.P. and

Booth, R., Phys. Rev. 108, 726 (1957).

12. Flerov, N.K. and Talyzin, V.M., J. Kucl. Energy 4, 529 (1957).

13. Hodgson, P.E., The Optical Model of

Elastic Scattering (Lond.) (1963).

14. Lane, A.I-i., Rev. of Mod. Phys. 29,

191 (1957)

46
GEOMETRIC FACTORS IN RADIATION PHYSICS IffiASUREIffiNTS

A.M. Ghose

Department of Physics

Bose Institute

Calcutta-700009, India

Optimisation of geometrical factors through symmetry

considerations is a powerful means of improving the accuracy

of measiirements in Radiation Physics. This has been illustrated for the cases of spherical and axial symmetries.

Design of double scattering fast neutron polarimeters as well

as of gamma ray linear polarimeter systems have been discussed.

Applications of the surface of revolution geometries to

various fields have also been considered.

(Absorption; accuracy; cross section; fast neutrons;

geometric factors; photon; polarimeter; radiation

physics; scattering; spectrometers.)

Introduction

One of the most important elements

in the design of experiments in many

areas of Radiation Physics is the

spatial distribution of the component

parts of the entire experimental arrangement comprising the source, the absorber

and the detector. The purpose of the

present paper is to indicate how the

effective signal strength at the detector

and hence the accuracy of the measurements can be increased, sometimes even by orders of magnitude, by making the

distribution of the components symmetrical. The symmetries correspond

naturally to those inherent in the

quantities or processes under investigation. These considerations are particularly important when scattering

cross sections are either being

measured or differentiated from other

interaction processes.

Spherical Symmetry

When total scattering from all

directions is being measured (or discriminated) the inherent geometry is

spherical. This is the basis of the

well-known sphere transmission technique

which can be used, at least in principle,

to effect a separation of scattering and

absorption processes (Fig. la). In

practice, the application of the sphere

transmission technique depends upon the

validity of .several implicit ass-omptions

and the accuracy obtainable depends

critically on how closely these assumptions are obeyed by the actual experimental arrangement. Since the method

of spherical symmetry has been discussed

elsewhere in other publications-^ we

shall not discuss it further.

Axial Symmetry

When the phenomenon or the process

under study shows no explicit dependence

on the azimuthal angle, the symmetry

natural to the experimental arrangement

is axial (Fig. lb) . Thus in the measurement of the differential scattering cross sections 03(6) of unpolarised radiations

the symmetry is around the scatterer - detector axis. Other instances where

axial symmetry is important includes

simple angular correlation experiments,

study of nuclear fluorescence radiation

using Compton scattered gamma rays etc.

Extensively used ring geometry is the

simplest version of axially symmetric

arrangement and it has the additional

virtue of being adaptable to the time-offlight technique. However, in plane

geometry constant angle 9 corresponds to an arc of a circle and this fact was utilised by Tandon and I-Iclntyre^ in their

investigations on nuclear fluorescence

radiation (Fig. Ic). Obviously a surface of revolution shaped geometry of

the scatterer aroimd the soxxrce-detector

axis is a nattiral extension to the three

dimensional case (Fig. Id); in a separate paper^ we have shown how this

geometry has been utilised as the basis

for the measurement of differential

scattering cross sections of fast

neutrons. A version of the arrangement

proposed for the measurement of differential incoherent scattering cross section of gamma ray 3"+ is shovm in Fig. 2.

A possible use of the axial

symmetry lies in the field of angular

correlation experiments involving prompt

radiations or radiations from shortlived nuclei emitted by a source, which,

in turn, is produced by irradiation in a

*Work carried out under a PL 480 project sponsored by the National Bureau

of Standards, U.S.A.

^7
PROCESS GEOMETRY TECHNIflUE

e or*

(ig. tie)

Fig.l. Geometrical arrangement for different types of symmetries.

S

S- Soorce F FUUr D- lelecLor X; ScaiUrer Direct Bedin Stopper

Fig. 2. G-eometrioal arrangement for the

measiirement of differential incoherent scattering cross section

of gamma rays.

wide beam. In the usual angular correlation arrangement, source absorption and

scattering can be reduced only at the

expense of intensity. In the arrangement shown in Fig. 3 the source has the

shape of a surface of revolution about

the line joining the two coincidence

detectors as axis; since the extended

source can be thin there is considerable

gain in intensity over the usual point source geometry. The arrangement is also

potentially useful for inner bremstrahlung

experiments.

Fig.3« Proposed arrangement for angular

correlation measurements.

Double Scattering Fast Neutron

Polarimeter

In measurements involving linearly

polarised radiations we come across

symmetry considerations of a different

type. We shall illustrate them first by

considering the design we have proposed

for a double scattering fast neutron

polarimeter

Fig. 4 shows the essential elements

of a double interaction fast neutron

polarimeter^ . Unpolarised beam of

neutrons incident on the polariser

gets polarised after scattering through

an angle e^. The flux of particles

V issuing out from the second target ^2

at a fixed angle of scattering 62

depends on the azimuthal angles 9

through the relation

w(e2,9)=No(e2)[i+Pi(ei)P2(e2)cos 9]

... (1)

where Nq is the flux in absence of

polarisation and Pi is the polarisation

vector in the initial interaction while

P2 is the polarisation that would result

had an unpolarised beam been incident on

S-p. Using the Basle convention", the

differential cross sections for scatterings to the "left" ((p=n) and to the

"right" (9=0) in the common plane

becomes respectively

= a^(e2)[i-Pi(e^)P2(e2) J ... (2)

Hence the asymmetry ratio A(e2), defined

to be equal to aj^/a^i, becomes

i-P3_(e^) P2(e2)

^^®2^ = rrprre^Tp^Tep- •••

i-A(ep)

so that P^(e^)P2(e2)=CTep- •••(5)

Hence a measurement of A(©2) yields

product Pi(9^)P2(62) > which, in turn,

gives Pi(6i) or P2t62)» when one of the

two quantities is known.

The usual method for producing a polarised beam of fast neutrons is based

on the polarisation during the production of neutrons e.g. by using d-t or d-d reactions well above their corres- ponding thresholds; P2(62) usually

obtained from phase-shift analysis if

the second interaction consists of

elastic scattering from a spinless

target like He or C. Near the threshold (e.g. for "14" MeV t-d neutrons)

Pl(9i) is very small and the above

method is therefore difficult to apply.
Fig. 4. Elements of a double interaction

fast neutron polarimeter.

An alternative method is to use the

technique of double scattering. If the

second reaction is again an elastic

scattering from target nuclei which are not too light, the energy change during the

scattering can be neglected and further

if is set equal to 62 » we can write

1*1(61) = 1*2 (©2) hence

^i^^i) = rTirefy

Thus a measurement of A yields P and once

the polarimeter is calibrated, it can be

used to analyse diverse polarisation

processes

In the conventional approach,

without optimising geometry, the double

scattered beam intensity is lO"-'-^ to

10~-'-5 of the primary total beam strength

and this figure is too low to have any

practical utility. A possible arrangement of double scattering fast neutron

polarimeter based on the surface of

revolution geometry is shown in Fig. 5. The neutrons are successively scattered

by two sectors of angular width 6 and

forming a part of the surface of

revolution. The number of neutrons

detected by the neutron counters in the

two symmetrical positions depend upon

the polarisation induced in the first

scatterer '^2.* -^^ S®"*' estimate of

the typical counting rate we note that

the number N]_ of neutrons issuing out

of and passing through a hole H of

effective radius a is given by

aa^yN t . fr.^ +f

%"g9/2j_2 (^f^)^=an4e sece j

f(x,e)dx

... (7)

Fig. 5. Double scattering fast neutron

polarimeter.

where y is the number of nuclei per c.c. of the scatterer, t is its normal

thickness, Nq is the no. of neutrons

emitted by the source S per sec, 21 is

the length of the SH axis, 6 is the

scattering angle, x = z is the distance

along the axis SH of the projection of an element of scatterer from the centre of

the axis and where the integrand f(x,6)

which is taken over the scatterer "^-^ given by

f(x o)_ (l-:g)V^l+(l-x^)tan29-l

l+(l+x)tan^e-/l+(l-aP)tan^e

1

^[sec^e-x2tan2ej'^

1

[l+(l-x)tan2e-Vl+(l-x'^)tarfe]

... (8)

The limits of the integral in P^n.. (7)

correspond to the two extreme positions

at the ends of the scatterer. In the

above derivation we have assumed that

the scatterer is "thin" enough to replace

3expressions of the type £s(i_e~°"^tY j ^t

by aOgYt where a is a numerical factor

of the order of unity. With this approsimation the mean coimting rate after

double scattering becomes

C=€fi^[f^J^an8sec2e[ff(x,e)dx]2

... (9)

49
where we have assumed that Xi and T2

have the same dimensions, € is^he

efficiency of the detector and -^is the

solid angle subtended by at S. If ^SIq^ and"S^ are made of sulphur, typical mean counting rates (neglecting the polarisation factor) obtainable by this method

is shown in Fig. 6. It will be seen that

C is several orders of magnitude more than the corresponding values using

conventionsil geometry. In the calculations we have assumed the following

parameters,

6 = 0.1, f

= 0,1, € = 0.01

... (10)

t = 1 cm and f = 0.75

32^ 208

If instead or S one uses v Pb, the

double scattered coixnts are even higher

as shown in Fig. 7. In the calculations we have used the same set of parameters

as given in (10)

The surface of revolution geometry

thus promises to furnish us with a method for polarisation measurement of

fast neutrons by double scattering.

However the design of filters and slits

poses a practical problem of some difficulty.

?

Fig, 6. Expected mean double scattering

counts for sulphur in a typical

polarimetric arrangement

9

ScalUrIn) angle indejrtti

Fig. 7. Expected mean double scattering

counts for lead in a typical

polarimetric arrangement.

Gamma Ray Polarimeter System

For gamma photons the linear

polarisation is transverse rather than

longitudinal and this, therefore, calls

for different type of geometrical

considerations. We shall briefly

consider a polarimeter system proposed

by Rudra and Ghose' consisting of a ring

^1 of scatterer (and partial polariser)

followed by an analyser ring X2 which

scatters radiations through 90° to a specially shaped detector D in position

I after channelling them through

suitable filters. (Fig.8). The source

of unpolarised photons S is placed on the axis of the system. Fig. 8 depicts

the plane of the first scattering - the

a-plane. To measure the polarisation,

it is also necessary to measure the

intensity of photons scattered by

through 90° in 7[ - plane, which is

normal to 0-plane. The detector D has now to be moved to the position II

concentric with 51 to receive the photons.

The path of typical ray in the ix-plane

is shown in Fig. 9. The cross section

of D transverse to the axis of the

system is ring - shaped and the path of

a photon through the ring is inclined

at an angle (p. In order that the

50
Fig. 8. Basic elements of a double

scattering polarimeter system for

photons

where (D,h) are' the coordinates of 0 in

the plane of the figure, with the source

S situated at the origin and (X,Y) are coordinates of the projection of X t . But

X = Y Cot (G - 9)

,

02)

where © is the angle of scattering inS3_,

This makes

^ = ^-^ x-Y°co? e ^

••• ^3)

and hence [X-i(D-ah) ]2+[Y4i(aD+h)

= =J(DSh'^)(a%l) ... a4)

where a = Cot 6. This is arc of a circle, as expected from sec. 3. The

loci of the projections of D are given by the same eqn.

Y^ = (x-D)2 + (y_h)2

Thus as the point (X,Y) moves over an arc of a circle, the coordinates of 2?

aarif describe two branches of the same parabola. The complete arrangement in

space is obtained by generating surfaces

of revolution by rotating the arc and

the parabola around the symmetry axis of

the system, nearly conical parts of the

latter being suitable for practical

systems.

Fig. 9. Path of a typical ray in the

u-plane.

geometry of paths in -n and a positions

of the detector be symmetrical, the

photons must traverse the detector in

position I in a similar manner and the , longitudinal cross section of D must be

a section of a ring with the point 0 as centre. Hov^ever if D has a large

efficiency these considerations need not

be enforced rigidly.

For a more extensive arrangement,

it can be shown that if the points S and 0 are kept fixed, the locus of the

projection of is a circle, while

the points corresponding to ^'^'^ ^ lie on the same parabola. In fact, in

Fig. 10, the locus of the projection of

"2 3_ on the plane is determined by the

equation:

D = X + (Y + h) Cot (p. 01)

Fig. 10. Earlier version of proposed yray linear polarisation.

A more elegant system^ for linear

transverse polarisation measurements can

be derived from Fig. 11 which shows a section through the positions Dj_ and D2

51
of the detector in the a and n planes

respectively. If the scattering planes are distributed normally to the plane

of the Fig. 11, the rays PiUi, ^2^2 ^tc. are in the a-plane while the corresponding

rays P1D2, ^2^2 '^^^ 71-plane,

where the points P]_, P2, etc. on X2»

which now assumes the form of an arc of a circle. To find the form of the

scatterer we consider the a-plane

SQ]_P-lDq_ corresponding to the point

on X2 (Pig- 12). The ray SQ^ emerging

from the source is scattered by 21 ]_ at

the point Q-^ through an angle ©; QiPi

corresponds to the scattered ray which

is further scattered by ^2 ^'^

Let the equation of Z j_ be

I.e. X + y

2 _ 2yll (Pig. 11; :6)

It vj-ill be seen that the projection

Z of Q-|_ along 3Dj_ satisfies the equation

cos B - -r= (7)

since the points P-^ and Q-]_ have identical

X and y coordinates. From (6), we immediately have

z2 = 2yR Cot^e (8)

Fig. 11. Improved version of the proposed

Y-ray linear polarimeter.

Fig. 12. Plane of polarimeter.

showing that for any given angle of

scattering 6, the projection of the

points on on y,z plane describes a parabola i.eT X.^ lies on the intersections of a parabolic cylinder with a right circular cylinder.

For this system it is relatively

easy to design and fabricate systems of

slits. Incidentally, gamma ray polarimeter systems of the type discussed

above are going to be useful for estimating the individual contributions of

different types of coherent processes

to the total coherent scattering cross section of gamma rays.

Other Uses of Geometrical Factors

One of the early use of axial

symmetry was made by Potenza and

PuubbinoS in their design of fast neutron

spectrometer. Another important area where surface of revolution geometry can play an important role is the generation

of neutrons of predetermined energy from

a intense source of neutrons of higher

energy (e.g. 7 to I4 MeV neutrons from

t-d neutrons) by elastic scattering in

a low z scattering. If the sour-ce neutrons have anisotropic energy distribution in the laboratory system, the

scatterer might be shaped properly to

take this account . For isotropic or nearly isotropic sources the arc of a circle geometry discussed in sec. 3 is

adequate. For practical systems, the

difference of counts with equivalent

amounts of paraffin (GH2)m and polythene

(CH)n scatterers can be ascribed to

elastic scattering from hydrogen

Acknowledgement

The author wishes to thank his

students who have been associated with

different phases of the programme outlined here. He wishes to thank Dr. S.H.

Sircar, Director, Bose Institute, for

his interest in the present work.

References

1- Bethe, H.A., Los Alamos Sci.Lab.

Report LA-1428 (1952).

Ghose, A.i'I. and Gangiily, N.K., Ind

Jour.Phys. 285 (1956).

Bethe, H.A., Beyester, J.R. and

Carter, R.E., J. Wucl. Energy ^, 275

(1956).

Fast i\,feutron Physics, Vol. II, Edited

by J.B. Marion and J.L. Fowler;

Interscience Publications, (i960)

and references contained therein.

Ghose, A.K. , Kucl . Inst . and Methods

45 (1965) . 2. Tandon, G.K. and Hclntyre, J. A. - Huclr.Instr. and Methods 181(1968).

3. Wath, S. Ghatterjee, A and Ghose, A.M. paper presented in this Symposium.

4. Roy, S.G. and Ghose, A.li. (Private 1 communication)

52
5. Elwyn, A.J. and lane, R.O., Nucl

Phys. ^

78 (1962)

6. Proc . Int. Symp . Polarisation Pheno- men of Neutrons (Basle 1970) ed.

H. Huber and K.P. Keyer (Birkiiauser

Verlag, Basle, 1961).

7. Rudra, N. and G-hose, A.M. Nucl . Phys.

Solid State Phys. (India) 10, 581

(1967)

8. Ghose, A.M. (in press).

9. Potenza, R. and Rubino, A. Nucl. Inst.

Kethods 2^, 77 (1963)

Discussion

P.K. lyeni^ar

I must congratulate Prof. Ghose for

inventing these innovations , however I must stress that it is due to the

situation of limited resources that he

has been foimd to think of much clever

tricks.

What will be the effect of non- uniform energy sensitivity and direction

dependence of the detector on the overall resolution?

A.M. Ghose

Optimisation of geometrical factors

will not be effective unless suitable

detectors are devised to exploit the

full benefit vrhich would result from this

optimisation. In ovcc laboratory we have

developed suitable detectors for photons

and neutrons which have the desirable

properties. Iv'ith conventional detectors

the resolution will be poor indeed.

D.V. Gopinath

The spread in the angle and thereby

the resolution of the system depends on the distances between the detector and

so-urce and their sizes. One can improve

the resolution to the desired extent by

increasing the distances but thus one has to use larger detectors for the same efficiency

A. i-l. Ghose

In fact by increasing the sizes, one only gets a scaled up version of the

same geometry and angular resolutions

etc. are not improved thereby. It is

essential that the improvement in

detector quality must match the improvement in geometry.

B. B. Baliga

Is it necessary to shape the

detectors for good geometry ? If so uniform efficiency of one detector is a real problem to achieve.

A.M.^ Ghose

It is not always necessary to shape

the detector to improve their characteristics. For example uniformity of res- ponse in the gamma ray detectors can be

achieved by incorporating a suitable

detector in the system. Por fast

neutrons multiple bias method developed

by us achieves the same purpose. In

general the desired symmetry is also

applicable to the corresponding detectors

and their fabrications etc. is not

necessarily difficult.

P.P. Kane

1. It is perhaps appropriate to

point out that linear polarisation

measurements with gamma rays can some- times be made more accurately through

the use of (p,py) reactions with

selected targets such as magnesium. This

has been done at 1.38 MeV for example.

2. There is a real problem with

regu.lar to Delbriick scattering amplitudes

at large angles. On our work (Wucl.

Phys. 1970) and that of Schumacher et al

(Hucl. Phys. 1973) shows that empirically

the Delbriick amplitude at an angle such

as 1200 interferes destructiveLy with the

Rayleigh amplitude. Theory, as known at

present, predicts a constructive

interferences between the two amplitudes

at 1200.

Geometrical factors are important

in all measurements.

A.M. Ghose

I fully agree with Dr. Kane that

under suitable situations other methods

might have the same order of efficiency;

but here we have concentrated on general

methods applicable to almost all

situations. Delbruck scattering is

indeed an important area which requires

thorough investigation both theoretically

and experimentally and polarisation

measurements are expected to remove some

of the uncertainties in this field.

K. Gopala

Have you taken into consideration

the effects of multiple scattering

amongst the various parts of the

scatter er particularly in view of the

large size and closed shape of the

scatterer

A.M. Ghose

Multiple scattering is an important

problem. We have considered this aspect

and one of the incentives for the

53
present investigation came from the

desirability of using thin targets in an optimised geometry so that overall

intensity remains at a reasonable value.

S. Gopal

Can we really discriminate experimentally the phase differences exist

between Rayleigh scattering and Delbruck

scattering ?

A.M. Ghose

I am afraid that experiments alone are not sufficient to settle the relative phase problem. However, at each

angle of scattering, polarisation data

will furnish additional data which are sensitive to the choice of phases.

Hence a judicial mixture of theory and

experiment will certainly lead to a better understanding of the coherent

scattering phenomena.

5^
MEASUREMENT OF ANOTLAR DISTRIBUTION OP INCOHSRSNTLY

SCATTERED QAMlIk RAYS FROM ATOMS

B.Sinha ((xoswami) and N. Chaudhuri , North Bengal University, Darjeeling

India

There has been comparatively little experimental investigation on the whole-atom incoherent scattering of photons in

the x-ray and gamma-ray regions. A rigorous theoretical treatment of this type of scattering has not yet yielded enough

results and the incoherent scattering function approach is taken

to calculate the incoherent scattering cross section. Recently,

Cromer and Mann calculated using SCF Hartree-Fock wave functions

the incoherent scattering function over a wide range of momentum

transfer in the photon scattering process. These data are more

accurate than the earlier Hartree-Fock data in the low momentum

transfer range and form the only available most comprehensive

set of data over the range of momentum transfer upto 3.9 mc. In

the present work, the angular distribution has been measured for

incoherent scattering of 662 keV and 1.115 MeV photons by atoms

with low, medium and high Z in the angular range from l°to 165°.

The experimental values of the incoherent scattering function

have been interpreted on the basis of Cromer's theory.

(Angular distribution) cross section} gamma rays;

photon; scattering, incoherent; x-rays.)

Introduction

The incoherent scattering of photons by electrons of different atoms is

a topic of current interest. In absence

of exact theoretical calculations the

incoherent scattering function approach

is taken in the calculation of incoherent

scattering cross section. Highly accurate

values of incoherent scattering function

over a wide range of momentum transfer

upto 4 mc are now available from the

recent SCF Hartree-Fock calculations of

Cromer and Mann and Cromer2>3. Comparatively few experiments on the wholeatom incoherent scattering of photons

have so far been reported. The data from

the available experiment s4-» 5 cover only

small ranges of momentum transfer, have

large experimental errors and show considerable discrepancies at small and

large scattering angles.

Method . The whole-atom incoherent scattering experiment s4- reported have been

carried out by the auxiliary source

method. This method requires a photon

detector with efficiency independent of

photon energy. Instead of using this

method, we have compared, in the angu.l8.r

range 10° - 165°, the scattered counts

from a given scatterer at each scattering angle with the scattered counts from

an auxiliary aluminium scatterer of exactJy

the same size. The auxiliary aluminium

scatterer provides a secondary (scattering target) source of photons of energy

almost the same as the energy of photon

scattered at a given angle from the

given scattering target. The measurements were carried out with the main and

the auxiliary aluminium scatterers under

the same experimental conditions using

multichannel analyzer with spectrum

storage times in the range from 4 k sees to 100 k sees. Under the experimental

conditions mentioned, the detector efficiency and the solid angle factors cancel

out in the determination of the ratio of

the differential scattering cross section

for a given scatterer atom to that for a free electron in aluminium atom. This

ratio was divided by the atomic number

Z of the scatterer atom to obtain the

incoherent scattering factor S. The cylindrical scatterers used

were of pure aluminium, copper, tin,

mercury, tungsten and lead. The maximum

value of iir (li-photon attenuation coefficient, r-scatterer radius) for all

the scatterers was 0.7. Even for such

small scatterers, the corrections for

absorption of primary and scattered photons in the scatterer target were necessary and made using Dixon's" results

for calculating the self absorption cor- rection in small gamma-ray sources. For

angles 10° and 150° at which \ir values

were very small, S values were evaluated,

by extrapolating to zero scatterer radius a number of scattering measurements at

slightly different scatterer radii. Measurements were made using a 150 mCi Zn-65

55
source collimated over a distance of

80 cm in iron block. The source, provided

with adequate lead shielding, was at a distance of 130 cm from the scatterer.

The detector, a 3" x 3". Nal(Tl) scintillator head shielded -at sides, was couplFd

through a ND-52 PAD to a ND-1100 analyzer

with 512 channels. The distance between

the scatterer and the detector was 70 cm. For measurements at angles less than

10*^, a shadow-cone type experimental

arrangement was used. The Cs-'-3' source

in a conical shape collimator and the

detector head, 1" x 1". Nal(Tl) scintillator, were provided with adequate lead

shielding for reducing the background to

a very low level. The scatterers of lead

in the form of narrow width rings {'^l cm) were used for scattering measurements by

the auxiliary source method. At a fixed

source-to-detector distance of 3*3 m» the

angle of scattering in the range 1°- 5° was chosen by taking scatterers of different radii. In the arrangement used,

there was little background scattering

material, except the shadow-cone, the

light suspension threads for the shadowcone, the air mass between the source and the detector, and the foam rubber

scatterer holder. The detector pulses

were recorded by the NT) 1100 analyzer

using 512 channels and storage times in

the range 20 k sees to 100 k sees for a statistical precision near 1% . The total

scattering cross section at each angle

was determined and the incoherent scattering cross section was evaluated by subtracting from the total the accurate (^^^^

theoretical value based on recent SOP

Hartree-Fock calculations-'-~3 , The results

have been expressed as S. Results and Errors

The theoretical values of S included in

the Table are derived from the new work

of Cromer2 and Veigele et al'. Agreement

between our results and Cromer values

appears satisfactory at all values of

momentum transfer studied. The earlier

experiment s"* show greatest disagreement

with theory at low values of momentum

transfer.

Table 1

Experimental whole atom incoherent

scattering factors for lead (Z = 82) with

the corresponding Cromer-Veigele values.

(X = sin [e/2]/X , e - scattering angle,

X- photon wavelength in angstrom units.

The experimental errors are in parentheses) . Experimental Cromer - incoherent Veigele scattering values ofS.

factor S. 1. 92 0.894 0.374(010; 0.46

2. 65 1.232 0.558( 010; 0.55

3. 51 1.628 0.615 [010: 0.63

4. 64 2.161 0.669 rolo 0.72

10 7.84 0.937 030) 0.95

15 11.67 0.942( 032; 0.98

30 23.27 0.984 [022; 0.995

45 34.42 0.984 :022j 0.996

60 44.96 0.990( 028] 0.998

75 54.76 0.978( 030 0.999

90 63.59 0.980 :038) 0.999

105 71.36 0.976(;o55; 0.999

120 77.88 0.984 055 0.999

135 83.10 0.990(,051 1

150 86.86 1.007 100 1 165 89.17 0.999 '098J 1

References

The scattered counts in the shadowcone method were corrected for any difference in background counts with and without the scattering target. The experimental results for lead expressed as incoherent scattering factor S are given

in the Table 1. The measurements on other

elements mentioned above are not included

in the Table. The measurements on all the

elements studied give S ^1 in the angular

range upto 165°. The errors of the experimental S values have been computed by

taking into consideration statistical errors in all the measured counts taken

for evaluation of the experimental results

and errors in other factors involved in

the evaluation of results. At scattering

angles less than 5°* the energy change of

the 662 keV photons in the inelastic incoherent scattering is negligibly small

and no correction for this effect is

necessary in very small angle measurements.

1. Cromer, D.T. and Mann, J.B.,J.Chem.

Phys. H, 1892 (1967).

2. Cromer, D.T., J.Chem. Phys. ^,4857

(1969).

3. Veigele, Wm. J. et al, Kaman Sciences

Report, KN-71-431(R) (1971).

4. Sood, B.S. et al. Current Science, 33.

139 (1964), Indian J. Pure and Appl.

Phys. 1,305 (1963).

5. Quivy, R., Nucl.Phys.l6, 362 (1966).

6. Dixon, W.R., Nucleonics 8,68 (1951).

56
MEASUREMENT AND ANALYSIS OF A FEW 14

MEV NEUTRON CAPTURE CROSS SECTIONS

I'lanjushree Majumdar and B. Mitra

Bose Institute, Calcutta-700009

INDIA

Total 14 HeV neutron capture cross sections of seven representative nuclei have been meas-ured by activation method, in a relative

way. Data with an estimated error of + 2'/. have been presented.

Analysis of a(n,Y) total has been attempt»ed with (a) Statistical

evaporation type formula presented by Naguib and Luiyanov and

(b) Direct reaction formula presented by Lane and Lynn. It has been

shown that D.I. gives absolute estimate of values agreeing with

experimental ones. Statistical model analysis with carefully

adjusted neutron width function yields rather high radiative strength

function.

(Activation; P-counting error; capture reaction,- cross

section; measurement; neutron)

Introduction

The Bose Institute 250 kT Cockcroft

V/alton accelerator has been used as a 14 MeV neutron generator for quite a few

years in measuring cross sections of

various nuclear reactions. V/e report

here a few(n,Y) cross sections, with

adequate stress on experimental methods

of obtaining reliable results by activation method.

Method

The soirrce of maximum error in

activation results by p- counting has

been tracked down to errors arising out

of self-absorption and self-scattering

of p-rays . In case of 14 MeV (n.y) cross sections, additional trouble is

in low counting rate of the relevant

activity. Hence we propose to deal, in

this report , with our method of minimising

p- counting errors in activation. The

result presented here are all relative

measurements, i.e. cross sections

relative to a standard cross section.

This standard is (n,2n) cross section

of i^Cu nucleus and (n,a) cross section

in ^Al, the values of which are taken

as 540 mb and 117 mb at 14-8 HeV

respectively.

It has been reported previously

from OTxr laboratory that self-interaction

errors in jB- measurements can adequately

be taken account of, even by using end

window (j.M. counting set up. Mitra and

Ghose^ proposed a semi /empirical formula

for preconstructing efficiency curves of

such G-.i-I. counters for different P-ray

energies, where useful parameter

referred to j3-energies rather than maximum

P-energies. For establishing such a relation they had to make very thin

foils of elementary copper and

aluminium, irradiate them for generation

of suitable ^-activity and draw efficiency curves for a realistic thickness

of 20 mg/cm^ samples, neglecting

Z-dependence. We have tried to verify

the same analytic relationship, viz

by going down to much lower values of

sample thickness in which tracer

activities are uniformly dispersed. For

this, we first followed the method of

physically pouring out in pots, a uniform suspension in solvent ether, of

finest mesh metal dusts with tracer

elements added. These tracers used were

35s, 90sr, 204ti and 32p, all in liquid

chemical forms, to scan a P-energy

range of = .047 to 58 MeV.

V/e have assumed that, as in fig. 1,

the efficiency is defined by

T] = l/cg ^1 = count

rate at a minimum value of thickness

of the sample achieved and C2 = count

rate at a standard thickness of 20 ng/^m^

The results of obtaining (ct. rate vs thickness) ciirves in all the four above

cases are shown in figs. 2-5.

Fig. 6 is the constructed (''tel'^^

Eq) curve. To construct this we determined the value of the constant

'b' from experimental t] for °*^Sr. In fig. 5, the solid curve is the

analytically constructed curve, and

the experimentally obtained values

for 35s, 204T1 and 32p are plotted.

57
210-

ThicKTwss in ms/en* Thickness m Tng^cm*

200

Thickrtess in mg/cm*

0 as O-i 06 0.8 1.0 1.2 H Average Energy Ep in MeV

I I L. 8 12 16 Thickness in mg/cm^

58
Therefore it is seen that the analytically

sinple expression remains valid, within

the li.iiit_s of experimental error, for a ran^e of Eg = C.C47 to C.5, HeV.

Our sole assumption is that, in the

(Sp. count vs Thickness) carve, the so called 'Zero-thickness' value is given hy

that actually obtained for the ' minimum ' prepared thickness. To give more credence to the method, V7e are now producing very thin, doped saznples by

electro spraying. V/e assume albeit

drastically, that going dovm to a thick- ness one order of magnitude smaller,

will not appreciably alter the r\ values

as defined. In electrospraying method,

'.'e can go dow. to few iig/cm^ thickness.

The (n,Y) reaction cross section of a few nuclei relative to a(n, 2n) of °3Cu = 540 mb. and to a(n,a) of 27a1 = 117 mb,

obtained in our laboratory, are shown

in the Table 1.

In this table we have also presented

cross section values ' as predicted by

calculations according to a classical

statistical model formula presented by

iJaguib and Lukyanov^, also presented are

the values from crude Direct Interaction

(D.I.) model calculations according to

Lane and Lynn^, along with the experimental values, '/e have analysed the

ITaguib formula viz.

a(n,Y)=Ka(c)E"-'-U^

Table

exp[-2yVauJ

14-l4eV (n,Y) cross sections

Target Exptal Author Calc.

anv a ( mb

)

(mb) statistical

model acc

to Ilaguib

Calc. cT^^ (mb) acc.

D.I. model

of Lane

"and Lynn

51y oo .37

.49

Csikai

Present

.076

^^aa 1

1

.9

.29

Perkin

Present 1.44 0.2

1 .39 Present 1.55 0.129

127j 2

2

.5.74

Perkin

Present

1.20 0,19

1

1

.3

.12

Perkin

Present

1.29 0.24

141pr 33

2

• 33

.00

.19

Perkin

Csikai

Present

2.727 0.6

and made a change in their method of

obtaining the values of K and y. ilaguib et al have proposed an arbitrary

energy, Eg, of incident neutrons in the

experimental cr vs Ej-j^ curve and the value

of a at the point so specified yields

his K. But vre have shown that it is

not necessary to have arbitrary E3

values; instead, one could choose the

exact E3 value at the point where the

last bump in the a vs E^ curve disappears

for each nucleus, in their a(n,Y) vs E^ curves obtained from data accumulatedin

a single set of experiments of a single

laboratory. Eor this, we have consulted

BI'IL 325 data4. In general, Johnsrud

et al data (1959) and Stavissky's (1959)

data have been compared as instances of

a single laboratory's single set of

data in the neighbourhood of E^.'

Presiimably, Eg is a critical energy

belov; which partial v/ave analysis is . possible and at which point g-wave

contribution comes in and the synthetic

curve for that nucleus becomes exponentially decaying. Above S^, the

classical statistical formula with

suitable level density parameter is

applied

Conclusion

V/e conclude from our comparison of

values in Table that it is highly

debatable v/hether at this high energy,

a(n,Y) is quantitatively given by the

classical statistical formula.

Certainly the Naguib formula has the

character of a statistical formula, butthere is no way of checking it, since

it contains constants, t\io of v^hich, x and y are energy independent . Calculation from Perkin 's estimation of

'y and Hi - the respective v^idth, the

values of a obtained were 10-4 orders

lower than the experimental ones, while

D.I. calculations yield values nearly

of the same order of magnitude as the

experimental ones, obtained by Perkin

and the present author.

References

1. Kitra, 3. and Ghose, A.k. - Nucl.

Phys. 82, 157 (1966)

2. llaguib, K. and L\ikyanov, A. - J. of

ilucl. Energy 20, 373 (1966).

3. Lane, A.K. and L^mn, J.E. - 2nd

Geneva Conf. Report, 1^, 38 (1958).

4. iTeutron Cross sections - EITL 325 published by Signa Center, Brookhaven

National Laboratory, 2nd Edition (1966). 5. Johnsrud, A.E., Silbert , K.G. and

Bnschall , H . H . -Phys . Hev . 116 , 927 (1955).

6. Stavissky, Y.Y. - Atomnaya Energiga

I, 259 (1959).

7. Perkin, J.L., O'Connor, L.P. and Coleman, a.P.-Proc.Phys.Soc. 72,505(1958).

8. Csikai, J., Peto, G., BncZke, l-l. , iiLlli/jv.Z* and Eissa, K . A . -i-Iucl . Phys

- A21, 2^5 tl967)

59
INTERMEDIATE ENERGY APPROXIMATION OF THE BETHE-HEITLER

FORMULA FOR THE BREMSSTRAHLUNG CROSS-SECTIONS

K. Gopala and B. Sanjeevaiah

Department of Physics

University of Mysore

Manasagangotri, Mysore-570005

INDIA

Bremsstrahlung cross section calculations are still attracting

attention because of the inadequacy of the existing formulae. The

Sommerf eld-Elwert formula holds good upto 0.1 MeV. Bethe and Heitler

gave a relativistic expression for the bremsstrahlung cross sections

using Dirac's electron theory and Born approximation. Coulomb and

screening effects were not included in their calculations. Calculations of the bremsstrahlung cross sections using the B-H formula are tedious. Approximations of the B-H formula in the nonrelativistic

and extreme relativistic regions exist. But no such approximation

is available in the intermediate energy region. An attempt is made

to obtain an approximation of the B-H formula in the intermediate

energy region. Several approximations are made to reduce the B-H

formula into a polynomial in x, the ratio of the photon energy to

the total energy of the incident electron. The coefficients of the

polynomial turn out to be a long series of terms which are

functions of incident electron energy. The validity of the

approximate formula in the intermediate energy region will be

discussed

(Approximation; bremsstrahlung; cross section; electron;

intermediate energy; photons.)

Introduction

Calculation of the bremsstrahlung

cross section using the Bethe-Heitler

(B-H) formula is tedious. Approximations

of the B-H formula in the nonrelativistic

(NR) and extreme relativistic (ER)

regions exist. But no such approximation

is available in the intermediate energy

regions

The present paper attempts to arrive

at a simple form of the B-H formula by

affecting certain approximations to make

it hold good in the intermediate energy

region.

The B-H formula for the bremsstrahlung cross section, diff erential in photon

energy is given byl

|a ^ a(^^2 £2 a _ _2 (ii!:_i2!:!^

dk x^ ^2^2^ Y1Y2

3 Y1Y2 R 2fi 2 ' 2ytY

^1 ^^2 1>2 YtP

2

-^1 1^1

_

'^1"^^2^2

-L 2W

^2^2^ ^ Yl"'^2'^l"^2 2— ~^—2 Q 2 ^ •[} •••• (1)

where c< = fine structure constant=l/l37

Z = atomic number

r^ = e^/m^c^ = classical electron

radius

2 W = k/m c = photon energy in

terms of the electron

rest energy

= v^/c;(i = 1,2) is the velocity of the

electron in units of c (subscript 1 refers to the

incident electron and subscript 2 refers to the

scattered electron)

Yi = (1 -

p^ = momentum;

2^-4 i = 1,2

i = 1,2

L = TT-TT— 2 m, [rIil2ii!?i?2Llii rj j

We now write

Y2 = Yi(l-x) ....(2)

60
where x = W/y-i = k/E^ = photon energy in

terms of the xotal energy of the incident

-electron

^2 '^2 /I 1

where K = ln(b)

2(1 - |2)

..(3)

..(4)

and

ft 3 o 5 2" 3 ...(5)

The appro xi 1 at i on made in (4)

underestimates the B-H cross sections in

the low photon energy region and over- estimates them in the higher photon

energy regions. Calculations show that

the overall effect of the approximation

made in (5) is negligible, 'rfith the

above relations, equation (l) becomes

ar 2 2 Z X

....(6)

where a ,a-. etc. are ftmctions of and

X i.e. functions of incident electron

energy and fractional photon energy. ^2 can be written as ,

P2 = tl - 2m

IT (7)

using (7), ^2 ©"fcc. being expanded

binomially upto the term containing

2 g

7-, (1-x) . Further simplification

limiting to the term involving x^ leads

to

which are of course functions of incident

electron energy only)

Calculation of the cross sections

taking three, four and five terms in

equation (8) for various incident

electron energies in the region 0.05 to

4. 54 MeV shows that the contribution of

the fifth term is negligible. So,

V If 0.o:r/(A^+A^x+A2x2H-A3x5). ..(9)

can be taken as the required approximation

of the 3-H formula in the inter-mediate

energy regions. The coefficients A to

A^ vary with Y]_ as shown in Fig. 1.° For

values of Yt^ 3 we can approximate the

various coefficients as

A^ = (18.5 + 0.55 Yj

)

A^ = -(42 + 0.33 Y^)

A2 = (37 + 0.20 Yi)

A^ = -(18.0 - 0.20 Yi )

(10;

da

dk = ar^^( Aq+A^x+A2X^+A3X-^+A^x^;

(8)

where A , A-j^ etc. are functxons of xncident energy of the electron only (each

of A , A-, etc. comes out to be a long

series 0f terms involving l-j^ and y^^

Fig. 1 Variation of the coefficients

A to A-, with Yn • o 3 1

The cross sections calculated using

equation (9) with the coefficients given

in (10) are plotted along with those of

B-H formula (l) and the experimental

results in Figs. 2. The experimental

61
100 200 300 ''00 500 PHOTON eNERC-y.-keV Fig. (b)

0.2 0.A 0£ 0.8 1X1 PHOTON ENERGY, MeV

Pig. (c)

10-

f 8

-ft 6

—I r~

T. • 2.50MeV

'GOLD

• TIN

« COPPER

» ALUMINUM

4

-

2-

0.5 W 1^ 2.0 2.5 PHOTON ENERGY.M«V

Fig. (e)

14

12-

lO

2-

to 2J3 iO 4.0 SJ3 PHOTON Efii5fi(5Y.WeV Fig. (f)

Pigs. 2a to 2f Bremsstrahlung cross sections as a function of emitted Photon

energy for different incident electron kinetic energies Uq-'-

Bethe-Heitler formula, present approximate formula

The points are the experimental data.

62
results were taken from Motz- for ^ 0.5 MeV electrons, from Dance et al

for 0.2, 1.0, 1.7 and 2.5 MeV electrons

and from Starfelt and Koch^ for 4.54 MeV

electrons. It can be seen from the

figures that the approximate formula (9)

deviates considerably from the B-H

formula for low energy electrons and in

low photon energy regions of the

spectra

But the approximation is justified

by the fact that it is closer to the

experimental data.

References

1. Jauch, J.M. and Rohrlich, F., The

Theory of Photons and Electrons,

Addison-V/esley Co., Mass., U.S.A.,

1955, p. 369.

2. Motz, J.W., Phys. Rev. 100, 1560

(1955)

3 . Dane e , W . E .

, Rainwat er , W.J. and

Rester, D.H., Investigation of

Electron Interaction in Matter, LTV

Research Report No. 0-71000/ SR-2 Feb.

1968; see also Rester, D.H. and Dance,

W.E., Phys. Rev. 161, 85 (1967).

4. Starfelt, N. and Koch, H.W., Phys.

Rev. 102, 1598 (1956)

63
A NEW ME'x^HOD FOR THE MEASUREtlEUT OF DIFFERENTIAL

ELASTIC SCATTERING CROSS SECTIONS OF FAST NEUTRONS*

S. Nath, A. Chatterjee and A.H. G-hose

Nuclear Physics Laboratory

Bose Institute, Galcutta-700009 , India

A new method has been

reduces the problem of low

scatterer has been taken in

elastically scattered neutr

from the inelastically scat

bias technique. Experiment

tial elastic scattering cro angles for 14 I'leV neutrons

resuJLts have also been comp

prediction

described which successfully

scattering intensity. The

the form of a spheriod. The

ons have been discriminated

tered ones by using multiple

ally measured values of differenss sections for sulphur at four

have been presented. The

ared with the optical raodel

(Cross section; differential; elastic; mialtiple

bias technique; neutron; scattering).

Introduction

This paper deals with a new method

suitable for the measiir ement of elastic

scatterini- cross sections of fast neu- trons over a wide range of incident

energy. In the present method, eraphasis

has been laid on the geometric factors

involved .in the experimental arrangementl so as to avoid two limitations encoun- tered in the usual measurements. The

size and shape of the scatterer, predeterrp.ined by the design of the experimental set-up, sets out a limit to the

intensity of the scattered count. This

factor has been carefully considered in

designing the experimental set-up. The

aethod also gives an effective v/ay to

discriminate betv;een the elastically

scattered counts and the non-elastically

scattered ones. The method described is an absolute one in the sense that it does

not require kno;:ledge of any other

related cross section and the final cross section value can be derived from

the data obtained in the present

experiment alone.

'jeometry and Underlying Theory

In this method, as mentioned earlier,

the shape of the scatterer plays the

most important role. The scatterer is

shaped in the for;;! of a surface of

revolution obtained by rotating an arc

of a circle about the corresponding

chord as axis. Fig. 1. depicts section

of such a surface truncated at sections

AA ' and B3 ' , and the positions of the source and detector v/ith respect to it.

The distribution of a function directly

related to the exposed area of the

scatterer plotted against the length

(measured along source - detector line)

of the scatterer surface, has also been

shown in Fig. 2. This function is obtained by theoretical evaluation of

scattered intensity to be presented below

The length of the scatterer is determined

by the necessary aperture to be left to

make the entire surface of the scatterer

available to neutrons emitted from the

target and by the intensity of the sca- ttered beam desired. The length and

position of the scatterer (symmetrically

placed w.r.t. source and detector), in our set-up, have been confined to the

central section of the scatterer intentionally; this is to avoid the steeply

rising portion of the curve, incl"j.sion of

which vfould have otherwise made the

scattering more critically dependent upon

the scattering angle. Referring to fig.l

the number of neutrons scattered elastically towards the detector D can be

shovrn to be.

ua'^y N^t

V

da if

' +f

^1^. Secif' tan>J^ f(x,T/^)dx

wnere

f(x,V^)

(1-x) (^l+d-xS) tan^i^ -1)

[l+d+x) tan^y) h+il-x^) tan^VJ

1

[l+(l-x) tan^Y Xl+ (l-x2) ta-n^f

(sec^Y c2 tan^lj/ )l/2

iVork carried out under a PL-480 Project sponsored

by the National Bureau of Standards, U.S.A.

64
and

21

No

V

ta

= z/1

= source to detector distance

= ntunber of neutrons emitted/sec.

= number of scattering nuclei/c.c.

of the scatterer

= radial thickness of the scatterer

= aperture of the detector

scattering angle

Fig.l. Schematic of ths scatte^rtss^:

geoaetrj.

spectrum of elastically scattered neutrons

(including distortion caused by the multiple scattering effects) while it is zero for neutrons of significantly lower

energies. This scattered count is

compared against the experimentally

measured counts obtained as a difference

of counts with and without the shadow bar

in position.

Absolute knowledge ofeis not necessary, as the expression for the direct

count also involves 6 i.e.

N ^ 2

and this € can be eliminated out by

taking the ratio of N to n i.e.

^=^'t./2.ii.—I^.Sec^f' tan> r f(x,f)dx

-f

The count recorded by the detector

has to be corrected, as it contains

contributions from both elastic and nonelastic events. This has been done by

the double bias technique developed in

our laboratory. The method consists of

recording the counts at two bias levels

simiiltaneously and utilising the relative

efficiency vs. energy curves^ for the

corresponding set of biases.

.2 -A -6 -8 1.0

Fig. 2. The intensity function f<x,>^) between the soiirce and the detector.

The coxinting rate registered by the

detector D, is then given by

wa^Not da (iLi) . +f

N=^-=-75—5-. —2 tan^V^ Sec'^ \ f(x,V)dx

-^^'^ 1 d-n. ^

20^

301PHUB

DIP. ELASTIC COHJEAUB et al.

PE2SEi'T EIPT. CAI/CULAIIOS

72

Cos e (C.K) -f Fig. 3. Differential elastic apeetrm® of

14 MeV neutrons from sulphur.

Here, the mean detector efficiency € is

assumed to be independent of the

65
Results and Dlecusslons

The differential cross section of

sulphur has been measured for 14.8 MeV

neutrons at 4 scattering angles 30°, 40°,

60°, 70°. The results have been com- pared with the experimentally measured

data of Conjeaud et al5 in fig. 3. The

experimental values have also been com- pared with the optical model predict ion^

(fig. 3). This set of average parameters

has been obtained by simultaneously

analysing all the experimentally measured

non-elastic cross section data in our laboratory by Pal, Chatterjee and Ghose^.

The measured values, though in fair

agreement with the other experimentally

measured ones, are not so close with the

theoretical values obtained with the

above mentioned set of parameters. This

is probably due to the over-emphasis

placed on the non-elastic set of data

while arriving at the set of parameters.

We are extending the measurements to

large angles of scattering.

The authors wish to thank the

Director, Bose Institute for his kind

interest in this work. One of the

authors (S.W.) wishes to thank the

Council of Scientific and Industrial

Research for awarding him a scholarship

which enabled him to carry out this work

References

1. Ghose, A.M.; Proc. Int. Symp. Rad.

Phys., India, 1974 (in press).

2. Chatterjee, A. and G-hose, A.M.; Nucl.

Inst, and Methods, 1967.

3. Conjeaud, M.j Fernandez, B., Haror,

S., Picord, J. and Souchere, G.,

Nucl. Phys. 62, 1965.

4. Pal, B., Chatterjee, A. and Ghos9,

A.M., Proc. Int. Symp. Rad. Phys.,

India, 1974 (in press).

66
COMPTON SCATTERING OF 1.12 MeV GAMMA RAYS BY K-SHELL ELECTRONS

P.N. Baba Prasad, G. Basavaraju and P.P. Kane

Physics Department, Indian Institute of Technology

Powai, Bombay-400076

Two sodium iodide counters in coincidence and a twenty channel

pvilse height analyzer have been used to determine the pulse height

distribution of 1.12 MeV gamma rays which are Compton scattered by

the K-shell electrons of gold, lead and thorium. The angular variations of the differential cross section ratio, "-^K , have already

been reported. The present measurements were made at 60 and 100

scattering angles. At 60°, lead targets of 50 mg/cm^ and 143

mg/cm2 were used. At 100°, targets of gold (13 mg/cm^), lead (143

mg/cm^) and thorium (14 mg/cm^) were used. In all cases, pulse

height distributions of false coincidence events were determined

and subtracted from the measured distributions in order to obtain

the true distributions. A broadening of the K-shell electron

Compton peak has been observed. The results of these measurements •• are discussed. . * (Compton scattering; differential cross section; electron

binding; gamma rays; K-shell; photons.)

Intro duction

In a recent paper"^ where references

to the earlier works have been listed, a report has been given regarding the

angular variation and the target-Z dependence of the energy integrated cross sections for the Compton scattering of

1.12 MeV gamma rays by K-shell electrons.

The energy distributions of 0.662 MeV

gamma rays Compton scattered by the

K-shell electrons of thin targets have

been studied in only a few of the earlier

experiments. A broadening of the K-shell

electron Compton peak and a peak shift

of about 35 keV towards lower energies

relative to the free Compton line were

observed by Missoni et al^ . The present

work was undertaken in order to provide

new information on Compton scattering

by K-shell electrons at as high an energy as practicable.

Experimental Methods

Some of the details of our experimental arrangement have been given

elsewhere^. The pulse height distributions of 1.12 MeV gamma rays Compton

scattered by K-shell electrons have been

measured at two scattering angles with a coincidence gated twenty channel

analyser. At 100°, targets of gold

(13 mg/car), lead (143 mg/cm^) and

thorium (14 mg/cm^) were used. At 60°,

only thicker targets of lead (30 mg/cm

and 143 mg/cm ) could be used on account

of counting rate considerations. In all

cases, pulse height distributions of

false coincidence eveni s were determined

and subtracted from the measured distributions in order to obtain the true distributions. The usual procedure for the

estimation of false events is to record

a coincidence spectrum with an aluminium

target of a thickness equivalent to that

of the given target under consideration.

Such a procedure assumes that Z-dependent

false events are negligible. The reliability of this procedure has been

examined experimentally at 60° as

follows. Firstly, the false event

spectra were measured with targets of

aluminium and copper equivalent to 143

mg/cm^ lead. For 1.12 MeV gamma rays,

the binding energy of the copper K-shell

electrons can be considered relatively

small. Moreover, on account of the narrow pulse height window used with the

x-ray counter, there was a negligible

probability of true events due to the

copper K-shell electrons being I'ecorded.

The integrated false coincidences

per hour determined with aluminium and

copper targets were 26.30 + 0.85 and

38.20 + 1.07 respectively. After

subtracting the 'target out ' coincidence

rate from these numbers and assujning the

Work supported in part by a grant from the National Bureau of Standards

under the Pl-480 programme.

.67
differences to be proportional in each case to t2, where t is the thickness of

the target, we estimated the corres- ponding differences for the thinner

targets of aluminium and copper equivalent to 30.3 mg/cm^ lead. Then, with

the addition of the 'target out' coincidence rate, the false coincidence rates were calculated to be 18.09 + 0.97 and

18.54 + 0.97 respectively and, further, were in agreement with the rate 17.83 + 0.42 actually measured with a copper

target equivalent to the 30.3 mg/cm^

lead. In view of this agreement, the

equivalent aluminium substitution

procedure can be seen to be reliable to

about 3a in the case of thin targets for

the determination of the false coincidenc3 rates. However, the above

mentioned data show that the same procedure is unreliable in the case of

thick targets. This is an important

point to remember during any discussion

of several early experiments.

leo

iftlSO OX

o

0120

o 90 u

Ulu

D

z.

30 -

t.l2 MeV LEAD (BO-ng/cm*^ 0=60°

{ COINCIDENCES - SINGLES

532 KEV

^0 14 18 22 26

PULSE HEIGHT IN VOLTS_..,

30

The true pulse height distributions

obtained at 60° with the lead (30 mg/cm^)

target and at 100° with the gold (13

mg/ cm^ ) target are shown in Figs . 1 and

2 respectively. The solid curve in each

figure represents the pulse height distribution of single events corresponding

practically to scattering from free

electrons. There is a noticeable rise

in the coincidence spectrum at lower

pulse heights. A similar rise was also

observed by Missoni et al \iith 0.662

MeV gamma rays . On the basis of an

'exact ' non-relativist ic calculation,

G-avrila^ has shown that such a rise is

connected with the well-known infrared

divergence in quantum electrodynamics.

The present measurements also indicate

a broadening of the K~shell electron

Compton peak. In Fig. 2, a slight

shift of the peak towards lower pulse

heights is clearly seen. In each case, as expected, there is an appreciable

number of scattered photons with

energies considerably in excess of that

corresponding to Compton scattering from

free electrons at rest.

The response of the gamma detector

has been determined for several known

energies so as to enable the determination of the energy distribution,

d^av/d dE ' , of the scattered photons.

1.12 MeV is the highest photon energy

at which electron binding effects have

been studied so far.

Fig. 1. Pulse height distributions

obtained for 1.12 MeV gamma rays

for lead at 60°.

PULSE HEIGHT IN VOLTS Fig. 2. Pulse height distribution ohtaSorBd for 1.12 MeV gamma rays for

gold at 100°.

68
References Discussion

1. Baba Prasad, P.I^. and Kane, P.P.

ms J. Res. 78A, 15 (1974).

2. I'lissoni, G-. and Di Lazzaro, M.A.,

Istituto Superiors Di Sanita Reports

ISS-66/7 and 65/8 (1966) (unpublished) . 3. Baba Prasad, P. IT. and Kane, P.P.,

Ifuclear Physics and Solid State

Physics (India) 123, 81 (1969) and

13B . 187 (1970).

4. Savrila, H. , Phys . Rev. Ao, 1348

(1972).

S. (jQpal

Is it possible to measure K-shell

incoherent scattering cross section at

0° scattering angle in view of the theoretical prediction of non-zero cross section by Whittinghaan?

P.P. Kane

a) Firstly, it does not seem possible to do this actually at 0°.

b) G-avrila- et al have argued that

this conclusion of Whittingham is

probably an erroneous . one .

69
NUCLEAR THEORY BASED CROSS SECTIONS OF

TH-232, TH-233 AND U-233 AND THEIR

APPLICATIONS IN REACTOR TECHNOLOGY,

S. B. Garg and Ashok Kumar

Bhabha Atomic Research Centre, Trombay,

Bombay, India.

Thorium fuel cycle is an active subject of research - more so for us since we have large deposits of thorium.

Because of various reasons thorium has not found much favour

with the reactor technologists and therefore its cross sec- tions have not been studied with the desired accuracy. Cross

sections make their impact on reactor design right from its

inception to its completion and therefore a coherent study

of the cross sections of thorium and uranium-253 has been

made. In Reactor Physics studies emphasis is placed on total,

fission, capture, elastic and inelastic scattering cross

sections. Generally, the measured information on inelastic

scattering cross section of heavy nuclides is not sufficient

in the MeV energy range for reactor applications. In order

to correctly predict the neutron spectrum and its effect on reactor parameters the inelastic cross sections have been

evaluated with the local optical and statistical models. The

total and elastic scattering cross sections have also been

evaluated together with the angular distributions of elastically and inelastically scattered neutrons. Multigroup temperature dependent cross sections have also been generated

for thorium and uranium-253 in the entire energy range extending upto 10 MeV.

(Calculation ; cross section ; optical model } reactor

technology; scattering - elastic , inelastic, total ; thorium ; uranium )

Introduction

Thorium fuel cycle is an active

subject of research particularly for us

since we have large deposits of thorium.

Because of various reasons thorium has

not found much favour with the reactor

technologists and therefore its cross sections have not been studied with the

desired accuracy. But, with the upcoming

of fast reactor technology in this country thorium is bound to find a place as

a fertile material to produce uranium233. It is, therefore, imperative for

us to estimate the cross sections of

thorium-232, thorium-233 and uranium233 in the MeV energy range based on nuclear theory.

In reactor physics studies emphasis

is placed on total, fission, cap-fcure,

elastic and inelastic scattering cross

sections. In the high energy region the

neutrons lose energy mainly by inelastic

collisions and therefore the neutron

spectrum, in a fast reactor, is very

sensitive to inelastic cross sections.

Generally, the measured information on inelastic scattering cross sections of

heavy nuclides is not sufficient in the

MeV energy range for reactor applications. This information can be generated

with the optical and statistical

modelsl' 2, 3,4 . For short lived elements

such as thorium-233, the fission cross section can be estimated with the channaL

theory of fission^' and the capture cross section can be predicted either

with the dipole radiation theory of the , compound nucleus" or with the direct^ ori serai-direct-'-'-' dispersion theories.

The reactor oriented studies of

nuclear cross sections are concerned with

the generation of group cross sections

70
from the basic energy point data. In

order to adhere to the spirit of this

symposium we shall not discuss this

subject in this paper but only concentrate on the analysis of Th-232, Th-233

and U-233 cross sections in the energy

range 0.1 MeV to 20.0 MeV.

Optical and Statistical Models

The local optical model with the

Saxon- Woods fonn of the real part,

Gaussian form of the imaginary part and

Thomas form of the spinorbit part of the

potential has been used in these analyses. The Schrodinger equation is numerically solved to obtain the reflection

coefficient which is then used to evaluate the transmission coefficients,

shape elastic, compound nucleus and the

total cross sections.

The statistical decay of the com- pound nucleus leads to the calculation

of compound elastic, inelastic, (n, 2n)

,

(n>p ), (n>a) and other energetically

possible reaction cross sections. However, the customary application of the

statistical model is in the calculation

of inelastic cross sections. This model

also yields the differential elastic and

inelastic cross sections. The relevant

formulae for these cross sections are given in reference 11.

The X Criterion

The six parameters of the optical

model potential, namely, U,W, r,a,b and

V are varied in such a way that a minimum value of X? is obtained. A computer programme AUTO, which allows the

simultaneous variation of five parameters, has been coupled to another programme ABACUS-2 and the search has been

carried out for U,W and r. This search

was terminated when the calculated elastic scattering cross sections matched

with the measured ones. In this study

it was, however, noticed that U and r

did not show much variation with energy

and therefore to save time they were not

varied throughout the entire energy

range. The values of V , a and b were

fixed at 7.0 MeV, 0.6 f^Snd 0.6 f respectively.

Calculations

a) Thorium-232 : The local optical

model parameters have been derived by

obtaining correctly the elastic scattering cross sections in the energy range

0.1 MeV to 15 MeV. Since no measurements

have been reported beyond 15 MeV, the

model predictions of total, elastic and

inelastic cross sections have been extended upto 20 MeV and they are recorded

in Table I. The optical model parameters

are given below:

U =40 MeV J r = 1.32 f ; = (1.32A^/^ + 2.0)f.

(i)W = 20 MeV ; 0.14E < 6.0 MeV.

(ii)W = 26 MeV ; 7.0:^B ^ 20.0 MeV.

14 energy levels were used to obtain

the level excitation cross sections, but

due to space limitation these cross sec- tions are not given in this paper.

b) Uranium-233 : In this case the

energy dependence of the parameters was observed to be very weak. The following

parameters were chosen for the entire

energy range:

U = 40 MeV ; W = 24 MeV 5 r = 1.32 f ; Rg= (1.32 A

1/3

+ 2.5) f. The total, elastic and inelastic

cross sections are tabulated in Table IL

The excitation cross sections were evaluated with 9 energy levels.

c) Thorium - 233 J Because of very

short haif-life of 22.2 minutes cross se- ction of Th-233 have not been measured.

Only the thermal neutron cross section

is reported in the literature. The cross sections of Th-233 may be very

significant in the production of U-233

when thorium is used as fertile material

in high flux fast reactors. The situations in which the neutron captures in

Th-233 occur at a faster rate than betadecay would not be conducive to the production of U-233. Then the capture cross sections of Th-233> in the MeV

energy range, assume a special significance. We have calculated the total,

shape elastic and compound nucleus formation cross sections with the following

optical model parameters:

U

(i)W = (ii)W =

40 MeV ; r = ,1.32 f

R = (1.32 A^/5 + 2.5) f.

20 MeV } 0.1 6/MeV.

26 MeV ; T.O^E 4 20 MeV.

Capture and Fission Cross Sections;

The capture and fission cross sec- tions can be estimated in terms of com- pound nucleus formation cross section

by knowing f ' P • fy given by

the We iskopf^ formula^. Using Newton's

level spacing fonnula Cameronl^ recently

obtained an expression for (y in terms

of the effective total angular momenta

of single particle states near the Fermi

surface. These momenta are listed by

71
ITewton ^ . Based on this fonnula and

choosing the appropriate values of

various parameters we have obtained Py

for Th-233 at 0.1 MeV to be 22.5 MeV,

In general, fy for even-odd nuclei

(Z>90) in the MeV energy region is

negligibly small and for Th-233 Cramer

and Brittle have neglected it in their

recent evaluations.

Table I

16 Fujimoto and Yamagnchi have derived an expression for ?^/Vf in terms of fission i threshold and neutron binding energies.

Based on these considerations we obtain

V^/Vf c:3^ so that Fy /p = . 003 and

Twf = .024. We now assume that these

ratios of reaction widths do not vary with

energy and calculate the various reaction

cross sections. These cross sections are given in Table III.

Total, Elastic and Inelastic

Scattering Cross Sections of Th-233.

E (MeV) ''t

i m; ^t

(m)

^e

( n\ \o)

^in

-LX • U y in IP u

0.57 6.91 7.29 5.37 5.41 1.36

1.5 6.61 6.55 4.06 3.96 2.37

3.0 7.35 7.60 4.62 4.63 2.54

4.0 7.18 8.00 4.61 5.00 2.40

7.0 5.93 6.25 3.38 3.37 2.20

15.2 5.44 5.70 2.92 2.95 0.98

17.0 5.58 3.06 0.97

19.0 5.75 3.23 0.98

20.0 5.82 3.30 0.98

Table II Total, Elastic and Inelastic

Scattering Cross Sections of

U-233

E(MeV) a (°) a

("1) e e

a.

0.1 10.63 11.03 8.06 8.24 0.15

0.5 7.23 7.66 4.82 5.04 0.40

1.0 6.44 6.41 4.81 3.71 0.74

3.0 7.12 7.67 4.35 4.12 1.01

5.0 6.67 7.34 4.16 4.23 1.03

7.0 5.98 6.51 3.36 3.05 0.43

9.0 5.49 5.95 2.85 2.91 0.39

10.0 5.37 5.78 2.75 2.90 0.45

12.0 5.33 5.85 2.71 2.98 0.40

15.0 5.41 5.99 2.87 3.01 0,13

18.0 5.69 3.16 0.12

20.0 5.89 3.34 0.13

B(Me^

Table III . Reaction Cross Sections

(c) (c)

t ce

(c) (c) cn f

of Th-233 —T^l—ITT

r seat

0.1

0.5

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

12.0

15.0

17.0

20.0

10.

7.

6.6.

7.

7.

6,6.

5.5.

5.

5.5.

5.

5.

5.

85 7.07

13 4.63

30 3.57

97 3.86

33 4.39

18 4.45

82 4.18

40 3.76

97 3.28

70 3.00

51 2.81

40 2.69

34 2.69

41 2.83

57 3.00

81 3.26

2.88 0.069

2.50 0.060

2.73 0.066

3.11 0.075

2.94 0.071

2.73 0.066

2.64 0.063

2.64 0.063

2.69 0.065

2.70 0.065

2.70 0.065

2.71 0.065

2.65 0.064

2.58 0.062

2.57 0.062

2.55 0.061

0.0086

0.0075

0.0082

0.0093

0.0088

0.0082

0.0079

0.0079

0.0081

0.0081

0.0081

0.0081

0.0079

0.0077

0.0077

0.0076

9.87

7.06

6.23

6.89

7.26

7.12

6.76

6.34

5.91

5.64

5.45

5.34

5.28

5.35

5.51

5.75

— yC ^ is given by Bohr and Wheeler in terms

of the exit fission channels and effective

level spacing D. Making use of these expressions at 0.1 MeV, we get D = 0.46 ev and

= 0.18 ev.

<v' Discussion

The simple approach of local optical model used in the cross section calculation of the deformed nuclides Th-23^

Th-233 and 0-233 appears to be reason- ably good. The calculated elastic and

total cross sections match with the measured ones at several energy points as can be seen in Tables I and II. The

maximum deviation observed between them

at some of the energy points is 10% or less which is well within the experimental error. This error can be minimized

further if the potential is generated by

fitting the experimental data on inelastic and differential elastic cross sec- tions. This approach is quite time con- suming and is feasible if there is no restraint on computer time.

The level excitation cross sections

of these elements have not been measured:

in the entire energy range. These caleu72
lations serve to fill this void. The cross sections of Th-233 have not been

measured and their evaluation based on various nuclear theories may be of some use in certain applications.

Acknowledgement s Our grateful thanks are due to

Shri V.N.Meckoni, Director, Reactor

G-roup for encouraging us throughout the course of this work. Also, we owe our sincere thanks to Dr. P.K. Iyengar,

Director, Physics G-roup for suggesting

to us to undertake the cross section

study of Th-233.

References

1. Feshbach,H., Porter, C. and

Weisskopf, Y., Phys. Rev. 96,

448 (1952). ~

2. Hauser, W. and Feshbach, H., Phys.

Rev. 87, 366 (1952).

3. Auerbaoh, E.H., BNL-6562.

4. Moldauer, P., Engelbrecht, C. and

Diuffy, G., AKL-6978 (1964).

5. Hill, D.L. and Wheeler, J. A., Phys.

Rev. Q3_, 1102 (1953).

6. Strut insky, V.M., Nucl. Phys. A95,

420 (1967).

7. Vandenbosh, R. and Huizenga, J.R.,

2nd UN Intern. Gonf. on Peaceful

Uses of At. Energy, 1^,284 (1958).

8. Blatt, J.M. and Weisskopf , V.

,

Theoretical Nuclear Physics, John

Wiley, New York (1952).

9. Lane, A.M. and Lynn, J.E., Nucl. Phys.

11, 646 (1959).

10. Brown, G.E., Nucl. Phys. 57, 339

(1964)

11. Garg, S.B. and Rastogi, B.P., Fast

Reactor Physics (IAEA) 1, 339 (1967).

12. Cameron, A.G.W., Can. J. Phys. 37,

332 (1959).

13. Newton, T.D., Can. J. Phys. 34» 8O4

(1956).

I 14. Cramer, J.D. and Britt, H.C., Nucl.

Sci. Eng. 11, 177 (1970).

15. Bohr, N. and Wheeler, J. A., Phys. Rev.

^, 426 (1939).

! 16. Pujimoto, Y. and Yamaguchi, Y.,

Progr. Theoret. Phys. 5, 76 (1950).

i

1

73
THE DEVELOPMENT OF RADIATION SHIELDING STANDARDS IN USA*

D.K. Trubey+

Radiation Shielding Information Center

Oak Ridge National Laboratory

Oak Ridge, Tennessee,, 37830, U.S.A.

The American Nuclear Society (ANS) is a standardswriting organization-member of the American National

Standards Institute (ANSI). The ANS Standards Committee

has a subcommittee denoted ANS-6, Shielding, whose charge

is to establish standards in connection with radiation

shields, to provide shielding information to other

standards writing groups, and to prepare recommended sets

of shielding data and test problems. This paper is a progress report of this subcommittee.

(American Nuclear Society, radiation, shielding,

standard)

By Standards, we mean voluntary

Standards - sometimes called industry

Standards - promulgated through the

American National Standards Institute

(ANSI) consensus procedure whereby all

interested parties have an opportunity

to comment on and contribute to the con- tent in a manner avoiding any conflict of

interest

The purpose of a Standard is to set

forth acceptable practices, procedures,

dimensions, material properties, specifications, etc., which have been agreed

upon by representatives of a broad segment of the subject activity.

The management organization of

Nuclear Standards has accepted a definition propounded by an international

standards organization as, first,

•Standardization: The process of

formulating and applying rules for an orderly approach a specific activity for

the benefit and with the cooperation of

all concerned and in particular for the

promotion of optim\im overall economy

taking due account of functional conditions and safety requirements.

It is based on the consolidated

results of science, technique, and experience.

It determines not only the basis

for the present but also for future development and it should keep pace with

progress," and a Standard is "The result

of a particular standardization effort

approved by a recognized authority."

Our interest here, however, is primarily in American National Standards, of

which about 5,000 exist. Perhaps the best

known to the lay public are a few PH2

Standards defining the speed of photographic film and Cl-1971 which, when given

legal stature through adoption by a municipguLity, is the well-known electrical ; code.

The organization responsible for

promulgating voluntary standards is ANSI.

The Institute, a nonprofit corporation, is a federation of leading trade, technical

and professional organizations, government

agencies and consumer groups. ANSI's

principle functions are to coordinate

standards development, minimize duplicati- on and overlap, and provide a neutral

forxun to consider and identify standards

needs.

The Institute does not develop standards. It makes use of the combined

technical talent and expertise of its

member bodies j technical, professional,

and trade organizations together with the

companies and industrial firms that

comprise the Institute. A standards

writing organization, such as a technical

society, having developed a standard and

seeking approval by ANSI, prepares a list

of the organizations, companies, and

other groups with substantial concern and

competence in the scope of the standard

and then conducts a canvass of them on I approval of the proposed standard.

The final results are reported to the

MSI Board of Standards Review for determination that a consensus exists and

declaration of the proposed standard as a *Research sponsored jointly by the U.S. Atomic Energy Commission and Defense

Nuclear Agency under contract with Union Carbide Corporation.

"''Chairman Shielding Standards Subcommittee, ANS-6, Standards Committee,

American Nuclear Society.

74
yoluntary American National Standard.

The standards-writing organization

of interest here is the American Nuclear

Society (ANS). Among its several administrative committees is one on Standards

composed of nearly 30 Subcommittees (see

list below) . Parenthetically, as presently constituted, the Committee consists

of all individ-uals assigned to Standards

tasks within the Society, some 800, and

is, obviously, not a working or workable

group. There is, therefore, an elevenmember Steering Committee. The ANS

Standards Subcommittees are grouped along

lines of common interest and assignments

\inder supervision of a Steering Committee

member. The Subcommittees, in t\im, have

established ad hoc Working G-roups for

preparation of individual Standards!

ANS-1 Performance of Critical Experiments

ANS-2 Site Evaluation

ANS-3 Reactor Operations

ANS-4 Reactor Dynamics and Control

ANS-5 Energy and Fission-Product Release

ANS-6 Shielding

ANS-8 Fissionable Materials Outside

Reactors

ANS-9 Nuclear Terminology and Units

ANS-10 Mathematics and Computation

ANS-11 Radioactive I'laterials Handling

Facility and Specialized Equipment

ANS-13 Fuel Assemblies Criteria

ANS-14 Operation of Pulse Nuclear Reactors

ANS-I5 Operation of Research Reactors

ANS-16 Isotopes and Radiation

ANS-18 Environmental Impact Evaluation

ANS-19 Physics of Reactor Design

ANS-20 Systems Engineering

ANS-21 PWR Design Criteria

ANS-22 BWR Design Criteria

ANS-23 GCR Design Criteria

ANS-24 LMFBR Design Criteria

ANS-30 Nuclear Power Plant Systems

ANS-31 Engineered Safety Features

ANS-32 Reactor Plant Process Systems

ANS-33 Containment

ANS-34 Radioactive Waste Systems

ANS-35 Fuel Handling and Storage

The subcommittee on shielding standards, ANS-6, now composed of seven working groups, was established in 1964

with the sponsorship of what is now the

Shielding and Dosimetry Division of the

Society! The standards development

of the subcommittee is carried on within

working groups composed of members from

reactor vendors, architect-engineers,

national laboratories, the Atomic Energy

Commission, and universities. The goals

and accomplishments of the working groups

are briefly described below.

ANS-6. 1; Shielding Cross Section Standards

Because of the changing state of

knowledge of neutron cross sections, no standard is possible with anything near

the time constant of the usual standard

such as, for example, the classical ASTM

code for unfired pressure vessels. At present it is better to think of recommended cross-section sets as reference

sets rather than standards. Within

ANS-6, "Shielding Cross Sections' has a broad interpretation, which includes

neutron interaction cross sections for

all common reactions, photon-production

cross sections, photon interaction crosssections, and secondary angular and

energy distributions for all these interactions. Since the Evaluated Nuclear

Data File (ENDF) represents current

reference data, no action in this area

seems to be required. The group did

recommend in 1970 that the Lawrence

Livermore Laboratory evaluated photon

interaction cross section set be accepted as reference data and be distributed

with the EI\[DF neutron data.

Current projects include standard

flux-to-dose rate conversion factors and

reference coupled neutron-gamma-ray

multigroup cross sections for the

elements normally found in concrete.

ANS-6. 2; Benchmark Problems

The primary objective of the benchmark problems effort is to compile in

convenient form a limited number of welldocumented problems in radiation

transport which will be useful in testing

computational methods used in shielding.

The compilation and publication of

solutions to benchmark problems are expected to accomplish several things:

1) attention will be focused on typical

problems where careful work should

produce solutions which are representative

of the state-of-the-art in solving radiation transport problems, 2) specifications

of standard configurations and data will

make comparisons of different computational methods and theory- experiment

comparisons more meaningful, 3) discrepancies between calculation and experiment may suggest refinements in the

numerical approximations or nuclear data,

or may suggest new experiments to resolve

the disagreement, 4) reliable solutions by

several methods will be made available

to help judge the precision and efficiency of different computer codes, and to

suggest if new codes ought to be developed, 5) newly acquired codes and codes

75
converted to new machines may be verified

by duplication of the benchmark problem

solution, and 6) mistakes in existing or new codes, or their options, can probably

be detected by independent calculations

of the benchmark problems.

Four problem solutions were published in 1969 in loose-leaf form in Ref

[2j by the Radiation Shielding Information Center. Revisions and a new problem were issued as a revision in

1970. Two new problems were recently

issued as Suppl. 2 of Ref. [2j and are available from RSIC upon request . They are Neutron and Secondary Gamma Ray

Fluence Transmitted Through a Slab of

Borated Polyethylene by C . E » Burgart and

A Benchmark Experiment and Calculation

for Neutron Transport in Thick Sodium by

R.B. Maerker et al. The work slowed for

a period but now additional problems are being developed including several for

typical reactor configurations.

ANS-6.3i Shield Performance Evaluation

The initial goal of this group was attained in 1972 with the publication of

Ref. [3]- Shortly after publication, the

U.S. Atomic Energy Commission issued a Regulatory Guide^ based on this _ standard for research and training reactors. The current goal of the committee

is to completely revise Ref. [3] to make

it more applicable to current practices

in the nuclear power industry.

ANS-6.4; Shield Materials

Initial efforts involving materials

per se , e.g., lead as a shielding material, have failed. The current work has

produced the draft of a standard, ANSI

N403s on the Analysis and Design of

Concrete Radiation Shielding for Nuclear

Plant

. The draft underwent balloting by

ANS-6 in September of 1974 ^ The standard

is much more general, in many respects,

than required for designing concrete

shields only. That is, the approach to

radiation analysis and the methods recom-

- mended can be applied to many shielding

analysis problems.

ANS-6 .5; Shielding Nomenclature

The effort of this group is directed

to the preparation of a list of shielding

terms and definitions and maintaining

liaison with the Nuclear Terminology and

Units Subcommittee (ANS-9). The latter

subcommittee is assisting the Nuclear

Terminologjr , Units, Symbols, Identification,, and Signals Committee of the

American National Standards Institute in

the preparation of definitions for the

ANSI Glossary of Terms in Nuclear Science

and Technology. It is planned to have

the special shielding terms and definitions prepared by the ANS-6. 5 working

group published separately since the list

is sufficiently long and specialized to

not be included in the glossary covering

all of nuclear science. A draft glossary

is presently being reviewed.

ANS-6. 6; Calculation and Measurement of

Direct and Scattered Radiation from

Nuclear Power Plants

Organized in late 1973. the group has

adopted the following scope:

"This standard will define calculational requirements and measurement techniques for estimates of exposures near nuclear power plants due to direct and

scattered radiation from contained sources on site. On site locations outside

plant buildings and locations in the offsite iinrestricted area will be considered.

All sources that contribute significantly

to exposure levels will be identified and

methods for calculating the source strength of each will be given. This standard

specifically excludes radiation from

gaseous and liquid effluents. The standard will review the considerations

necessary to compute exposures, including

component self- shielding, shielding

afforded by walls and structures, and

scattered radiation. Finally, the

requirements for measurements and data

interpretation of measurements will be

given. This standard will include

normai operation and shutdown conditions

but will not address accidental or normal

operational transient conditions. Nitrogen-16 gamma rays are a prime consideration.

ANS-6„7; Radiation Zoning for Design of

Nuclear Power Plants

This group was organized in early

1974 to standardize radiation level

zoning in power plants. The tentative

goals were 1) definitions of radiation

zone designations, 2) maximum and/ or average dose rates in each zone, 3) methods

for determination of access time to each

zone, 4) precautions, posting, survey

requirements, access control, and alarms,

and 5) responsibility of issuing entry

permits for admission to areas of limited

access. Related Standards Work

Most nuclear standards are listed in

Ref. [5,6]. Two other organizations

writing standards of direct interest to

shielding specialists are:

76
1. American Society for Testing and Materials

ASTM, publisher of the world-renowned

Book of ASTM Standards, is* the world's

largest source of voluntary consensus standards for materials, products, systems and services. Since 1898, the Society

- mainly through the intensive activities

of standards committees - has conducted

vast numbers of investigations and re- searches leading to a better knowledge of

the properties of materials and the development of more than widely used

standards - specifications and methods of

testing for materials.

Beginning with the 1974 edition of

the Annual Book of ASTM Standards , the

Society plans to provide a separate part

of volume on ASTH's nuclear related

standards. Part 45 of^ the 1974 Annual

Book of ASTM Standards' contains all

ASTM standards dealing »/ith nuclear ma- terials and materials related to nuclear

reactors. There are 104 standards in the

book of which 159 are new, revised or changed in status since 1973. Sixty-six

have also been approved by AI^SI and a number of others by other organizations.

The standards in Part 45 cover: concrete

products for nuclear applications,- graphite products for nuclear applications^

metal products for nuclear applications

(hafnium, nickel and nickel alloys, steel,

tantaliim, titanium and titanium alloys,

zirconium and zirconium alloys) ; nuclear

grade materials; radiation effects in

organic materials,- radioactivity-, inorganic materials in water; analysis,

dosimetry and radiation effects in metals;

and temperature measurement.

The ASTM Headquarters staff of 150

is located at 1916 Race Street, Philadelphia, Pa. 19103; William T. Cavanaugh,

Managing Director.

2. U.S. Atomic Energy Commission

Under the Atomic Energy Act, the

Commission has the responsibility for

establishing licensing procedures and

regulatory fimctions for the control of

materials and facilities essentiaO. to the

atomic energy industry. These functions

are carried out by a Director of Regulations who reports directly to the Commission. The Director is responsible for

the Directorate of Regulatory Operations.

The tvro basic reasons for the regulatory

duties of the AEC are to protect the

public health and safety, and to promote

the common defense and security. Regulations of the AEG are included as parts of

Title 10 of the Code of Federal Regulations, and are published in the Federal

Register. Regulatory Gruides are issued

to describe and make available to the

public methods acceptable to the AEC

Regulatory staff of implementing specific

parts of the Commissions 's regulations,

to delineate techniques used by the staff

in evaluating specific problems or postulated accidents, or to provide guidance to applicants. Regulatory G-uides are not substitutes for regulations and

compliance with them is not required.

Methods and solutions different from those

set out in the guides will be acceptable

if they provide a basis for the findings

reqialsite to the issuance or continuance

of a permit of license by the Commission.

Published guides will be revised

periodically, as appropriate, to accommodate comments and to reflect new information or experience.

Copies of published guides may be

obtained by request indicating the

divisions desired to the U.S. Atomic

Energy Commission, Washington, D.C. 20545

Attention: Director of Regulatory

Standards. Comments and suggestions for

improvements in these guides are encoura- ged and should be sent to the Secretary

of the Commission, U.S. Atomic Energy

Commission, Washington, D.C. 20545?

Attention: Chief, Public Proceedings Staff.

The guides are issued in the following ten broad divisions:

1. Power Reactors

2. Research and Test Reactors

3. Fuels and Materials Facilities

4. Environmental and Siting

5. Ifeterials and Plant Protection

6. Products

7. Transportation

8. Occupational Health

9. Antitrust Review

10. General

The USAEC Division of Reactor Research and Development (RRD) is responsible

for the safe development of reactor technology in the U.S. Toward that end, they

are concerned with the development of

standards covering design, analytical

methods, materials, equipment, systems,

fabrication, construction, quality assurance, inspection, testing, operation,

and maintenance for government-owned

civilian water reactors. Toward this end,

standards are being prepared, reviewed,

reproduced, distributed and revised in

order to incorporate latest developments,

information, techniques, and experience.

This work is being performed under con- tract to Oak Ridge National Laboratory

(OREL) with the assistance of other AEG

offices and contractors as a continuing

77
activity in this program. The standards

program will serve as a base on v/hich to

build current and future reactor programs

with greater quality assurance and the

attendant improvement in reactor reliability and safety. A thorough investigation

of records, experience, knowledge, expertise, and evaluation from all available

qualified sources is required for the

successful attainment of the goals for

the standards program. Initial efforts

have been directed toward converting

available standards into a form that may

be used for engineering current (RRD)

experimental activities and demonstration

reactors and provide usable technical

guides for the AEC Directorate of

Engineering Standards, Directorate of

Licensing, and the Advisory Committee of

Reactor Safeguards. ORNL is responsible

for overall management of the RDT

Standards Program under direction from

RRD. Standards are being prepared by

ongoing development projects and by ORNL

in its specific areas of expertise for

which each writer is qualified. Such

standards, designated as RDT standards, are also listed in Ref. [5].

References

1. Claiborne, H.C., Dudziak, D.J. and

Schaeffer, N.M. , Activities of the

ANS-6 Subcommittee on Radiation Shielding Standards, ORWL-TM-3271 (1970)

Oak Ridge National Laboratory.

2. Profio, A.E., Editor, Shielding Benchmark Problems, ORNL-RSIC-25 (ANSSD-9) (1969$ Suppl. 1, 1970 J Suppl.

2, 1974), Oak Ridge National Laboratory.

3. Program for Testing Biological Shielding in Nuclear Power Plants, ANSI

N18-9-1972 (1972), American Nuclear

Society, 244 E. Ogden Avenue,

Hinsdale, ill., USA.

4. Shield Test Programs for Evaluation

of Installed Biological Shielding in

Research and Training Reactors,

Regulatory Guide 2.1 (1973), U.S.

Atomic Energy Commission, Washington

D.C., USA.

5- Catalog of Nuclear Industry Standards

(1974) , American National Standards

Institute, Inc., 1430 Broadway, New

York, N.Y. 10018.

6. Standards in Nuclear Science and Technologv, a Bibliography, TID-3336

(1973) . Available from National Technical Information Service, Springfield,

Va., 22151.

7. Part 45, Nuclear Standards, 1974 Annual Book of ASTM Standards, Publication

Code No. 01-045074-35,

Discussion

Shank er Singh

The shielding requirements for the

two types of Past reactor concepts namely

Loop type and Pool type reactor being

different, are there any specific experiments being conducted or planned for

either of these concepts and if so which

concept is being pursued more vigorously?

D.K. Trubey

Experiments at Oak Ridge are in

support of the US LMPBR program which

employs the pool concept.

A.K. Gangxilly

1. Do you measure the scattered

spectriim in open air below 0.21 MeV as given in the table?

2. Do you still have a programme of

investigations on Multilayer shields?

D.K. Trubey

1. Not with sodium iodide detectors,

but measurements at lower energies are made with Ge (Li) detectors.

2. Many of the experiments are with

multilayer shields which mock-up particular

systems. Por example, iron-polyethylene

and iron-sodiim systems have been studied.

78
INTEGRAL EQUATION METHODS IN RADIATION TRANSPORT

D. Y. Gopinath

Health. Physics Division

Bhabha Atomic Research Centre

Bombay - 400085

This paper presents a review o opment of integral equation methods

radiation transport. The cases con sional (XTZ) geometry and (ii) One

transport for the transport of (a)

radiation. The methods are develop

sotropy, and their simplification in are discussed. Few typical results

of integral equation methods are di

f the Work done on the develfor different problems in

sidered are:(i) Three-dimendimensional time-dependent

Charged particles and (b) Opticaled for arbitrary degree of anithe case of isotropic scattering

are presented and the advantages

SGucsed.

( Int egral e quat i on transport

)

Introduction

radiation ; semi-numerical ; scattering;

In this paper we present a seminumerical technique for the solution of

radiation transport problems. The methods

developed here are applicable to energy

dependent radiation transport with arbitrary degree of anisotropy in scattering.

The purpose of the paper is to give a brief review of the work done in our group on integral equation methods for

such problems. This is also intended

to present a unified formulation for

most problems in radiation transport and

to show that any variation in the treatment for different types of problems are only marginal.

Mathematical Formulation

Basic equations :

^ The essential feature of the

approach that is followad here is to

separate the spatial and energy-angle

transmission in radiation transport.

Whence, the transport can be represented

as

<^{t,E, Ji,t ) = JjJ dt • dJT.' , dr'

S(r',B, Jl.',t')z T(E, JiTh-Ti: ,!^'-). 7, .

1;'-*t). .. (1)

srr,E,2l, t) =JJ d^,dJi. 9S(r,B',Ji',t)

G(r',E'-»E,-n.'-»-n. )+ s'(r,E,jl ,t)

(2)

where

SCr,E,X)L,t) = radiation source at

r?,E,JT. ,t) • -

• T(E,-n.—^^,= spatial transmission

—>•,-',' . \ kernel

r'->-r , t —j-t ). G(r",E'->-E, = energy-angle transmission

-^s kernel

S fr^, E,_Q,t)= external source.

In the above formulation, eqn. ( 1)

represents transmission of radiation

through space and eqn. (2) accounts for

what happens at a spatial point during

the collision. In obtaining the solution

for the above equations, we have two

options: (i) develop the solution for the

most general case and obtain the simplifications for particular problems, (ii)

obtain the solution for a simple system

and introduce modifications for more general cases. While the first appnoach is definitely more elegant and scholarly, the second

method has the advantage of being simpler

and easy to follow. We adopt the second

approach.

The simplest case is that of timeindependent radiation transport in one- dimensional slabs. This problem has

already been worked out in detail and

published elsewhere However for the

sake of completeness and to introduce the

broad principles of our approach, I start with this case. Further, in our formulation, we consider only gamma rays and

neutrons. Towards the end we deal with

the changes needed for other types of

radiation.

radidation flux at

(r,S,^ ,t)
One dimensional slabs :

In one dimensional slab geometry

eqns.(l) and (2) simplify to (cf.Fig.l)

Pig.l. Pictorial representation

of spatial transmission of

radiation in one dimensional

geometry.

.. (3)

S(x,E,n) = JJ^^Cx.s'.^i') G (x,e'-^E,

Jl'->-0: )dil',dE'+ s'(x,E,(i) .. (4)

and

T(E.,,x'->x)= (5)

G(x,E'-)'E,3a'->.Jl) = Z^(E^E)6{:a.7l',|(E,E'')j

(6)

where

^ (E,e' )= 1 - + for Y-rays

' E ^ ?l±if~E— - O.' for neutron

2 • E' E elastic scattering. M is the target

mass. For inelastic scattering of neu- trons

G ( X , e'->- E , A'-^il ) = 2 ( e'-^ E ) ^ ( X ) P

^ n

{SI. JX ) Throughout our formulation we use discrete ordinate representation in n'andx

for spatial integration and legendre

polynomial approximation in |i for the

evaluation of collision integral . Whence we obtain

9f)'^(x^,Eg,Hg)=Z S^(x^,Eg,^g)T(g,l, j-i)

9^V,.Eg)=Z/(,^^,^,^^)p^(^^),^^

^^^^^i'\^=^>^^^i'^g^^^^'«'-*s) +

s;(x.,Eg)

S^+l(x^,E^,H^) =^ S^(^i'Eg)P^(^ii)

(7)

where k is the iteration index.

Starting with S'(x^,E the set of

equations are solved fteratively till

they are self-consistent within a preset criterion.

Spherical Geometry

In this case, only the geometry

differs from the earlier one. As such,

equation describing the collision pro- cess remains unaltered.

Referring to fig. 2.,. the spatial

transmission equation for spherical sys

tems can be written as (for a given

energy)

,

Pig. 2. Pictorial representation

of spatial transmission

of radiation for spherical

system.

5ZS(r^,^^)= Jjs(r' ,nO T ( r'-^ r,

dti',dr'. .. (8)

80
and Tir-^T, \x-^\x^) = e~^^^^^

(- 1^)6 I

/.V l-r^/^2(l-4)}..(9)

where

jir)=T.^^ + V"r2-r2 ^ for T \i ..(10)

using exp.(9) in ezp.(8) and with the

discretization of space as in the slab case exp.(8) becomes, for

^(r.,u^)= 9S(r._^.u(r._^))e-^y(^j-l>

+ ( S (r,n(r))e-^y dy ..(11)

o Writing

S(r,n(r))l . . , = S(r,^i(r ))

A3

Ar J,J-1 ^"-"j-1^

the integral in exp.(ll) will be

i{s(r...3_) - S(r._^,.(r._^)e-^^(-J-r .-Zy(r, J

As C

o V y2-2yrj.^3_+ r^

(12)

The integral in exp.(l2) cannot be

integrated analytically. However one can note that the integrand contains

the generating function for Legendre

polynomials. Hence, expanding this,

the integral can be obtained as fast

converging series. Denoting this intefral as ^ and combining exp.(ll) and (12)

for n + ve)

<^(r.,^^) = !i^liill^ {^ir^_^,^(r._^))

S(r i.i..(r.,, ))?-2y(r,_,)^43(

^(r,-.,) =!l^.|^(r^,,,.(rj^,))

- ^^-'i.r^^^.i.i )j.-2y(^j..)

(14)

Having thus obtained expressions for

flux in terms of source, further procedure is the same as that of slab geometry. We go through the same iterative

scheme till the final solution is obtained . Next, before going to multi-dimensional geometry, we shall discuss one- dimensional time-dependent radiation

transport. Of these the slab case is of

little practical interest and only the

spherical case is presented here.

Time-dependent Radiation Transport in

Spherical Systems . As in the stationary case, even here

the equation accounting for the change

during collision does not alter. (This

is strictly tirae only if we neglect metastable states of target nuclei and delayed neutron emission. However this

assumption is not a serious restriction).

The spatial transmission equation will be

(cf .Fig.5):

.. (13)

Pig. 5. Pictorial representation

of ti«e-d«p©jQden©e of radiation transport in spherical

systems.

^(rj,|i^,tj^) = JJJdt,d^,dr. S(r,^,t) x

T(r->rj., .. (15)

On exactly same lines it csm be shown

that for ^ - ve

81
and

^[ti. Vl-rJ/r-^d-n^)! 6 I

t-tj^.iir)j • • (16)

where y(r) is, as before, given by

eqn.(lO).

Introducing eip.(l6) in (15),

because of the '6' functions in ezp.(l6),

we can either integrate over |i. and t and

obtain the final expression as an integral over r or integrate over r and \i to have the final expression as an integral over t. Integrating exp.(15) over

t and (1 y(r ^)

o

.. (17)

Alternately, integrating exp.(l5) over

r and \i

7

i^(Tyix^,t^)^. J's(r(t).|i(t).t)e-'^^(^k-*^-

d(tj^-t) +^^r(tj^-l),ti(tjj.-l),tj^_^j

e-ZT(Wl)

Making the transformation t' = t, -t,

the integral in exp.(18) becomes

At

js |r(tj^-t' ),n(t^-t' ),tj^-tj e-^^^'dt'

o

.. (20)

To evaluate exp.(20), as before we use linear interpolation between spatial,

directional and time modal values of source. Within the range of integration o to At, r(t) in exp.(20) may not

be within r. and r. ^ but may fall between different spatial nodes. Hence the

range of time integration is subdivided

at ^2.*^2 that (cf.exp.6).

vt^ _ 2vt, r . .1 ^ =

of- t .= i/r 11 + \f^2 2/ , 2x „ 1 v| 2 1 -r.(l-^ll) -

and the maximum of i given

by

(21)

I^ax= ^.i^ t VAt-^-r^(l-nf ) for ^

.. (22)

With this subdivision, S in exp.(20) in

the interval t^ and t^^^ can be written

as

(18) ^J-i'^^ - At

J-i

k,k-l

AS

Ar j-i+1

where

r(t)=V(tj^-t)'^-2v(tj^-t)r.^+rJ

v(t -t) - r Ai >i(t)= . <^ i -I' > r(t)

(19)

Expressions (17) and (18) are exactly

equiv8.1ent. However in evaluating exp.

(17) one has to remember fluxes at all

points for times earlier than t . In case of exp. (18), it is necessary to

know the fluxes and sources only at t, Purely from the causal considerations,"

this is also the necessary and sufficient information to compute the fluxes

and sources at t, . Hence we deal only

with exp. (18) in the sequel.

_(r(t^-t.) - r._,j

A^S

k,k-l

At. Ar

.t'ir(t -f)-r I j-i,j-i+i I

^ j-v

(23)

Taking only upto first order differential terms of exp. (23) in (20), completing the integration and using it in

exp. (18)

82
z

-S

+ -.1-1+1. g' .k ".1-i.uJc (e-^'y-"-e--^yi+l)]

1-1 ^

As

At

1

(24)

where

(25)

Having thus obtained the expression for

flux in terms of source, we go back to

the main iteration scheme. One difference

to be noted in this case would be that

the index k in eqn.(7) refers to time

and not the iteration number.

Next, we consider the multi-dimensional systems. In this, the two dimensional case (finite cylinder) will be

discussed in detail by my colleague in

another paper in this symposium. Hence,

I will skip that case and go directly

to three- dimensional systems.

Stationary Radiation Transport in three

dimensional systems . Here we discuss only 3-dime-nsional cartesian systems and as before

we assume discrete ordinate representation in X,Y,Z cordinates. The basic

equations in this case would be

^(R,E,2t)= Js(R;E,il ) T(it,R'->-R)dR

.. (26)

S(R,E,2t)= Jj</(R,E;-ri)(J(R,E'-)-E,Jl'-»il)

. dE'd/l'+S' (R,E,^) .. (27)

where R—>R(x,y,z)

Referring to Pig. 4, the flux at a given

space point will be computed in 26 directions corresponding to 26 adjacent modal

points. Thus flux at k,j,k due to sources

ht.J.k'l

t.J-t. A-» Fig. 4. Pictorial representation of

radiation transport in three

dimensional cartesian system.

^i-l,J,k-^"

along X axis is

j-Z.Ax

i.Ax

+ j

S(x',y.,Zj^)e-Z/'^j-^') dx'

(1-1) Ax

S. . ^ "i>j>k ^ As

Z 2

Ax

1,1-1

.. (28)

and this flux will be in the direction

-1 Ax \X = 0, = COS

V Ax^+ Ay^

Similarly flux due to sources along y

axis is

i,k

id) - •'^>.l--^'^ ) e ^l,j-l,k I

i k- , As

Ay

-2Ay

(l-e ^ ) .. (29)

and so on.

83
In general, we can represent the flux

equation as

An

= 1-1' k-k'/^ -2

i'fS. . ^ - S. .,^,e-2^^ -V i,j,k 1-1, J, k'-

As

1, 1-1

2^ I

i. j .k ~ i, j-j'

k'/s. . , - S. . - ,e~l^^

+ 2 t

^'"^ i,J,k-k'

I ( k,k-k'

(50)

where

^ " ^i'.Ax^+j'.Ay'^+k'.Az'^

(31)

and i,j',k' can have values 1,0 or -1.

It is evident that in this case the flux

will not have any azimuthal symmetry.

Hence, to evaluate the collision integral

we express the ans^lar dependence of the

flux in terms of Associated Legendre

polynomials. Writing

( x . , y . , z, , -fh , E ) 1 1 k g

, j,k,g)P^^)Cos mcp m m / n °-

(32a)

S(x. ,y . , z, ,-n, E ) 1 J k g

= L L S^(i, j,k,g)P^(ti)Cos mcp ..(32b)

n m

the main iteration scheme described in

eqn.(5) get modified, as :

T(n,9,i'-).i, j'-^j,k'^k ) (33a;

</>V,j,k.g) = 2 Z.'J^i.j.k.g^^^n-'V)

in' ) Cos m m ,x w^ ^ ..(33b)

m' m,n,mjn'

S^(i, j,k,g) = 2, <f>l (i, j,k,g)G(n,g'-^g)

..(33c)

^i,j,k,g(^'^^-Z Z s;(i,J.k,g)

. .(33d)

n m

P^ ( ^ ) Cos m<p

It may be noted that and S in eqn.(32)

with their 6 subscripts would need enor- mous computer memory even for modest

mesh number. However in actual computation the angular fluxes and sources need

to be remembered only at two space polnls

at a time and the information is actually

retained in and^.

Charged particles

As charged particle transport will

be discussed in detail in another paper

by my colleague in this symposium, I will only briefly outline the major

differences.

In the case of charged particles

we consider two types of interaction

with the media:

1) Coulomb

2) Catastrophic collisions

Though Coulomb interaction can also be

considered as collision, because very

84
small angle and energy change per such

collision and very large number of such

collisions per unit track length, it is

better to treat this phenomenon as to

continuous process. Thus, the charged

particle can change its direction and

lose energy continuously along its track

even without any collision. To take into

account such changes in energy and direction our first equation describing the

spatial transmission modifies to

^(R,E,2l ,) = JIJ S{R',E,jri! )

-n. R E'

T(E^E,-a'-*il,R'-^R)dR;dXL',dS' . .(34:

However if we are considering heavy par-*

tides the directional change is negligible and the eqn.(54) simplifies to

^(R,E,5i) = J I

s(r',e;Ji)

R E

T(2l ,R'-»R,E'-?-S)dR'dE' ..(35)

where

T(J1, E R'-^-R) = e"*^-^^"^'^

6| r-r; ^(E,S') ..(36)

The function -^(E.E') in exp.(36) is

obtained by the relation

R-R'

E

f dE /dz dE

Because of the 6 function in exp.(36),

eqn.(35) can again be expressed as an integral over space only. Beyond this

point, the treatment is essentially the same as in the case of non-charged radiation. As I mentioned earlier, the details will be discussed in another paper.

Optical Radiation

The three characteristics that

make optical radiation transport different from others are:

1) Energy decoupling in the

collision,

2) non-linearity of the system,

3) polarisation status of the

radiation.

In optical radiation we are mostly con- cerned with Rayleigh scattering which is

coherent. That is, energy (or wavelength)

of the radiation does not change during

scattering. Hence our second equation

which accounts for the collision process

reduces to

S(x,E,n)= J(^(x,B,n' )a(^^/3)d/L'+S' (x,E,n)

(38)

Of coarse, to be exact there is an indirect energy coupling in exp.(38)

through S' . S'(x,E,|i), which accounts

for the emission of radiation is a function of temperature at x, which in turn

depends on the absorption of radiation of

all energies. However for the case planetary radiation, with which we are interested S' does not contribute to the wavelengths of our interest.

Further, for Rayleigh scattering

aiSl-^Sl) = <J (^q) = + 02^2^^o^ ••(59)

using exp.(39) in exp.(38), in our formulation, the source eqn. further redaces

to

S^(x,E) = 0^ (x,E)

S^(x,E) = o

'AO)

For the intensities of our interest,

the system could be non-linear. That is

the radiation intensity may be sufficient

to change the characteristics of transport medium while this may pose a serious

problem in other methods, in the present

approach it is handled in a natural way.

In our main iteration scheme (cf.eqn.5)

each iteration corresponds to a collision

generation. Hence the only change necessary would be to have T and G matrices,

which are dependent on medium properties,

as a function iteration number. Of course, evaluation of the change in the media can

be very much involved but that is an

input for this problem.

Any analysis of optical radiation

transport is not complete unless we consider the polarisation status of the

radiation. Even in this case, equation

governing the spatial transmission does

not change. But equation governing the

collision process does alter. Following

Chandrasekhar*^, we specify the polarisation status of the radiation by the

vectors

85
S — S (S^,S^,u,, v^)

<p{ ^2.' ^r' ^2' ^2^

Then, to take into account the change

in polarisation during scattering,

instead of eqn.(40) we will have the

matrix eqn.

where the elements of the matrix |;P| are given by Chandrasekhar*

References

1. (ropinath, D.V. and Santhanam,K.

,

Wucl.Sci.Eng. 186 (1971).

2. Gropinath, D. V. and Santhanam, K.,

Nucl.SGi.Eng.,il, 197 (1971).

5. G-opinath, D.V., Santhanam, K. and

Burte, D.P., Nucl . Sci . Eng. ,^2, 494

(1973).

4. Chandrasekhar, S. , Radiative Transfer,

Dover (1948) P. 25-42.

86
NEUTRON TRANSPORT PROBLEMS IN SPHERICAL GEOMETRY

D. C. Sahni

Reactor Engineering Division

Bhabha Atomic Research Centre

Bombay - 400085

The density transform method has been extended to cover spherically symmetric neutron transport problems. The density transform is

expanded in plane geometry normal modes and explicit singular integral

equations are derived for the expansion coefficients. The method is

thus an extension of Case's method of singular eigen-functions to

spherical geometry problems. The Green's function approach for transport problems in spherical geometry has been considered. It is shown

that the reduction operators used in this method can solve only some

of the problems in the interior of a solid homogeneous sphere,

(Density transform ; expansion coefficient ; Green' s function ; neutron ; spherical ; symmetric ; transport)

Introduction

Analytical solutions of neutron

transport equation have been obtained

only for the narrow class of one dimensional plane geometry problems by using

singular eigen -function techni-que of

Case^. Straight forward extension of

Case method to spherical and cylindrical

geometries is not possible because in

these cases Boltzmana equation is not

translationally invariant.

In this paper we present a generalization of the density transform

method for solving one speed spherically

symmetric transport problems with isotropic scattering. The method consists

of defining suitable integral transforms

of the total flux (density) which satisfy the plane geometry transport equation

in transform variables. This gives an expression for the total flux (and hence

the angular flux) in teras of plane geometry singular eigen-functions, the

expansion coefficients being determined

as the solution of a singular integral

equation. Finally we examine the Green'

function approach for spherical geometry

problems as given by Case at al^. These

authors have introduced the expansion

coefficients which are related to ones arising in the density transform method.

However, the singular integral equations

derived by them are not correct because

of the use of reduction operator. This

can be seen most readily from their

expression of linear extrapolation distance in spherical Milne problem which

is independent of the radius of the

black sphere, contrary to the well known

result of Davison'. We indicate the

procedure for deriving the correct equations using the boundary values of a sectionally holomorphic function related

to their definition of expansion coefficients.

Density transform method

We consider one speed spherically

S3rmmetric Boltzmann equation with isotropic scattering and isotropic source density Q(r), in which angular flux

Njf(r,p.) depends only on the radial distance 'r', measured in units of meanfree-path, and 'n' the cosine of the

angle between the position vector r and

the direction of motion of the neutron.

= I f(r) + Q(^) (1)

2 2

'c' is the mean number of secondaries

per collision and the total flux

(density) P(r) is given by

1

f(r) = j \i'(r,n) dn .. (2)

-1

The transport equation (l) is to be solved for range a ^ r ^ b and -1 ^.ji ^ 1,

subject to the prescribed incoming distributions ^i'(a,n) } 04:^1^1 and y(b,n>, — 1^(1^0. It is seen that equation (1) can be integrated to the following form

>Kr,n) = ^{a, yi-r^(l-n2)/a2)exp(-fir +

^/a2-r2(l-^•2)) + 1

f^P(y)-HQ(y)]dy , JV y2^^ r^(l-fi2)

.exp(-nr +^yj^- T^{l-\^) .. (3a)

if /v/ 1-a^/r^ ^ 4 1

87
eip( -bn0\p (-|ir- y b' -r'^'-( l-ji'' ) )

b

(5b)

Thufi csin t>6 determined once the

density f(r) is determined. Integrating

equations (^a) and (^b) we find that

r(r) is the aoliitlon of the inte>?;ral

equatl on

_b r f(r) \^ \'y[c \Hy) ^ Q(y)]

b (1-^)

f(r) ^- I j

j*y[c r(y) f

[exp(-sly - r| )-exp ( -s\fy2-a2-s Vr^a^ )]dy

1

+ a^ j'^i^ V|;(a,|i') exp ( a^' - fr'-'-a"-(l-^'"' ) )d|ii(- o ^72

'r -a

rri

( —7^

)

1r 2 ^2,, 2^ ^ (5) 'J^^ -b (1-n )

We define the density transforms

<j)(r,n) > r e (a, b) , ^ e (-1,1)

by the equation for in >o

r

<^'(r,^) exp (r/ii) = ~j [y[c f(y)+Q(y ) ]

2 exp (y/|.i) dy + "2 \ |i' M'(a,|j') exp (a|a') ^ o

^o ( ? viiT"^!:^ ^

b

'

I

jK(^,y) y[c f(y) + Q(y)] dy

a

- fx (r' ) r' exp (- r'/n) dr'

^ 1

^

U(b,- ^i' )exp (-b ^' )Io .

Vl - a2/ b2

1,2 U/ ^i/(b,-^l') exp(-bn'-Vr'^-b^l-n'2) )dn/+ . b y 2 iT^

7 2 ) ^' d (i'

f l-a-/b^

(6a)

00

2 ^;.osh (sr) j'x(r')r'exp (-sr')dr'

1 b

.. (4)

where the function x(r) is related to the

incoming angular flux 4:'(b,-p)j |i > 0 at

the outer surface of the shell a ^r 4 b

by the equation

while for li <o

'|>(r,n) exp (r/n) = - i_ ry[c p(y)

2li J

Q (y)] exp dy

) r^ exp (r' /|i) dr^

.. (6b)

88
where

X

fl^^ and are the noraaliaatlon

constants while the unknown coefficients

a^^ and have to be determined by

applying the following boundary conditions } n> 0

i) 4' (a,n)eip(a/ji) y)y

an Ii (a/i/^2 . 1/^2 1 exp (-1^7^/^/)

(7)

Then it is seen from equation (4) that

r f(r) = dn .. (8)

Prom the equation (6a), (6b) and (8) it can be shown that 4)(r,^i) satisfies

plane geometry transport equation

(9)

Thus <t^{r,[i) and hence f(r) can be

obtained by carrying out an expansion

in terms of full range + Y ; -l^^y ^1

Case's singular eigen functions. This

gives the following representation for

f(r).

r f(r) = a^^ eip (-r/V^)+ a^_exp(r/VQ)

b

1

+ [A(/\))exp (-r/V)d'^ + |^ j i'Q(r')dr'

[cf(y)^Q(y)]dy - lj^(^)r'exp

o2 it (-r'/n)dr'+ -2

J ji'M/(a,n')exp(an')I(

(ay- 2 f, -p^W-

\i ' 1 - \i ' 1 - n'

2 r- \ W ^(b,-n')eip(-t'|l')I„

-1 ]i i-n ' i-fi

ii) 4>(b,-n)exp(-b/n) = i rx(r')r/exp

-1

[exp (-Ir-r^lZ-t)^) - exp( - |r+r'l/Vo) ] +

1 b

|r^(rOdH:exp(- |r-ri/V)- exp

0 ^ a

(-|r + r'|/V)] .. (10)

.(-r'/pi)dr'

.. (11)

This gives the following singular integral equations for determining the co- efficients a^^ and A('^). Por'fe(o,l).

1 Or" ^

1 D _

f cTdi' [t'G^(r')e^/^dy

... (12)

89
while for <^e (~l,o)

1

r

^

I.e. the e tion (14)

in the bou

holomorphi

the comple

from {-±00

tion, has

function

flux M^(b,

xpansion coefficients of equaare related to the difference

ndary values of the sectionally

c functions T (k) and A (k) of

X variable k having branch ctlte ,-i) U (i^i'-o ).A(k) in additwo simple poles at + i/'^o- l^tie IS (k) depends upon the angular

li) on the surface r = b

2(-i>o+i))

a

T^(k) = - b^ In' vp(b,n')dn'

(1)

^ |;i^(2n+l)P^(fi') 1^ (kb) ffn^^^!!

(13)

These equations can also be derived

from the Green' s function approach of

Case et al. They have shown that for

interior problem (when a = 0) the angular flux \p(r,n) in the sphere of radius

'b' is given by

n=o

(1)

-1

(19)

f (kb) being the Hankel functions of

n

of first kind. By proving that the function <j?^(k)

H^(r,^)=VK,(r,,i) + ^^<^ii/^,r,n) h- <p (j,) = ^ [ [iVill^/^W'

<1 'to ° ^ Jl +11'*' l+ik-^. X ]k^{i) 4'(i/'t,r,n)d'^/'^

Jl +il'*' -1

(14)

Y a ' 00

where 1-ikV A(k) .20)

4>(i/»?,r,n)= f[p X('^)6(Y-t)]e-T^*

_| 2('y-t)

A(^) ^ 1 - ^

(15)

(16)

-1

and

(i/'f) A'Ci/y)

vanishes everywhere and using Plamely

4 formulae for the boundary values of a sectionally holomorphic function we obtain the same equation as obtained by the

density transform method above. Similarly

we have also treated the other problem,

considered by Case et al, the exterior

problem (b-»>oo) with same concliasions.

References

1. Case, K.M., Ann. Phys. (N.Y. )2, l( I960).

2. Case, K.M. , Zelazny , R. and Kanal,M.,

, J. Math. Phys., 11 223(1970).

3. Davison, B., Proc.Phys. Soc.Lond. , 64,

981 (1951).

4. Muskhelishvilli, N. I . , Singular Integral Equations} Foordhoff, G^roningen,

Holland.

.. (17)

< ^

1 T3^(-i/'»o)

' 2Y^A'(»i/^^)

(18)

90
TRANSPORT OF NEUTRONS DURING REACTOR TRANSIENTS

Sushil K.Kapil

Reactor Engineering Division ^ Bhabha Atomic Research Centre

Bombay-400085.

INDIA

The study of time dependent behaviour of nuclear reactors

is important from operational and safety considerations. In this

paper, situations requiring an explicit time dependent solution

of the transport equation are identified. The range of validity

of the approximation methods in different situations is discussed.

Finally, severe transients in a Fast-Thermal coupled reactor are computed with various commonly used approximations and also by an explicit time-dependent solution of the Boltzmann equation, using

a set of computer codes which were specially developed for the

purpose. It is shown that the commonly used approximate methods

can lead to erroneous results. The reasons for the deviation of

the solutions for the different approximations from the correct

behavipur of the reactor under transient are discussed.

(Approximations } fast-thermal couple reactor > neutron jreactor

transients } solution } time-dependent j transport ; transport

equation)

Introduction

The behaviour of neutrons in a reactor is described in detail by the

linearised Boltzmann equation. Analytical solution of this equation for situations of practical interest is not possible at present and various approximations

have to be used. Time dependent Diffusion

Equation is one of the most commonly used

approximations. It is quite satisfactory

for most situations encountered in the

dynamic studies with spatial effects. But

a consequence of this approximation is

that the effect of a disturbance anywhere in the reactor is instantaneously

felt at all points i.e. the transport

time for neutrons is zero (though the

diffusion time is not). Diffusion approximation is therefore satisfactory for

power excursions where neutron transport

delays do not play a significant role.

Approximate Methods

Some of the other commonly used

approximations are given below:

Point Kinetics

In the 'point' approximation^ the

parameters for use in the equation determining power variation are obtained on

the basis of initial flux and adjoint

distributions. D^iring an excursion in a large or coupled reactor appreciable

change in flux and adjoint distributions

can take place. The integral quantities

defined in terms of initial distributions would be inaccurate. In such a system point kinetics equation cannot

be expected to be accurate.

Adiabatic Approximation

In this approximation-'-'^ the

flux is factorised into shape and time

functions, the shape function is taken

to be step wise constant in time. Although

this is more accurate than the point

kinetics approach the use of a static

calculation for shape function involves

the assumption that the flux changes

adjust instantaneously everywhere to all

perturbations made in the system. This

could be valid only if the time derivative of shape function is small and the

flux distribution reaches its asymptotic

value within a span short compared to

that for any significant change in power

level. Furthermore, this approximation

does not distinguish between the shapes

of prompt and delayed neutron sources

and thus neglects the time lag in the

adjustment of the delayed neutron pre- cursor distribution. If the power excursion produces any variations in spatial

flux distribution, the adiabatic approximation cannot account for it. Spatial

dependence of this type has been studied

elsewhere and is not considered here.

Quasi-static Method

This method^ lies between the

time dependent diffusion equation and

the adiabatic approximation since it

includes a term for t ime derivative by

91
first order backward difference. This

method also avoids the error due to the

neglect of the lag in delayed neutron

precursor distribution which is found

directly from flux history.

Exact Method

It is 'exact' to the extent that

the Boltzmann equation is solved without

any of the above assumptions and it can

be used as a touch-stone for validity

of these assumptions. A DSn solution

of the time-dependent Boltzmann equation

is taken as 'exact' here.

Computer Codes

A system of computer codes was

developed^- which permits solution of

the time-dependent neutron transport

equation in various approximations discussed above as well as by the 'exact'

method. The delayed neutron effect and

feedbacks have not been utilised in the

present study because it is intended to

study only the space dependent effects

arising mainly due to the neutron transport . System Model

The system chosen for this study

is similar to thB one described by

Avery and ToppeP for a coupled fastthermal steam superheating reactor. It consists of a central steam cooled fast core and surrounded by a water cooled

and moderated thermal region. To prevent

thermal peaking at the boundary of the

fast core the two are separated by a buffer region. The thermal region is

then surrounded by a thermal blanket and

a high density uranium blanket. The

region dimensions and core compositions

are shown in Table I.

The calculations are performed in spherical geometry with an appropriately derived

four energy group structure.

Calculation of Reactor Transients

The transient is induced in the fast core by a linear increase in the number

of neutrons emitted per fission and totalling 5*/. over a period of 0.1 msec, after

which it stabilises at the final value.

Total reactivity change caused by this

is 4.66;;: . Rather than applying various appro- ximations in the conventional manner, the

effects of these approximations are simulated directly as discussed below:

A. Basic assumption of ' point ' kinetics

is that all the subsequent behaviour of

the system can be described in terms of

the initial flux and adjoint distribution.

In Fig.l, Curve A shows the inverse of the

aS . "0Vo

o

'

FRACTION OF THE MMP. X

Table 1

Fig.l. Plot of inverse of the

period of power rise

against the fraction of the

ramp obtained from various approxima- tion methods.

Region No. 1 2 3 4 b Region Fast Core Buffer Thermal Core Thermal Blanket Uranium

Blanket

Outer Radii ^S cm

40 cm

52 cm. 58 cm. 98 cm. Material

Pu02 .08556

•37369 .42016 .29456 .29611

.00075 .00084 .00214 .00059

Depleted U .3715

Pe .156 .157

Zr .4151 .4151 .4372

.014131 .01553 .2087 . 2087 .1350

92
period of the power rise against the

fraction of total addition due to the

raup, for this situation.

B. ?or adiabatic approximation sequential shape calculations are made in

w-mode (solution of Boltzmann equation

with inverse period as an eigen-value )

The res'ults are shown by Curve B. The

circles on the curve are the check points

calculated by a statics code. The ramp

insertion in fast region reduces its

dependence on thermal region for criticaiity and the effective prompt ^neutron

lifetime for the system reduces . Therefore, the inverse period curve deviates from Curve A as more and more reactivity is added to the fast part.

Curve A does not take account of this

fact and is significantly wrong as the

excursion proceeds.

C. The curve marked C shows the 'exact'

space-time soluvion for the transient.

The curve shows the upward curvature as

in Curve B but the inverse period is

significantly higher.

Diiring the ramp the inverse period

is higher for Curve C than for Curve B due to the 'bottling' of low energy

neutrons in the thermal core. They are produced in the thermal core by moderation of fast neutrons created in

fission and by those coming from the

fast core. Fast neutrons from the fast core can travel to the thermal region

in time short compared to that for significant rise in power. On the other

hand, the low speed neutrons cannot

travel far out from their place of birth

in the corresponding time. Thus finally

a dynamic equilibrium is reached with

the neutron density higher in the thermal

region compared to what it would have

been under the adiabatic assumption

(Curve B). A plot of the difference in

the fission density distribution between

the adiabatic approximation (Case B) and

the space-time (Case C) calculations

also shows that thermal neutrons which

are dynamically trapped in the thermal

region during the transient, are permitted to spread (majority of which are lost by capt^are in surrounding region)

in the adiabatic approximation. The same fact is shown by a softer spectrum in the

riermal region for Case G during the

3.nip than for Case B. In the 'exact'

. ilculation this trapping leads to highfission density in the thermal part

and a higher contribution to reactivity

due to it. On the other hand, feed back

of the thermal neutrons to the fast core

is reduced leading to some loss in overall reactivity. Since in this system

the fast core contributes most of the

reactivity and drives the thermal core,

:nis loss is small and there is a net

over-all gain. In a system where the

return of thermal neutrons to the fast core is very important for maintaining

the chain reaction, the effect CQuld be

opposite. When reactivity becomes constant and flux transients have died, it is

known that the asyroptotic inverse period

would be the w-mode solution of the

Boltzmann equation. Therefore, at the end

of the ramp, the inverse period quickly

drops to that for the adiabatic case. Physically, it corresponds to a redistribution of neutrons.

D. Finally, if the reactivity is added

to the system infinitely slowly so that

at any time the flux distribution in

space is in quasi-static equilibrium for

the reactivity at that instant the adiabatic approximation and the 'exact'

method should coincide. To check this,

the same reactivity is added at half the

ramp rate in the 'exact' calculation. The

result of the calculation is Curve D in

Pigiure 1. It is seen that for a lower

ramp rate the inverse periods are closer

to the adiabatic case curve. A plot of

fission density distribution for this

case confirms that the differences observed between Curves B and C are due to

the reasons mentioned.

Conclusions

The spatial effects in reactor power

transients may arise due to changes in

region and spectral coupling, delayed

neutron precursors' lag, loose coupling

in parts of a large reactor and neutron

transport effects. For the particular

case of neutrons transport/diffusion

effect it is found that an accurate spacetime calculation may be required under

certain conditions. Depending on the

importance of various effects care must

be exercised in the use of different

approximations.

References

1. Henry : Nucl. Sc. Sngg. , 1, 52 , 1958

2. Henry and Curlee: Mucl.Sc.Sngg.,22,

171, 1965-

3. Ott : I'Tucl, Sc. 3ngg. , 26, 563, 1966.

4. Kapil : SPURT series of Codes, Report

to be published.

5. Toppel and Avery: IAEA Seminar on Physics of Fast and Intermediate

reactors, Vienna, 1962.

6. Avery : Second Geneva Conf .

, P/1858,

1958.

93
CRITICALITY CALCULATIONS BY SOURCE-COLLISION

ITERATION TECHNIQUE FOR CYLINDRICAL SYSTEMS

V . K . Sundaram and D.V.Gopinath

Health Physics Division , Bhabha Atomic Research Centre

Bombay-400085

This paper presents a fast-converging iterative technique

using first collision probabilities developed for obtaining

criticality parameters in two-region cylindrical systems with

multigroup structure in energy of the neutrons. The space

transmission matrix is obtained part analytically and part

numerically through evaluation of a single- fold integral. Critical

dimensions for condensed systems of uranium and plutonium computed

using this method are presented and compared with published values.

(Criticality; collision; cylindrical; energy; integral;

iterative; neutron; transmission matrix.)

Introduction

An analytic treatment of integral

equations for neutron transport in

infinite, homogeneous, isotropic media

on the one-velocity model is possible.

Beardwood et al-'- have used first collision

probabilities along with successive over- relazation for the solution of group

fluxes in their computer code for

calculations in finite systems with

multigroup structure for neutron energy.

Gaussian quadrature has been employed in

the Swedish code Flurig to obtain the same probabilities.

A fast-converging iterative technique for criticalit;V calculations in tworegion spherical systems with multigroup

structure has been reported by Gopinath

et al-^. This paper presents an extension

of this technique to finite two region

cylindrical systems. The collision

probabilities are obtained numerically

through evaluation of a single-fold

int egral

Mathematical Formulation

Finite Difference Equations

In an isotropic medium, the collision density C(E,r) per unit energy E and at space point r is given by

C(E,r) = \s(E,r ' )K(E,r'-^ r) d r'

Where K(E,r'->-r) is the first collision

density kernel for neutrons of energy E and represents the collision rate at r due to unit neutron source at r'.

S(E,r') is the source density per imit

energy interval for neutrons of energy E

and at space point r.' Given C(E,r) for

all energies, S(E,r) is obtained as

S(E,r) = jc(E' ,r)G(r,E'-^ E) dE

(2)

V/here G(r, E'-^E) is the mean number

of secondary neutrons generated per unit

energy interval at E and space point r due to the collision of a neutron with

energy E'. S(E,r) and C(E,r) are uniquely determined by K(E, r'->r) and

G(r, E'-^E). Knowing K and G and

starting with an arbitrary distribution

of S(E,r), the true values of S and C can be obtained iteratively.

For a cylindrical system, dividing

the cylinder into a finite number of

coaxial annular discs and the neutron

energy range into finite energy groups,

Eqs. (1) and (2) are transformed to

^g„n,l =ZZ^g,nM' ^g,n •-^n,l'-^l

....(3)

^g,n,l T^g',n,l '^n,l,g'—>g 9' ....(4)

Where Cr. ^ and S„ , are the total g,n,x g,n,l

first collision rate and total birth

rate respectively for neutrons of gth

energy group in the (n,l)'''^ coaxial

annular disc (n referring to the number

of the cylindrical shell in the radial

direction and 1 the number of the axial

segment), and Kg^j^!__^^ 1 • —> 1

total first collision rate of neutrons

th in the (n,l) coaxial annular disc due

to a unit source of neutrons of g*^
I energy

J n,l g'

I born in

I collisi

group in the (n',1')^^ disc.

^ is the number of neutrons

th the g energy group due to the

on of a neutron of group g ' in the

disc. It is given by^

n,l,g'->g

n.l.g' n.l.s' n.l,g n.l.

tn,lM

In the above, Z-^ i and Z-^ are the axial

distances of the source and receptor

discs from the base of the cylinder.

Lumping the total source in each disc over a cylindrical surface of radius

equal to the mid radius of the disc

(r^i) and of height equal to the midheight of the disc

Z. ,n'->n,l

tn,l,f

(5) ^g(^n"\"^n-l'2l^J

Calculation of E

,n'-»n,l •- (6)

If the uncollided flux integrated

over a (receptor) disc of radius r^^ and

thickness (Z-]_-Z-]_ t) due to a unit source

of neutrons of gtn energy group distributed

uniformly over a cylindrical (source)

surface of radius r^, and situated at an average height, {Z-y-Z-y _^-2Z-^\) / 2, from

the disc is denotealy^^ii i , Z-j^ , , r^^, Z-, ) , •the uncollided neutron*flux integrated

over a coaxial annular disc with inner

and outer radii rj^_]^ and r^^ respectively

is given by

^(^n-'^.'^n'^i) -<^(^n"2i.'^n-l'2l)

The total number of first collisions in

the annular disc is then

has different forms

depending on the position of r ,,Z-, ,,r and Z^« . n 1 n

Computational Procedure

On the basis of the formulation in

Section 2, a computer programme has been

written for BESM-6. The scheme of

computation is the same as given in-^

Using the code, calculations have been

done to obtain the critical dimensions

of condensed bare as well as reflected

cylindrical systems. The results are presented in Table - 1, which include

the published values^ for comparison.

X, t^a^^n-'^i.'^n'^l)

-

Table - 1

System Density

gm/cc

Radius

cms Critical

height

Critical mass

(core bulk

Published values o parameters

1 critical

cms mass)

kgs

Radius

cms

Height

cms

( core bulk mass)

kgs

93.4/.

enriched

uranium

17.7

19.05

19.05*

8.269

8.259*

166.9

166.7*

19.05 8.26 166.7

93.5/.

enriched

uranium

18.8

9.434

9.434*

11.52

11.533*

60.56

60.6*

9.434 11.509 60.5

46/. enriched

uranium

13.44

21.49

21.49*

13.742

13.720*

367.6

367.1*

21.49 13.89 371.5

Plutonium 14-27 7.588

7.588*

8.596

8.579*

22.19 f 22.14^

7.588 8.286 21.39

Values obtained by treating the system as two regions.

95
Ref erences

Beadwood, J.E., Clayton, A.J. and

Pull, I.e., ANL-7050 (1965).

Carlvik, I., Nukleonik, 8 Band, S. 226 (1966).

Gopinath, D.V., Sundaram, V.K.,

Krishnan, L.V. and Santhanam, K.,

Nukleonik, 9 Band, 5 Heft, S. 252-256

(1967).

Reactor Physics Constants, AITL-5800

(1963).
STOCHASTIC METHOD OF CALCULATIONS FOR FAST SYSTEMS

B.K. Godwal and M.P. Navalkar

Bhabha Atomic Research Centre, Trorabay, Bombay

INDIA

Neutron slowing down is a Markov process in which the probability

for being in a certain volume element in phase space (space-time-energy)

at some future time depends only on the present state of the system and

not on the past. The process has been approximated to a discrete time,

discrete state by Williamson et al to determine state transition

probabilities. In this paper, this approach has been extended to

calculate Rossi-a which is an important dynamic parameter of the system.

The values of Kg-ff as a function of B^ for the bare core of Zero Energy

Fast Critical Facility, PURNIMA calculated from this method showed good

agreement with the bare critical experimental parameters obtained from

fission rate distribution. A method to extend this method of calculations to reflected system has also been described.

( BESM-6 ; JBZEBEL; I'larkov process; neutron? PURNIMA; Rossi-a;

slowing down; stochastic.)

Introduction

Multi-group calculations for fast

systems are basically static in character.

Apart from the cross-sectional uncertainties as well as errors arising due to

averaging over broad energy groups, the

multigroup method does not describe

adequately the physics of the slowing

down in fast systems.

An approach based on Markov chain

process to calculate temporal and

integral properties of fast reactors has

been proposed by T.J. Williamson et al^.

In this approach, the neutron slovring

down process is treated approximately as

a discrete time, discrete state Markov

process from which state transition

probabilities based on collision physics

are determined. The matrix is then

applied to evolve the time dependence of

a pulse of neutrons on a discrete timeenergy mesh from which integral parameters of the system are obtained.

In the present paper we have extended the earlier work to calculate Rossia which is a dynamic and important

parameter for the fast systems. In

addition, we obtain the neutron density

as a function of time due to a pulse of

neutrons introduced in the system. The

calculations using 26 group cross-section

library have been performed on BESM-6 to

determine Rossi-a as a function of subcriticality for JEZEBEL system which show

good agreement with the experimental data.

Method Of Calculation

When a piilse of neutrons having

fission energy distribution is injected

in a finite multiplying assembly, the

following processes take place:

(a) Scattering, elastic and

inelastic, (b) Non fission capture, (c)

Fission, (d) Leakage, (e) n,2n etc.

The flux^t'CEjt) for the source neutrons can be obtained by operating

the transition probability matrix on the

initial pulse. The source of first

generation fission neutrons is given by

k(t) = Jv(E) e^(E) <^>jE,t)dB

where symbols have the usual meaning.

The term k(t) can then be used to calculate the relationship between the nth

generation fission source S^ and (n-l)th

generation source, S^_3_.

Ob S^(t) = fSj^_i(*) K(t-f)dt' ...(2)

o The Laplace Transform of K(t) is related

to the Laplace Transform of a function

(J(t) by

... (3)

This can be inverted by using con- volution theorem in Inverf'e Laplace

Transform to give the fur. tion G-(t) as

t G(t) = k(t) + J k(u)k(t-u)du

t

o u' +

I k(t-u')du' J k(u)k(u'-u)du

0 o

+ I k(t-u")du" I k(u-u')du'J k(u)du

(4)

Thus Gr(t) gives total nvimber of fission

neutrons of all generation at time t.

97
Hence the slope of the logarithm of G(t)

gives Rossi-a.

We have applied above method to

calculate Rossi-a as a function of subcriticality for JEZEBEL for which the

results are shown in Fig. 1. It is seen

that Rossi-a varies linearly with

reactivity and intercepts the reactivity

axis at prompt critical, thereby indicating the self consistency in calculation of sub-criticality a. The delayed

critical Rossi-a agrees fairly well with

the quoted experimental results .

-I

-8 -»!-

ROSSI. «< AS A FUNCTION OF SUBCWTtCALITY IN | FOR JEZEBEL

FIG. 1

OELAYEO CRITICAL^

-« -» -I -» 0 .1 .J RCACnviTV IN f Fig. 1. Rossi-a as a function of subcriticality in $ for JEZEBEL.

We have also done calculations of

Kgff for bare case of Zero Energy Fast

Critical Facility, PURNIMA. The details

of the critical facility have been described by Iyengar et al3. It consists

of six zones, the innermost being Pu02

core whereas the outer most zone is

mild steel. Other reflectors such as molybdenum, stainless steel, copper are employed between the first and the last

zone. Fig. 2 shows 1-Keff as a function

of fuel pins for bare core (Pu02 only)

and gives a bare critical loading of 405

fuel pins. Using the axial reflector

savings as measured by Ramakrishna et al7

a critical loading of 360 fuel pins is

obtained which is in agreement with the

reported value^ for core consisting of

Pu02 and molybdenum reflector.

The stochastic method has been applied to the bare fast system. In order

to apply it ( 0 the reflected system, a combined Stochastic-Monte Carlo approach

is proposed. In this, the leakage term

for the bare core which gets modified

due to reflector is calculated using

Monte Carlo method.

The leakage lor bare core is given

1-K,ff AS A FUNCTION QF fuel PINS FOR BARE CORE (PuOa) FOR PUffNIMA

tM

Fig. 2,

ISO SSO too NOMBER OP FUEt PINS ^

l-Kgff as a function of fuel pins

for bare core (PUO2) for PURNI14A.

LB(E) D(E)B^

^j(E)+D(E)B'2

... (5)

The leakage in presence of reflector is

given by

D(E)B ,2

^j(E)+D(E)B ,2 (6)

Using Monte Carlo method and the leakage

distribution given by stochastic for bare

system, PlrCE) is calculated. This P^jjC^

gives us equivalent D(E)B'2 which is used

in the bare stochastic model. The advantage of using Stochastic-Monte Carlo

approach is the saving in the computational time as well as increasing the

accuracy over the conventional Monte

Carlo method. This is due to the fact

that the neutron history is traced in th^

reflector only in the Stochastic-Monte

Carlo approach unlike the complete history traced in pure Monte Carlo method.

Ref erenc es

1. Williamson, T.J. and Alberecht, R.W.,

Stochastic Calculation of Fast

Reactor Generation Times , Fast

Reactor Physics Vol. I. p. 513 (IAEA,

Vienna, 1968).

2. Reactor Physics Constant s, jUIL. 5800,-;

Prepared by Argonne National Laboratory, Second Edition, July 1963.

Iyengar, P.K., Chandramoleshwar , K.

,

Kapil, S.K., Krishnamurthy, T.N.,

Nargmdkar, V.R., Pasupathy, C.S., Ra^

A.K., Seshadri, S.N., Srinivasan, M.,

Subba Rao, K. , Preliminary Safety

Analysis Report for Critical Facility

3.

4.

of Pulsed Fast Reactor , B.A.R.C./I134 - 1971.

Ramakrishna, D.V.S. and Navalkar, M.P

Power Calibration for Purnima lrac&€-

dings of the Symposium on Nuclear

98
Science and Engineering, Bombay ,^^ndia_,

(1973). / Ilargundkar, V.R., 3asu, T.K.,

Chandramolesiawar , K., Job, P.K.,

Subba Rao, K., Pasupathy, C.S.,

Srinivasan, H. and Faramsivan, C. - Internal Note No. 071 BARC - (1974).

99
A RMDOM SAMPLINCt TECHJTIuUE FOR. CHOOSING SCATTERING ANGLES

FROM ARBITRARY ANGULAR DISTRIBUTIONS IN DOSIMETRIC AND

SHIELDING COMPUTATIONS

P.S. Nagarajan, CP. Raghavendran , P. Sethulakshmi and

D.P. Bhatia

Division of Radiological Protection

Bhabha Atomic Research Centre

Trombay, Bombay-400085

A random sampling technique has been developed for sampling the

cosine of the scattering angle of the neutron in the centre of mass

system. This technique could be incorporated in existing shielding

and dosimetry codes. Recent differential scattering cross section

data (from BNL-400 (1970)) is expanded in double Legendre polynomials

of incident neutron-energy and a random number. The necessary coe- fficients for the elements C, N, 0, Si, Ca, Fe and Pb for incident

neutron energies upto 15 MeV have been obtained and the same are presented along with typical results, checking the method and

coefficients

(Angle; centre of mass; coefficients; computations, crosssection; Legendre polynomial,- neutron,- random sampling;

scattering; shielding)

Introduction

In shielding and dosimetric computations it is necessary to take the

anisotropy of neutron scattering from

nuclei such as C, N, 0, Si, Ca, Pe and

Pb. In the course of our Monte Carlo

work for the computation of leakage

spectra through shields and in dosimetry

we have developed certain data and

procedures to sample the scattering angle

of the neutron in the centre of mass

system, using available datal.2 . If

sampling is needed from a unique angular

distribution, i.e., just for one angular

distribution, f(|i), simple schemes can

be thought of, including the one due to

Coveyou3. However, the distributions

are functions of energy too.

Method

Garber et al-'- provide da/d-Q.as a function of cos for various incident

neutron energies. From this f(|i.,E) the

probability density function in |^ is

obtained at neutron energy E, as given

0

where \i = cos and -1 ^ "C Graphically, the f(|i,E) data was interpolated to obtain f(|i,E) at uniform

intervals in E, from 0.5 Me7 to 15 MeV.

The usual procedure of sampling of value

\i by solving

-1

for [i-j (where R-, is a random number and F

is the distribution of f) is almost

impossible because F is usually a high

order polynomial in To overcome this

we have done the inverse interpolation to

obtain

^ = ti(R,E)

Among the many choices for least square

interpolation in R and E, it was found

that the coefficients of a double normal

polynomial expansion in R and E do not

lend themselves convenient and required a large number of terms- Hence a double

legendre expansion in R and E was resorted to, giving, m m

= L Z a P (E'j P.(R)

i:o j:o ^-^

where P's are the legendre functionSi

E' = (E-7.5)/7.5

and; R, a random mxmber in the interval

(-1, +1).

Results

The coefficients a^^^'s were obtained

for seven elements of interest in shielding and dosimetry C,N,0, Si,Ca,Fe and Pb

using data from ref.l.and in the case of

lead data from Langley^ was also used.

100
To increase the speed of sampling, coefficients b-^j 's were derived from aj^j'S;thus

enabling sampling as

= Z 2 bij E'i P (R)

Table 1 gives the coefficients

b^j 's. Sample results for carbon are given in Figs. 1 and 2 to illustrate the

efficacy of the method. The histograms

are the sampled data and the dotted lines

are the original data used. Complete

check results of this nature for all the seven elements smd over the range of

energies from 0.5 MeV to 15 MeV are available elsewhere5.

I CARBON

E

10

b I

1-0 MeV

2BMeV

1.0 OS 0 -05 COSINETHETA^ CCM Sy6tei*>)

.1.0

Pig. 2. Comparison of BNIi-400 data and

sampled results.

/

to ! +10 OS 0 -05 -1.0 COSINE THETA (CM eystem)

Fig. 1. Comparison of BNX-AOO data and

sampled results.

101
0

12

3

I.56

7

8

0

12

3

5

6

78

0

12

3

56

7

I ^

0

12

I

5

6

7 s

0

12

34

56

7

0

12

3

5

6

7

Table-1

NORMAL LEGENDRE COEFFICIENTS b^j

1 CARBON

-4,877?816710'^-O01

2 .7774066049'^-nn?

1 .4"» 10307761^-001

3.87O7964726'^-n02

-7.91 ni689011'=,-n02

-1 ,009 104019^^2-001

2 . 387965'?64=S's-on?

4.34897=.n78?0-00l

?.^4'^66Q44l "^1-001 -4.(S219041';7n4-OOl

-4. 3^^18614966^-001

1.28214626067-001

4. 16848722339-001

1 .04642761837-001

-3 . 82 78328S91 0-001

-3 . 27^82'^1 1 1 '^-^-001

-3.6051R1816S8-0ni

-1. 0070083 76 09-001

4.74898584566-001

-1.78755311314-00 1 -4.61 694986644-00 1 -7.27190210047-002

1.C4085643497+0O0

6.82361848404-001

-6.7 700474802 7-001

7.06348637O03-00P

2 . 53021*^85634-001

1.118181lS2lO-n01

4.89405090197-001

-3.08714596571-001

-1 .33865834776 + 000

-1 .63''37627586 + 001

1 .36778067023 + 000

1. .27969383879 + 000

2.87873281502-001

6.9''408923090-on]

-1 .a^5863O8673-.0C I -o. 174625«7760-OC 3 2 .0^6261 Q8?'^^-"0l

3.nflOi7;,ftl(SST_nni

-3.^86107'^0524 + O00

-2. 007978958^0 + 0 00

1 .9204661 51 in+non

7.822851324^0-007

-4.7024507230^-003

-1.172012115^7-001

-3 .23386041 380-001

2.0'^inp04Ci04o-nnT

1 .724017777^7 + 000

-3.06070^24611-001

-1 .6uO37^774O8+ 000

-l.B'=i8 5 5'=.S5 4'^=. + 00 0

•1.26081671612-001

7.05245659191-001

1 .91732776638-001

4.22680224343-002

4.01 f,7'^4641 12-001

-',.9TQ754678'^4-001

3.85F7'=1'=.5299 + 000

2.73164727438+000

-2.08131 151038+000

-3.20610352200-

1 .34832057746-

1.15156202639-

1.17717243261-

-4,9q5O7'^40ftq?.

-7,56500?^2776-

^.33729467946-

6.70039653361-

8.86103324505-

007

00?

001

001 007

• 001 001

•001

•001

1 ,7''O08341 147-007

7,^^P74<!-7147-'-om

1 .27179603514-001

5 .471 83'=iO760R-n07

-3 . 1-*16144043'^-001

1 .^01 280-S4?14-om

-1 ,371 7e;;jn7Sl 7 + O00

1 ,7O8876O7770+T00

8.ooo^ST5p7TO-,-\01

1 NITROGEN

3.41 6578^0470-noi

-1 ,09760SA90?q+000

-3.00629479720-001

1 . 11 629680701-001

2.21 O10227498-O02

-1 .3^124500084-001

-6 .'SO24601 8187-002

4.O7843881 37'=.-O07

1 ,^R'^,q07c,O400-

1.10279115600-

6.^67^9831607-

-1.10612681 247- •1.748832865] 8- -2.59829197176-

-2.34l004^qio7.

1 .34369401 0^"^-

001 3.7'^7532O8490-002

001 -7.20311381148-001

007 -1 .472'^7096682 + 000

001 4.81575447013-001

00] 0.212409=^6462-001

00] 4.6233^324974-001

007 -3.468765976O3-001

001 -5.26102605959-001

1 . 86433332547 + 000

7 .50699716537 + 000

-2. 70521262012+000

-1 .29724016087+000

0.87740448172-001

1 .75597754812 + 000

-6.3O2585'^0513-001

-1.4 77279OO244+000

1.71 719805400+000

•9.09583675308-0O1

1,71 504456271+COi

2 .08584552778 + 000

-4.5i=;8255<i9139+O00

-1 .27674813112+000

1 .67488^9'^n 3 + O00

1 .O43880'^0700 + ooo

-3.51622420442+000

-9. 27000057435 + 000

4. 14530'^761 S6 + 000

3.282069^0018+000

-3 . =^3 1 5488644=^-00]

-3 .08 01673701 0 + 00 0

1 .69 1541 604 = 0 + 000

3. 17a3394''^q8 + 000

3.9988761 1047+000

8. 7328779=^350 + 000

-3.07181128753+001

1 . 39343388752 + 0O0

6.70«7888871'^ + 0O0

7.1] '^36?640'=i4 + 000

-7.33479546056+000

-4. 50697506090+000

1 . 70117466471+00O

1 . 17006035143 + 001 -6.21566179594-001

-2 .14870996706+000

-2 .08038322072 + 000

I .'^«^136721 58 + 00O

-1 .41777348517 + 000

-7.82''642938'^0 + ooo

10 2 . 109 17S02586 + 000

1 .3«^662431861 +001

3 ,06970847500+001

0,00000000000+000

3»1'^322071 371+O00

-1,21037305817+ 100

1 ,05087059879+ )00

4,91 016553820+000

o.ooooooonooo+ooo

-4. 78957183066+000

-1 .016167=14777 + 000

0. 00000000000 + 0 00

1 .538528406^7 + 000

0, 00000000 000 + 0 0 0 3.51 166275844-001

9. 30600236660-001

0. onooOQOOOOO + OOO

6. 1405=^977899 + 000

-1 .08636268192 + 001

0,00000000000+000

O.OOQCOQOOOOO+OOO

0.00000000000+000

O.OOOOOOOOOOO+OOO

-1 .88826998151 + 000

102
J \

0

1 Oxygen 2 3

0 ,^«;370477367 -001 1.85071'=.86259-00l 2. 00751 228070 -002 1 .88937996427-001

1 -1 .06?471«;4837+n00 9 .79104^16547-OOp 3.67167830906-002 1 .1650^260199-001

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104
References Discussion

1. Garber, D.I., Stromberg, L.G.,

Goldberg, M.D. , Cullen, D.E. and May,

V.M. , "Angular distributions in

neutron- induced reactions". BNL-400,

3rd Edn. Vol. I (Jan 1970) and Vol.11

June (1970).

2. Langner, I., Schmidt, J.J. and Woll,

D., "Tables of evaluated neutron cross

sections for fast reactor materials"-

KFE:-750 (Jan 1968) . 3. As reported by D.C. Irving, R.M.

Freestone and F.B.Z.Kam, "The Coveyou

technique for selecting neutron

scattering angles from anisotropic

distributions" in Appendix 1 of 05

R - A general purpose Monte Carlo

neutron transport code ORNL-3622

(1965).

4. Langley, H.J., "Neutron cross sections"

- LA-2016 (1956)

5. Kagarajan, P.S., Sethulakshmi, P.,

Raghvendran, CP. and Bhatia, D.P. , "A random sampling procedure for

anisotropic distributions"BARC report

(to be published).

Godwal, B.K . Can the Coveyou technique be used for

taking into account the anisotropic

scattering in hydrogen due to neutrons ? How is it at Legendre Polynomial

preferred ? Nagarajan, P.S . In the energy range of interest to

us i.e. upto 15 MeV, assumption of

isotropic acattering in the cm. system

is valid. Hence the cosine of ©Loa> [cos Qy^i} J ^® directly sampled as the

larger of a pair of random numbers. At

thermal energies I have not developed any

sampling scheme. Perhaps one could assume

an isotropic law.

Makra , S . Are the differential cross sections

data available for all the mate Trials and

energies and if so from which library ?

Nagara.lan. P.S .

The reports BNL-400 (1970) and KPK750 (1968) yield the required data for all

the elements C ,N,0,Ca, Si,Fe and Pb. But in

the case of Pb there is an energy gap

where no data is available. We took the

data from an old reference of 1956.

105
MOfTTS CARLO CALCULATIOrTS OW DOSS DISTRIBUTIONS

FROM PLANE INFINITE OBLIQUE ELECTRON SOURCES

C.R. Gopalakrishnan and V. Sundararaman

Division of Radiological Protection

Bhabha Atomic Research Centre

Trombay,Bombay-400 085, India

A modified Monte Carlo method has been developed for

tracking electrons. In this method individual collisions wherein

the electron suffers a large deflection or loses large fraction

of its energy (denoted as catastrophic) are treated separately.

The history of the particle is divided into sections, within

which no catastrophic collisions occur and in which continuousslowing down is assumed. The angular distribution at the end of

a section follows a Gaussian distribution. In this method the

correlation between energy-loss fluctuations and multiple scattering deflections is preserved more faithfully. Dose distributions

for electrons in carbon, aluminium and copper have been calculated for oblique incidence using this method. Data have been

obtained for five different initial angles and covering a range

of energies from 0.05 to 10 MeV electrons.

( Aluminium ; carbon ; copper ; collision ; dose ; distribution ; electron ; Gaussian ; Monte Carlo ; scattering )

I ntroductioh

In this paper, we have reported

some of the results on electron dose distributions obtained by Monte Carlo Methods. First, dose distribution functions

have been computed for infinite plane

oblique sources of different energies

from 0.05 MeV to 10 MeV. These have been

obtained in Carbon, Aluminium' and Copper

for cosines of the angles varying from

0.2 to 1.0. Spencerl has calculated dose

distribution functions for plane perpendicular and point isotropic sources using

the moments method with the continuous

slowing down approximation. Berger^ has

calculated these distribution functions

using the Monte Carlo method. However, no results are available for plane oblique

sources. These are of some importance in

calculating doses in non-electronic equilibrium conditions on X or gamma ray

irradiation. Secondly, we have calculated

depth dose curves for high energy electrons. These are required in treatment

planning for high energy electron beams

from accelerators. Also the perturbation

in the depth dose curves due to the presence of cavity has been computed.

Method

Two Monte Carlo methods were used.

The first one, for electrons of energy

less than 2 MeV, was similar to the one used by Berger^. in this method, the

electron track is divided into predetermined sections, section size corresponding

to a distance in which the electron loses

energy by a fraction 2"-^°, on an average.

The energy and angle at the end of each

section are sampled from the Landau3

straggling distribution and Goudsrait and

Saunderson^ multiple scattering distribution respectively . Since the computations are for infinite plane sources, the

problem is one of one dimensional transport. The details of the method are presented elsewhereS. The range of electron

was divided into forty slabs and the

energy absorbed in each block was computed

2000 histories were used in the calcalation. The effect of secondary electrons

was ignored.

For higher energies we have used a modified Monte Carlo Method. This is a mixed procedure in which one excludes

from the grouping individual collisions

denoted as major or catastrophic in which

either the electron loses a very large

fraction of its energy in an inelastic

process or suffers a large change in

angle due to elastic scattering. Here

again the electron track is divided intc

sections. However, the section size is

not fixed earlier but is decided by the

probability for catastrophic collisions.

No catastrophic collision occurs in eacli

section and each section is terminated i by a catastrophic collision. The sectio:

size is sampled from the probability dif tribution function,

P(s)ds = exp j- (s')ds'jX (s)ds:

o total J total I

106
whers ^ (s) = (s) + (s)

total elastic inelastic

Cos9c

Lstic

and

ilas _ a (u,s)dLX

-1 elastic

0.5

. = ( a (£ ,s) d€ inelastic € ^ melastic

materials, viz., Carbon, Aluminium and

Copper, the obliquity of the angle being

Cos 0 = 0.5. As atomic number of the

material increases, peak of the distribu

tion increases due to the increase in

backscattering. Fig. 2 gives the energydissipation function for different energies from 0.1 MeV to 10 MeV in Aluminium

incident direction cosine being 0.8.

where Cos 9 is the cut off angle and£^

is the fracuional energy of the incident

electron above which the collision is

considered to be catastrophic.

In each section energy loss was com- pated using a continuous slowing down

model. The change in the angle was computed using a Caussian distribution.

?(«) dCO = 2C0

exiD do)

2 6

CO was derived from the Moliere multiple

scattering theory as

& z

z s

Ui <

2 MlV £i.ECTROiJ INCIOEHT ANC-.E COS 6 = C .

^COPPER

\ ALUMINIUM

-0.4 -0.2 0 0.2 04 0 6 DISTANCE (FRACTION OF R*NOE )

6)^ = 2tiNS J 00 a (a) da

Cos 0

c where M is the number of atoms per gram,

3 is the step size. The actual distribution was also obtained using (Joudsmit and

Saunderson'^ theory. It was found that the

Gaussian approximation agreed well with

the exact calculation. The catastrophic

collision results in either a large angle

scattering or production of a 6-ray.The

large angle scattering was sampled from

Mckinley-Feshbach' multiple scattering

distribution and 5-ray distribution from

the '!^ller° cross section. 6-rays above

a certain cut off energy (100 keV) were

tracked separately.

Photons produced can also be tracked

separately. In the present calculations,

however, bremsstrahlung losses have been

added to the stopping power. This is

because, the total radiation yield for a

10 wev electron in carbon is only 4*/. This method has the advantage that the

correlation between energy loss fluctuations and production of 6-rays is preserved faithfully. The spatial location of

the particle is also more accurate because

large angle collisions have been excluded

from the sections. Calculations for depth

doses were carried out by tracking electrons in all the three co-ordinates.

10,000 histories were used in these calculations.

Results and Discussion

Fig.l. Energy dissipation distribution for infinite plane oblique

(Cos 0 = 0.6) sources of initial energy 2 MeV in different

materials.

Fig. 2,

ALUMINIUM

INCIDENT ANCLE COS e = 0

0.2 0 DISTANCE

0.2- 0.« 0.6

( FRACTION OF RANGE )

1.0

Energy dissipation distribution for infinite plane

oblique (Cos 0 = 0.8) electron sources of different

initial energies in Aluminium.

Fig.l gives the energy dissipation

function for 2 MeV electrons in three

107
Figs. show the energy dissipation

function in Carbon for 0.05 WeV electrons for 5 different angles. (Cos 0=0.2,

0.4, 0.6, 0.8, 1.0). Here again, the

peak increases for higher obliquity.

10 0

7 5

5.0

2.5

(3a) -

•r 50 keV ELECTRON

IN CARBON

z

ION A COS e = 0,

I B COS e = 0 2

FIJI

/

—

0 2 c 0.2 0.4 0 6 0 8 DISTANCE (FRACTION OF F,

• '.GE i

3

1 /K 50 k«V ELECTFCN

i 2 / \ IN CARBON

1 ISSIPAl

JNITS /

^^^^

ENERGY

01

FUNCTION / c\ \ \

A CCS 3 . 1.0 \^ \ ^. B COS 0 = 0 ,8 C COS.? =0.6 \.\\

- O.i -0 .2 0 0.2 0 4 C 5 0.8 -..0 DISTANCE (FRACTION OF Ri. 'Z)

Figg„ 3a-, h : Energy dissipation

distribution for

infinite plane oblique electron sources

of initial energy 50 keV

in Carbon.

a) for incidence angles

Qos 9 = 0.2, 0.4.

b) for cos Q = 0.6,

0.8 and 1.0.

Fig. 4 gives the central axis depth dose

distribution in Carbon for a 10 MeV electron beam for a circular field of 14 cms. diameter. The central axis depth dose

data for this field size, of course,

corresponds to the data for an infinite

plane perpendicular source. This agrees

well with Spencer' s data. The higher

peak and lower doses at large distances

obtained by Spencer^ are due to the fact

that stragglin.g has been neglected in

his calculations. Fig. 5 shows isodose

DISTANCE ( FRACTION OF RANGE )

Fig. 4. Comparison of central axis

depth dose data for a 10

MeV electron beam in Carbon.

Fig. 5^ Isodose curves for a 10

MeV electron beam in Carbon for a circular field

(14 cm d ia ) •

curves for a 10 MeV electron beam for

the same field size.

The perturbation due to an air cavity in the beam has been given

in Fig. 6. It can be seen that the depth

dose curves are shifted downwards under

the cavity. Another effect is the presence of a region of overdosage under

the cavity (150X) This is because of

'focussing effect' associated with elec

tron beams, i.e., electrons scattered

into the cavity tend to stay there.

108
CM«64202468CH

Fig. 6. Isodose curves for a 10 MeV electron beam in Carbon in the

presence of a cylindrical cavity

(2.5 cm length, 2.5 cm diameter)

at a depth of 0.64 cm. whereas no electrons are scattered out

from the cavity. This has been observed

experimentally also. (Starchman and JenHtmg Chao9) . However, there is quite a large disagreement between our results

and those of Starchman ai;d Jen-Hung Chao-'. We are investigating the reasons for

this discrepancy. It may be because of

the bremsstrahlung contamination in the

electron beam. Also the experimental

measurements were made with photographic

films - the Cerenkov radiation produced

in the phantom material would have con- tributed significantly to the blackening

of the film. Attempts are being made to

correct for this.

Acknowledgements

The authors are grateful to M.A.

Prasad and P.S. Iyer for the many useful

discussions and help during the course

of this work. Thanks are also due to

K.G-. Vohra for his keen interest in the

work.

References

1. Spencer, i.Y., Energy dissipation by

fast electrons, NBS Monograph 1(1959).

2. Berger, M.J., Methods in Computational

Physics Vol.1., ed. B. Acller, S. Fernbach and M. Rotenberg (New York

and London Academic Press), pp 135-

215 (1963)

3. Landau, L., J.Phys. USSR, 8, 201(1944).

4. Goudsmit , S. and Saunderson, J.L.,

Phys. Rev, , 24(1940) . 5. Sxindararaman , V., Prasad, M.A. and

Vora, R.B., Phys .Med .Biol . , 18, 208

(1973)

6. Moliere, G., Z. Waturf . , 78(1948).

7. Mckinley, W.A. and Peshbach, H, , Phys.

Rev. 14, 1759(1948)

8. M011er, Zeits . f .Physik, 70, 786(1931).

9. Starchman, D.E. and Jen-Hung Chao,

Radiology, 10^, 177(1972).

109
BACKSCATTERING OF GAI-Il'IA RAYS

Tomonori Hyodo

Department of Nuclear Engineering

Kyoto University

Sakyo-ku, Kyoto

Japan

A survey of principal research on the backscattering

of gamma rays is described. This is a macroscopic phenomena composing many photons scattered backward from a surface of material. After a historical survey as an introduction, principal theme of research is described;

nomenclature of albedo, Monte Carlo calculation, measurement

of albedos, semi-empirical formula of the differential

albedo, exposure dose rate distribution outside a scatterer, distribution of scattered gamma rays on the surface.

(Albedo, backscattering, distribution, dose rate,

gamma rays, Monte Carlo, photon.)

Introduction

During last 20 years much progress

has been made toward the calculation and

measurement of multiple scattering of

gamma rays backward from the surface of

material, namely backscattering of gamma

rays. It may be said that the details

of this type of interactions are now known to considerable accuracy. Most of

papers are published in ten years, from

1959 to 1968. Review articles and books

covering this field were published in

the end of this period. -^"^ This paper

is a survey of works in this field

adding recent progress.

There are two large groups of published papers in this field. One concerns on the reflection characteristics of material, such as total albedo,

differential albedo, reflection build

up factors, and the other concerns

exposure rate field distribution outside

and on a scatterer.

Hine and McCall^ , Hayward and

Hubbell' measiired backscattering of

gamma rays as a macroscopic phenomenon

and they knew considerable amount of

gamma rays were scattered backward.

Bulatov and G-arusov""^ used a small

dosimeter without a collimator, Hyodo-'--'-

used a small point isotropic source on the surface of a scatterer and a Nal(Tl)

scintillator without a collimator.

After these experiments measurements of

total albedos have been continued-V^"^^

Monte Carlo method has been applied

successfully for simulation of multiple

scattering phenomena of gamma rays in

material with the development of computers. Hayward and Hubbell"^-^ calculated

albedos by a desk computer, Perkins^^^

Berger and Doggett^S and other workers^""

^ calculated total albedos using electronic computers. Total albedos and reflection build-up factors were calculated

using invariant imbedding method^-^,

Moment s^Methpd^ 4, and semi -analytical

method^-O^-l'^S

For the necessity of estimation of

exposure dose rate distribution outside a scatterer and estimation of duct streaming

gamma rays several Monte Carlo calculationi

of differential albedos have been carried

out with increasing of calculation speed

:5!?-4i^ Many experimental works measured

differential albedos to obtain total

albedos by integration"' ° »-'--'•". Precise

measurements of differential albedos have

an utility to compare calculated values.

Steyn and Andrews'^^ and other workers^5-48

measured them. Bulatov'^° compiled these

data in a form having good availability

to calculate exposure dose rate distribution. Chilton and Huddleston^^'^-^

derived a semi- empirical formula for the

differential albedo of concrete and

applied for the estimation of thej-distribution. Shoemaker and Huddi eston-'^" proposed an approximation method to

reduce the number of necessary angles for

the calculation and experiment.

Backscattered radiation of bremsstrahlung of betatrons was measured by

Pruitt^'^ and other workers55-57

Berger^^ calculated energy dissipation in a medium with the scattering

properties of wa,ter which consists of two ] semi-infinite regions, one of which is

much denser than the other. Titus-'"

110
simulated experimentally with iron. ^ , Clarke and Batter"'-' and other workers

measiired scattered gamma ray exposure

dose rate distribution. Chilton°4-65 and

other workers"""""^ proposed calculation

methods for the distribution and compared

to the experimental results.

Propagation of gamma rays at or near

an air-ground interface was measured by many

vforkers°°~ ' 9 and a review article was written by Clarke^O. G-arrett proposed a shielding benchmark problem and call for

theoretical calciilations and experiments.

Emergent gamma rays at an interface

with point source placed on the interface

was investigated by Bulatov9, Hyodo-'--'-,

Dag^s^gn and Beach°2 and other workeScattered gamma rays at an airgroiand interface from air atoms is skyshine. Several works has been published

on this problem"-^~94.

Several works95-98 -^ere published

on the backscattering from room walls, a spherical shell and complicated configurations . As an example of application of

albedo coi^^ej^^^ calculation of duct

str earning:s shown.

energy, and exposure dose rate are written by Jqn, Jjj; Jpj;, Jjj; Joi}» Jj)'

respectively. Niimoer differential

albedo a-^, energy differential albedo a-g, dose differential albedo a-^ is defined

as follows:

•^On/^^^O' ^0' ^' ®' ^^^^

Je = Jqe ^^e^^o' ®0'' ®' =

Jo:s[a^{SQ, eo; E, G, ^)dE ..(2)

JodJo:^(Eq, Oq; E, d,*)dE

Total number albedo A^, total energy

albedo A-g, and total dose albedo A-q is

obtained by integration of differential

albedos

,

Definition of Albedos

rrz ^ " J

^'^ Jo^N^^O' ®0' ®' ^^^^ ^®

Ag = Id^ aE(EQ, Gq; e, 0) sinG dG

Aj^ = jd<f> Jcj^CEq, Bo; e, <f) sine de

The quantities that characterized

the reflection probability of material

are called albedo. The definition of the

albedo is described in many books and

papers5~5 » 51? » op ^ Traditionally, the

albedo refers the ratio of the radiation

entering in and leaving from a small

area dS of the surface of a scatterer.

In this usage the albedo is a ratio of

current passing through dS and npt-pf

flux density. Several papers^'

discussed on this point in details.

Consider, for example, a monodirectional source of radiation of energy Eq

incident on a surface at polar angle Sq as shown in Fig. 1. The reflected

current of energy E per unit energy per

unit solid angle at polar angle G and

azim.uthal angle ^ is given by,

J(E,G,,^) = J(Eo,Go) a(Eo,Go; E,G,(#) ..(l)

where J(Eq,Go) is the incident current

and a(EQ,eQ; G, ^) is called (double)

differential albedo or energy-angular

distribution passing through the surface.

The quantities of current incident and

outgoing was measiired by photon number.

(3)

DETECTO«

Fig. 1. Reflejti on geometry,

111
Scattered radiation flux and exposure dose rate outside a scatterer can be

estimated if the value of differential

albedo is known for every emerging angle

of e and o. For the case of uniform monodirectional gamma rays are incident to a scatterer as shovm in Fig. 2 a. The

nximber and energy flux and exposure dose

rate at a detector caused by photons

emerging from an. incremental area dS is

d{Ei

dD =

nQ cosSq ttj^ dS

n^ EqCOS&q dS

n^ EqT] cosGq a-^ dS

(4;

where n^ is photon flux at dS, r is the

distance between the center of dS and

the detector, t] is the conversion

constant from photon intensity to exposure rate.

For the case of a point isotropic

source emitting Q photons/sec placed at

rQ from dS as shown in Fig. 2 b, formulas are,

dS^ =

dD =

Q COS0Q a.^ dS

_ _

Q Eq cose^ ttj, dS

2 2 4nrQ r

Q Eq T) cosBq a-j^ dS

_

4ixrQ r

(5)

Monte Carlo Kethod

The backscattering of gamma rays

has been the subject of a number of

Monte Carlo calculations and got great success. Practical methods of the

application^are described in several

books. 1°^"^^'

The reason of success is following.

Cross section of the interaction of

gamma rays with matter is well known and

monotonic functions with energy. The

standard deviation is given by^°

~ VN - 1 .(6)

Fig. 2. Geometry of scattered gamma-ray

calculation, a. Plane monodirectional source, b. Point

isotropic source. where A is the value of albedo and N the

number of histories. The value of A is

between 0.01 to 0.6, so small value of

standard deviation a is obtained.

The earlier works using Monte Carlo

method were calculation of total albedos

and reflection build up factors for

uniform materials having plane surfaces

and spherical shell24-52. After these

works sufficient histories for the

calculation of differential albedo have

been available since ten years ago with

increasing of calculation • speed of

digital computers. Numerical tables and

graphs were ;published on several papers

and books .5 » >'5-41 These calculated

results are shown in the following

paragraphs

Measurement of Albedos

Measurement of differential albedos

has been carried out by many workers.

Host of these works had a purpose partially to obtain total albedos by integration of differential albedos, but

several works had not the purpose

because data of differential albedos were very important to get an information

of scattered gamma rays in a definite

direction and to compare calculated

results as a benchmark experiment.

Measurement of photon current

incident to and emergent from a small

112
area dS on the surface of a scatterer,

truly to the definition, is difficult,

because most of the photons incident

to dS emerge from outside of dS or captured in the scatterer. Following

three geometries are approximately

possible to the measurement.

The first geometry is a narrow,

well-collimated beam of gamma rays

incident on a scatterer at a desired

angle, together with isotropic detectors

around on a hemispheric shell centered

around the irradiation area as shown

in Fig.ja. Bulatov and G-arusov°,

Efrimenko Clifford^^, and Elias et al

measured scattered gamma rays with this

well-collimated-beam geometry.

The second geometry is the irradiation of large scattering medium with

a wide beam of gamma ray to simulate an infinite plane monodirectional source of

gamma rays and use a well-collimated

detector to observe the angtilar dependence of the scattered radiation emitted

from a small surface region near the

center of the irradiated area as shown

in Fig. 3 b. §teyi^ ^^'^ Andrewr^,

Haggmark et al^^, and Barran et al^'

measured scattered gamma rays using well

collimated detectors.

48

Fig. 3. Geometry of measurement for backscattered gamroa rays.

Both case has a dead space of

measurements caused by beam of radiation,

shadow of collimator or shield. The

third geometry Fig. 3 c, is rather

special case, but it has not any dead

space of measurement. A small point

isotropic source placed on the surface

of a scatterer and a detector without

a collimator moves on a hemisphere of

sufficiently large radii. Bulatov",

Hyodo and his covrorkers-'--'-"!^, and

Pozdneev-'- measured scattered gamma

rays vrith this geometry

Albedo Data

Figure 4 shows Monte Carlo results

of the total energy albedo for several

elements as a function of energy. In

high energy region, the albedo value

decreases with increasing of energy

because the differential cross-section

of large angle scattering decrease with

increase of energy. Figure 5 shows the

total energy albedo value obtained by

experiment. The figure shows the albedo

value increase with increasing of

scatterer thickness. Bulatov and

Garusov^ derived following experimental

formijila

Aj,(d) = A2(°«)(l - e"'^/^) ...(7)

Eg. Ur«

Fig. 4. Energy albedo as function of the source energy (perpendicular

incidence, G=0). (ref. 26)

where d is thickness of the scatterer and

a is a constant. Figure 6 shows the

total energy albedo obtained by third

geometry. Figure 7 shows the value of

differential albedo. There is two

distinct group of curves in the figure.

Upper two curves obtained by third

geometry and lower group obtained by

first geometry

113
C —1 —4

;!os

h -|Fe

/, /

-I >• Cdr

'>

-k \

20 30 40 50

Scoiierer trKkness, g/cm'

Fig. 5. Energy albedo as fimction of

scatterer thickness ( °'-'Go,9_.=0)

(ref.8) : ... . ° _ 1 1 1 _

/ /"

POIYFTHVI.ENE ' _ ' .

>y^t\^2^

"

// r'

1 1 1

Fig. 6.

10.0 20.0 30.0 THICKNESS, g/cm»

Wixmber and energy albedos as fimction of scatterer thickness

( Co, point isotropic source placed on the surface), (ref.13)

Study of back scattered radiation

caused by high-energy bremsstrahlimg

from a betatron and a linear accelerator

is very important for the estimation of

exposure distribution and for the understanding of scattering phenomena of higa

energy photons.

Figure 8 shows energy spectra of

photons back scattered from aluminium

scatterer, incident and emerging angles

(Bq, e) = (0°, 20°). The energy of

photons in the spectra is less than 0.5

MeV or annihilation radiation because of

ATOHIC MUMftCR

Fig. 7. Differential energy albedo as function of scattering angle

(ref.48).

10 - E„ = 9.5 MeV nJl

E„ = 12.0 MeV

n

E„ = 15.5 MeV u

0.1 o.l 03 0.4 0.5 at 0.1 0.1 0.. oj ai o.S a* ».t

PHOTON ENERGY. MoV

Fig. 8. Energy spectra of scattered

radiation from aluminium, (ref.56

singly scattered gamma rays. Figure 9 shows the differential dose albedo for

aluminium.

SEMIEMPIRIGAL FORMULA OF DIFFERENTIAL ' ALBEDO ! For the application of albedo concej

for the calculation of duct streaming of

|

gamma rays, scattered gamma ray exposure

rate field, albedo values for many directions of emerging are necessary. A

semi-empirical formula is very useful to

interpolate albedo values from calculate;

and experimental data;

Chilton and Huddl eston^*^ derived

a semi-empirical formula for the diff er114
EXPOSURE DOSE B.ATE DISTRIBUTION

OUTSIDE A SCATTERER

1 "T"

!'

^ rk .V T . (30.2C.C;

j —

\l

i3i°cc''': i

1

! f.'O. J s.c r—-1

,25

1

i

'

i

H

!

<

,

i!

i 1

•

1

^

1

\\

1

i < S i 10 X

It is necessary very often to

estimate exposure dose rate distribution

outside a scatterer as shown in Fig. 10.

The exposure dose rate at the detector is

superposition of those primary gamma rays

from the source and those of scattered

gamma rays from the scatterer.

MEOIIM 2.

Fig. 9. Differential dose albedo as function of electron energy, (ref.

56

)

ential dose albedo of concrete on the

assumption: Scattered radiation can be

broken down into two parts, one is

proportional to single Compton scattering

and the other is isotropically scattered}

the effective attenuation coefficient

|i does not vary greatly during a scattering history. The differential

dose albedo a-^ is

C.IO 26

"d

= ^^(Eq, e^) f c- cos e

(8)

1 +

0 cos e where 0^ is the scattering angle between

the incident and outgoing ray, given by

follovring formula,

cos0^= sin6Q sine cos0 - cos©q cosG

...(9)

and Kg(EQ, 9 ) is the energy scattering

Klein-llishina crosssection per electron,

and C and C' are constants.

The value of differential albedos depends on the incident gamma ray energy and

three angles 0^^, ©, ^, excluding axial

symmetry case, 6„ = 0 or point isotropic

source placed on the surface of a scatterer. Shoemaker and Huddleston-'^

demonstrated a interpolation method to

obtain the differential albedo for the

direction (G, ^) from those of (0, 0°)

and (0, 180°).

Fig. 10. G-eometry of measurement.

Figures 11 and 12 show exposure dose

rate distribution in the case h = z in

Fig. 10. Medium 1 was air and medium 2 concrete. As shown in these figures the

ratios between the exposure dose rate

caused by gamma rays scattered from

concrete and those of primary gamma rays are fair agreement at the same h/D values.

Chilton64»65 calculated scattered

gamma-ray exposure dose rate using

formulas (5) and (8). The calculated

value is shown in Fig. 11. The cijxve

shows fair agreement with experimental

data.

67 Kitazume proposed a calculation

method. The scattered gamma rays to the

detector was calculated following formula,

_ { ^Q tig/dA exp(-^j^p.^ -1^2P2^ ^2 D _ ^]--

„ 2 .2 -dv

^^^ r'

where N is electron number per cm-^,

da/dJi is Compton scattering cross

section, p., and is path length of

primary ani secondary gamma rays in

scatterer, and B(pp) is the build up

factor for scattered gamma rays.

Calculated results are shown in Figs

and 12.

62 Hendee and Ellis calculated on the

assumption of isotropic scatt ;ring and

showed good fit for the experimental value

.(10)

the

. 11

115
in the range of the ratio h/D is more

than 0.5 as shown in Fig. 12

measured emergent photons normally to

the surface.

A review article on the propagation

of gamma rays at or near an air-ground

interface was written by Clarke^'^.

Fig. 11. POitio of scattered to direct

°^Co exposure dose rate as function of h/D. (ref. 60)

Dislonc* from sowfCt,rjCm

Fig. 13. Radial distribution of energy

back scattered from within

These data show that emergent

energy*^ is fitted by following formula,

-br

0 ... (11)

where Vq andti^are constants. Differentiating xhis formiila, we can get I(r) as emerging energy an unit area at r,

I(r)

s-ar

(12)

where C and a^e constants.

References

Fig. 12. Ratio of scattered to direct

"^Co exposure dose rate as function of h/D. (ref. 62)

DISTRIBUTION OF SCATTERED QAmiA

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Figure 13 shows the distribution of

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photons emerging in an annulus of unit

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77. Andryshin.N.P. and Bulatov.B.P. , At

Bnerg. 22,404 (1967).

78. Chilton, A. B. ,Nucl. Sci.Bng.22,403

(1967) . 79. Clifford, G.B. and Wait.C.D., Nucl. 104.

Sci.Bng. 21,483 (1967).

80. Clarke, B.T. ,Nucl. Sci . Bng.22, 394

(1967).

81. (Tarrett,C.W., Gamma-ray dose above

a plane source of 60co on an air/ 105.

ground interface, Shielding Benchmark Problem 4 .0, 0RNL-R3IC-25 106.

(ANS-SD-9) pp. 4. 0-1 - 22 (1969).

82. Davisson, CM. and Beach, L. A.,

ANS Tra3n.No.2,391 (1962).

83. Nakamura.T. and Hyodo, T. .Trans.

3rd Robutsuri Bunkakai, p.34 (1963)

(in Japanese).

84. Marenkov,0. 3., At. Bnerg. 21, 297(1966).

85. Waechter,K.H. ,Kemtechnik 2*62-64

(1967).

86. Andryushin,N.P. et al. , At . Bnerg.

22,110 (1967), Sov. At. Bnerg. 22,

802 (1967).

87. Nakamura,T. and Hyodo, T. , J.Nucl.

Sci. Tech. 6, 143 (1969).

88. Wechselberger, E. ,Atomkemenergie

16, 64 (1970).

89. Preiss,K. and Livnat, R. , Nucl.Bng.

Design 2i, 258 (1973).

90. Pozdneev,D.B. and Paddeev.M.A.

,

Kernenergie 16, 105 (1973).

91. Lynch, R.B. et al.,A Monte Carlo

calculation of air-scattered gammarays, ORNL-2291, Vol.1, 1958.

92. Trubey,D.K.. Nucl. Sci.Bng. 10, 102

(1961). —

93. Shimamura, A. , J.Nucl. Sci. Tech. 2»

300 (1966).

94. Zitazume,M. , J.Nucl. Sci. Tech. 2»

464 (1968).

95. Andryushin,N.F. and Bulatov,B.P.

,

At. Bnerg. At. Bnerg. li, 392 (1965).

96. Andryushin,N.F.et al. , At. Bnerg. 21,

298 (1966).

Bulatov.B.P. et al.,At. Energ. 22,

240 (1967), Sov. At. Bnerg. 22, 965

(1967).

Birchall Iv8ui. , Health Phys. 16, 47

(1969).

LeDouXjJ.C. and Chilton, A. B. , Nucl,

Sci.Bng. 11,362 (1961).

Zolotukhin, V.G. et al. , Radiation

Transmission through inhomogeneities

in Shields, Atomizdat,Moscva, 1968

(translation in English, ASC-tr-7175).

Groertzel, Gr. and Kalos,M.H., Monte

Carlo Methods in Transport Problems,

Progress in Nucl. Energ. Series 1,

Vol. 2, pp. 315-375, Pergamon Press,

London, 1958.

Cashwell, E.D. and Everett, C.J.

,

A Practical Manual on the Monte

Carlo Method for Random Work

Problems, Pergamon Press, London,

1959.

LeipunskiijO.I. et al.,The Propagation of Gamma Quanta in Matter

(translated from Russian) , Pergamon

Press, London, 1965, (original,

Atomizdat, Moscwa, I960).

Biro,G.G. 3.1- Application of the

Monte Carlo Method to Shielding,

Engineering Compendium on Radiation

Shielding, Vol. L, pp. 101-124,

Springer-Verlag, Beriiii,,1968

Gopinath, D.V. and Santhanam.K.,

Nucl. Sci. Eng. 12,186 (1971).

Gopinath, D.V. and Santhaneim.K.

,

Nucl. Sci. Eng. ^,197 (1971).

118
TRAfTSMISSION OF ^^^CF FISSION WaUTROfTS

THROUG-H VARIOUS SHISLDS

Yo Talk Song

Nuclear Physics Division

U.S. Naval Surface Weapons Center

White Oak, Silver Spring, Maryland,

U. S. A.

Measurements have been made of neutron transmission

through various shield configarations. A ^^^Cf source,

having a neutron yield of 1.02 x 10° n/sec was used with

a US Navy neutron dosimeter, AN/PDR-70. This detector was used to measure the integrated neutron dose equivalent (DE).

3 by 5 ft. slab shields of various materials were used, such as iron, lead, polyethylene, combinations of iron-polyethylene, lead-polyethylene, and iron polyethylene-iron. The

measured data were corrected for room-scattered contributions. The scattered neutron DE was calculated using the

differential dose albedo formula of Song, et all. The

experimental data thus obtained were compared with calculated values. The one-dimensionsal discrete ordinates neutron

transport code, ANISN, with 40 energy groups, 22 groups for

neutron and 18 groups for y-^ays, was used for the transmission calculations. Comparisons were made in terms of attenuation factors, the ratio of transmitted neutron DE to

free-field neutron DS at the detector point. Agreement was within the expected dosimeter range of 20/. for all cases.

For the case of two inches of iron and five inches of polyethylene, placing the iron on the source side was more effective than placing it on the opposite side.

( ANISN } Cf ; code ; configuration ; dose equivalent ; energy ; gamma rays; neutron ; scattering; shield ; transmission)

Introduction

The transmission of neutrons from

the 252cf source through various shields

was measured by a neutron dosimeter,

AN/PDR-70. The 252cf so urce is a small

cylinder of about 0.25 inches in diameter

and 2.5 inches long, and has a relatively

high neutron yield of /~ 10° neutrons/sec.

The AN/PDR-70^ is a U.S. Navy standard

neutron dosimeter of a modified Anderson

Brown type, that measures thermal neutron

flux with a BF-^ tube surrounded by cylindrical polyethylene moderator. The moderator is 8.5 inches in diameter and 9.4

inches in height.

The purpose of the study is to find

out the effectiveness of steel and other

materials for shielding fission neutrons.

The steel is commonly used as structural

material in conjunction with neutron

moderating materials such as the polyethylene. The experiment is simulated by

the one dimensional discrete ordinate

radiation transport code ANISN The

ANISN results are compared with experimental results of various shield configurations. If the agreement between experiment and computational results is

favourable, the effective attenuation

kernel for further shielding calculations

involving other shield configurations

with other materials can be obtained and

the confidence level in the computational

results can be established. Furthei^ore,

the choice of group structure and multigroup cross sections used in ANISN may be

evaluated by comparing the experiment

and computational results.

Experiments

The experiments were performed in a room about 28 ft. by 30 ft. in area and

about 20 ft. high. The walls, floor and

ceiling are concrete slabs. The source and detector were about 10 ft. above the

+ This dosimeter is calibrated to read dose -equivalent with units rem or millirem

per hr. Hereafter, whenever neutron dose is used it will be understood to mean dose-equivalent

119
floor. The shields were 3 ft. by 10 ft.

with various thickness and placed on the

rack so that the centers of the shield

faces lie on the source detector line

and the faces are normal to it. The

source-detector distance in transmission

measurements was kept constant at 2.5 ft.

Various shields were placed on the rack

and the distance from the source to source side face of the shield was kept

at 10 inches. In Table I, the various

shields used in the experiments are given. The left hand side material in

this table was facing the source.

In order to aid in determining the

component of the neutrons scattered from

walls, ceiling and floor, the neutron

dose rates were measured for various

distances from the source. Results are

shown in Figure 1. All data presented

in this paper were corrected for natural

background and have fractional standard

deviations less than or equal to 5'/ of

the measured values. The possible error

in measurements of distance between

source and detector is no greater than

3'/. of the measured values.

Analysis

In the calculation an 316 quadrature with 22 neutron and 18 gamma ray

groups gas utilized. The group structure, ^52q^ source spectrum, and DS

conversion factors used in ANISN, are given in Table II. The 252cf source spectznm in 22 neutron groups is based

on the data by Stoddard^. Basic cross sections are derived from the SNDP/B

library, and edited into ANISN Format

by Radiation Shielding Information

Center. Cross sections for polymers,

(polyethylene) were obtained by mixing

carbon and hydrogen cross sections with

the MACROMIX code. The basic cross sections have apto P-^ components in 22

neutron and 18 gamma energy groups. Monodirectional parallel beams of neutrons

nearly normal to the shields were assumed

in calculations. Based on the spectrum

in Table II, the neutron DE at 2.5 ft.

from the scirce was estimated to 1.69

mrem/hr, while the measured value was

1.64 mrem/hr with corrections for neu- trons scattered from walls, ceiling and

floor. The neutron yield at the time of

the experiment was estimated to be

1.02 X 10° neutron/sec.

The room scattered neutrons reaching the detector were calculated by the

method described by Song et al-*-. Utilizing the differential dose albedo concept with energy dependent parameters

for the differential dose albedo formula,

the scattered neutron DE was estimated

to be 0.05 mrem/hr at the source-detectorseparation distance of 2.5 ft, the experimental detector location. When the

shields were placed between the source and detector, the scattered neutron DE was estimated to be 0.026 mrem/hr. In Figure 1, the measured DE, measured DE

with corrections for room scattered

neutrons and the inverse square line fit

to the corrected data by the least squa- res method are presented. From Figure 1,

the room scattered corrections result in

a good agreement between experimentally

observed data and calculations. Therefore the room scattered data, 0.026 mrem/

hr with shield in between source and

detector, was subtracted to correct all

Table I Shielding Material and Configurations

Materials

Iron

Iron

Iron

Iron

Lead

Lead

Lead

Lead

Polyethylene

Polyethylene

Polyethylene

Polyethylene

Thickness

(inches

)

12

3

4

1/8

1/4

3/8

1/2

24

6

8

Materials

Polyethylene + Lead

Iron + Polyethylene

Iron + Polyethylene

Iron + Polyethylene

Polyethylene + Iron

Polyethylene + Iron

Polyethylene + Iron

Thickness

(inches)

6 + 1/2

1/2 + 5

1 + 5

2 + 5

5 + 1/2

5 + 1

5 + 2 Iron + Polyethylene + Iron 1+5+2

120
the shield transmission data. In Table

III, the experimental results and calculated data for neutron transmission

through various shields are given. In

this Table, the results are given in

terms of the attenuation factors, the

ratio of transmitted neutron dose to free

field neutron dose at the detector point.

Further, comparison of the experimental

results and theoretical results are presented in terms of the ratios of the calculated attenuation factor to the experimental attenuation factor.

Fig. 1. Dose Equivalent Vs. Distance.

Discussion

From Table III, it is seen that the

experiment and the calculated results are

in good agreement. The agreement is generally better for thin shields than for

thick shields as expected.

There are differences in the representation of the experimental geometry

by AI^ISN. In the experiment, the source

is a small cylinder, the shield is a finite slab and the detector is a cylinder. In ANISN, the source was assumed to

be plane-monodirectional beam normally

incident upon a semi-infinite slab shield

and the detector to have an isotropic

response. Therefore, neutrons scattered

from beyond the actual geometry of the

shield in ANISN.were not detected in

experiment. Further, in experiment, the

scattering angle of neutrons reaching

the detector by a single scattering in

the shield is larger than those in ANISN.

Therefore, the expected neutron dose

reaching the detector by a single sca- ttering in the shield will be larger in

ANISN than those in experiment. Consequently, the thicker the shield, the

greater the discrepancies between ANISN

and experiment, as seen in Table III.

It is also seen in Table III that iron

is effective in neutron shielding if

used with a moderating material such as polyethylene. Furthermore, the sandwich

shield, iron + polyethylene + iron, was much more effective compared to the

shield configuration of the same total

amount of iron followed by polyethylene

or polyethylene followed by iron, by

about 257. . The attenuation afforded by

one inch of iron followed by five inches

of polyethylene was almost the same as

five inches of polyethylene followed by

two inches of iron.

That is, if iron and five inches of

polyethylene are to be used for shielding of fission neutrons, place the iron

on the source side. This conclusion can

be drawn from both experimental and

ANISN results. In Figiare 2, the leakage

spectrum from three different shields,

one inch iron followed by five inches of

polyethylene, five inches of polyethylene

followed by two inches of iron and the

sandwich shielding, are presented. Between about 0.1 to 1 MeV, there seems to

be a window in the iron cross section

that permits the neutrons to pass through. The contribution of a neutron to

dose equivalent in the energy of 0.1 to

about 1 MeV is about a factor of 3.5

higher than that of a thermal neutron.

Although the iron behind the polyethylene is more effective in removing thermal neutrons, placing the iron in front

of polyethylene is more effective in

reducing the total neutron dose.

Acknowledgement s Assistance provided by D.C. Hugus

and his group at PANTEX Plant in experimental work, technical consultation by

D.E. Hankins at the Los Alamos Scientific Laboratory, CM. Huddle ston and N.E.

121
Table- II . - 252 Energy Group Structure, Cf Spectrum and DE Factors

NEUTRON GAMMA RAYS

Energy Upper DE-' Source Spectrxim Energy Upper Dose" Group Energy Factors (Fraction/ Group) Group Energy Factor

(Mev) (Mev;

1 15..0 5. 8(-8) 0.0

2 12., 2 4 .

6

0.0

3 10. 0 4.1 , 2., 70-3 23 10. 0 2

,

. 72(-9)

4 8.. 18 4.1 1.,57-2 24 8. 0 2.. 30

5 6., 36 3 .

9

3.,83-2 25 6. 5 1 .90

6 4,,97 3 .

7

4,,94-2 ZD 5. 0 1,. 60

7 4,.07 3.6 1.,19-1 27 4. 0 1 . 32

8 3..01 3 .

5

9

.

,05-2 O O zo 3. 0 1 . 10

' 9 2,.46 3 .

5

2 ,27-2 29 2. 5 .97

10 2,. 35 3 .

6

1

.

.19-1 30 2. 0 . 83

•1 1 11. 1,.83 3.7 2., 30-1 31 1. 66 . 67

Iz 1..11 3.3 2,, 14-

1

JZ 1. 33 .53

13 5..50-1 1 .

5

Q

y

,

.87-2 "it Jo 1. 00 lie . 445

1,,11-1 0 JM- 80 . 35

15 3 .35-3 .12 0 35 60 .256

16 5..83-4 .13 , 0 36 40 .177

17 1,.01-4 .13 0 37 30 .122

18 2,.90-5 .125 0 38 20 .066

19 1..07-5 .12 0 39 10 .039

20 3,.06-6 .115

S

> 40 05 .084

2l 1,.12-6 .110

22 4,.14-7 .105 0 * rem/neutron/cm ^

, rem/gamma ray/cm

Dose Attenuation For Cf^^^ Neutrons Through Various Shields

Shield

Material

Iron

Iron

Iron

Iron

Thickness

(inches)

0

1

2

3

4

Dose Attenuation

(D/Do)

ANISN Experiment

1.000

.992

.878

.749

.624

.000

.890

, 793

.663

.588

D/Do

Ratio

(ANISN/Exp)

1.000

1.115

1.108

1.130

1.061

Polyethylene 2 .568 .529 1..073

Polyethylene 4 .235 . .225 1 .044

Polyethylene 6 .096 .083 1,.156

Polyethylene 8 . 040 .. .033 1 .212

Lead 1/8 1..005 .929 1,.082

Lead 1/4 1,.009 1,007 1..002

Lead 3/8 1..011 .953 1..061

Lead 1/2 1,.011 .949 1,.065

Poly.+ Lead 6 + 1/2 .083 .083 1,.000

Iron + Poly. 1/2 + 5 .122 .109 1..119

Iron + Poly. 1+5 .099 .089 1..112

Iron + Poly. 2+5 .065 .051 1..275

Iron + Poly. 5 + 1/2 .137 .114 . 1..202

Iron + Poly. 5 + 1 .123 .092 1..337

Iron + Poly. 5 + 2 .099 .082 1.,207

Iron + Poly. + Iron 1+5+2 .064 .057 1.123

122
r.—; =7:—

1

-

'

1 -, ~—j- 1 tj

-1- —

—f— H 1 1 :k rt Thrcu gh Varlouj 5 nltldi («' • sure*

? 1 i J—

-4-

-

- „

1 ^.

brH

-I r:

= r

-

f

;/

'ri- ftT-F

4

I ran

=

: 1 \ -1

-

1 1 + 5" tel7.-< -4 1

1 f

- -

1

1

i 1 - H

. i

1

1 _L

i ....

-

r

! —

u J3

i

: i —!

Fig. 2. Neutron Leakage Spectrum

Through Various Shields (Cf

source)

Scofield at the Naval Surface Weapons

Center for their giaidance and helpful

assistance, and Jack Finkel at the Naval

Surface Weapons Center for his numerical

calculation of room scattered neutron

dose, are all great fully acknowledged.

References

1. Song, Y.T., Huddleston, CM., & Chilton.

A.B., Nucl. Scl. Eng. 35, 401 (1969).

2. Technical Manual, Set AN/PDR-70.

NAVSHIPS 0967-871-5220, Nov. 1969.

3. WANL-PR(LL)-054, Nuclear Rocket

Shielding Methods, Modification,

Updating, and Input data preparation, Volume 4, One-Dimensional,

Discrete Ordinate Transport Technique, Augiast 1970.

4. Bngle, Jr. , a'. W. , "A User's Manual for

ANISN, A One-Dimensional Discrete

Ordinate Transport Code with Anisotropic Scattering".

5. DP-939 Savannah River (Diipontj Radiation Properties of Cm^44 Produced

for Isotopic Power Generators, Savannah River Laboratory, Aiken, S.C.,

Nov. 1969 by D.H. Stoddard.

Discussion

S. Makra

Could you give me the exact difference in attenuation when reversing the

sequence of the shield layers?

Y.T. Song

It will be shown in proceedings of

this symposium. However, the following

is one of the results of your interest.

2 in. Iron + 5 in. Poly ANISN 0.065

Exp. 0.051

5 in. Poly + 2 in. Iron ANISN 0.099

Exp. 0.082

As you see reversing the order, it gives

as much as about 30? difference.

D.V. (jopinath

ANISN is a one-dimensional code and

your* experimental system seems to be

away from one-dimensional geometry . Still

the agreement between theory and experimental seems to be very good. Will you

please comment ? Y.T. Song

Mock up of experiment depends largely on how you use the facilities. ANISN

results and experimental results should

agree very well for a thin shield if you

use ANISN properly. However, for thick

shield, agreements expected are poorer.

Note for the shield arrangements of my

paper within this range of shield thickness, rather good agreement in terms of

D/D is expected and we have it.

123
BACK-SCATTERING (SZT-SHINE) OF GAMMA-RAYS PROM A

650 CURIE COBALT-60 SOURCE BY INFBflTE AIR

J. Swarup and A.E. Ganguly

Health Physics Division

Bhahha Atomic Research Centre

Trombay, Bombay- 400 085

The paper reports the preliminary results obtained on the skyshine spectra from a 650Gi^'^Co source located at the centre of a gamma

irradiation field of radius 90 m. fenced by a stone wall of thickness

--^75 cm and height 3-66 m. The source is in the form of small pellet.

The height of the source when raised for irradiation is 1.2 m above

ground level and it is shielded on top by a lead cylinder of 10 cm diameter and 25 cm length. Thus, only the scattered radiation can reach the ground level beyond the fencing wall. There is a field Qf

100 mR/hr on the inner side and 2 mR/hr on the outer side of the wall

with the source raised. Experiments are carried out for the measurement

of sky-shine with a well-shielded Nal detector assembly coupled to a 400-channel analyser. The detector is placed 55 cm above ground

looking vertically up through a lead collimator of diameter 12 mm

(.or 20 mm; at distances from 150 m to 325 m away from the source. Energy calibrations of the spectra have been carried out before and

after each experiment using standard sources of gamma-energy ranging

from 60 keV to 662 keV. It is found that the spectrum extends upto

400 keV with a pronounced peak at 72 keV for all the distances.

There is no evidence of the presence of primary gamma-photons in the

spectra. Total eovmts under the sky-shine are observed to follow an

exponential decline with distance, with a slope of -0.50 + 0.02 for

both the collimators used. The ratio of peak counts (72 keV) to total

sky-shine is 0.24 + 0.02 for both the collimators. Also, the nature

and intensity of the spectra remain unchanged when the lead shield

around the detector is provided with an internal lining of 2.5 cm thick aluminium.

(Back scattering; ^^Co; gamma rays; sky-shine; spectrum)

Introduction

Swarup-^ has investigated the backscattering of gamma rays obtained from

137gs inside a large room for different

source-to-detector distances. The

present work is a preliminary report on an extension of the same work in the

ope , to study the back-scattering of

cobalt-60 gamma, at different source-todetector distances, by infinite air

above the source. This back scattering

is also known in literature as sky-shine.

Field Description and Experimental

Arrangements

The cobalt source for these observations is located at the centre of a large (90 m radius) circular gamma

irradiation field and has a calculated

strength of 650 Gi. The active material

is in the form of small pellets of 1 mm diameter x 1 mm height filled in an annular stainless steel container of

18.5 mm outer diameter, 11.5 mm inner

diameter and 40 mm length. Thus, it is

effectively a point source when viewed

from distances beyond 100 m.

The height of the source when raised

for irradiation is 1.2 m above the ground

level. It is shielded on the top by a plug of lead cylinder of 10 cm diameter

and 25 em length. ! The gamma irradiation field is ; fenced by a stone masonry wall of height t 3.66 m, and thickness 1 m at the base ] tapering to 75 cm at the top. There is a J field of 100 mR/hr on the inner side and

2 mR/hr on the outer side of this wall

when the source is raised. Because of

this wall, only the scattered radiations,

scattered by the air above the source, can reach the ground level beyond the

fencing wall

Observations on the sky-shine

spectra are taken with a 5.08 cm x 5.08cm

Nal (Tl) Harshaw integral assembly

coupled to a 400-channel analyser. The

detector is placed inside a cylindrical

(50 cm high) lead shield made of inter- , locking rings of 5 cm thickness, 5 cm , height and 15 cm inner diameter (Fig. 1) .

,

In the central hole of the top ring, a , lead collimator or a lead plug to close

It as the case may be, could be placed. 'j,

i

124
This whole assembly is motmted on a trolley of mild-steel 25 mm thick, for easy

morement. Height of the detector head

in this position is 55 cm above gro\md.

Fig. 1. Detector assembly inside the Pb

shield with Al-lining.

Whereas the detector is kept in the

open at atmospheric temperature, the

analyser is located inside an air-conditioned room of constant {'^23°0) temperature. This necessitated long cables

of 100 m length to couple the two. For

driving the pulses through such a

length, the emitter follower of the

pre-amplifier is fitted with a driver

for coaxial cables which are appropriately terminated.

To avoid large changes in temperature of the detector in shade and simshine

the entire set of observations are taken

in the night . Changes in the gain of

photomultiplier with temperature variations are discussed by Zinard^. E.H.T.

of the photomul.tiplier is adjusted to

less than the optimum working potential.

This helped in keeping the gain constant

throughout the interval of aboat five

hours of one set of observations. By

reducing the E.H.T. , sensitivity of the

photomultiplier is reduced and inspite

of temperature changes of upto 8°C

during one set, the spectra from 0.662

MeV to 0.060 MeY remained reproducible.

To take the observations at different distances from the source, a road

radial to the source is used. This road,

being inside the premises of Radioactive

Solid Management Site used for burying

radioactive wastes, however, has a significant background of its own

(0.5 mR/hr) and therefore its own areaskyshine. This area-skyshine is measured

and subtracted from the sky-shine

obtained with "'^Co source raised. The

spectra are taken with the detector

looking vertically up for distances from

150 ffi to 325 m from the source at

intervals of 10 m.

On the side of the experimental

field is the sea and on the other side

well beyond 400 m from the source, a vegetation covered hill gradually rising

to a maximum height of about 75 m above

the sea level. The contribution to the

sky-shine from the hill is negligible as the observations have been taken in a narrow collimated vertically upward

direction.

For taking the sky-shine spectra for

distances between 325 m and 255 m collimator of 12 mm diameter and 5 cm length

is used. The spectra with 20 mm collimator have also been recorded for

distances of 150 m and 155 m. Recording of Spectra

The procedure for recording the

spectra is as follows:

i) First the detector is calibrated

with thin standard sources of gamma

energy ranging from 60 KeV to 662 KeV

kept at the opening of the collimator

(with the 6O00 source down) . The

strengths of these sources are known to

a confidence level of . The sources used are 24lAm 109cd 57cp l4lce,

203Hg, ^'-^Cr, l^^Au, ^^Sr, 137cs,

ii) Keeping the ^*^&'o source down,

the area-skyshine is determined for 30

mins. This shine is subtracted from the

spectra of the standard sources. Then,

by plugging the collimator, the background spectrum in the shield is determined. Subtracting this from the areaskyshine, true area-skyshine is obtained.

As the area-skyshine could not be

determined for all the individual experimental points, it is measured at one point and assumed to be the same throughout

iii) The source is raised. First

the spectrum is taken for 30 mins. with

the lead-plug in position. This

spectrum is termed the back-ground

spectrum in this work.

(iv) Finally, the plug is replaced

with an appropriate collimator and the

sky-shine spectrum is recorded for 30

mins. The channel calibration is tested

again with standard sources. From this

sky-shine the sum of the spectra of

back-ground and the true area-skyshine

is subtracted to^get the true sky-shine

spectrum due to °^Go source. Typical spectra of sky-shine and

area-skyshine with their respective backgrounds are shown in Fig. 2.

It is observed that the background

continued upto almost the 60co energy

125
0 50 TJ ISO 2m J50 300 3:0 «0

CHANWeL NUM3SR Fig. 2. Sky sliiae Bpectrum at 255 m. source dietanc© (Golliaater j20 mm).

without any peaking at that energy and

increased continuously with decreasing

source distance. A five-hours counting

at 150 m source-distance did not show

any °^Qo peak. At the distance of 255 m the back ground increased considerably

(about 25*7. of the sky-shine at 72 KeV)

and it is reduced to 8/. when the shield

is provided w^th a single layer castling

of 5 cm thick lead bricks all around.

But the back ground subtracted sky-shine

spectrum remained unaffected by castling.

The remaining sky shine spectra upto 150 m are recorded with this 10 cm lead

shielding arrangement

Discussions

There is no data available in the

literature for the measurement of spectra

of sky shine of °'-'Co source in the

geometry used in the present work. Mary

Alberg et al^ have measured the spectra

of scattering of gamma by water

and have inferred the scattering by air

(sky shine). But because of the lead

plug (10 cm. diameter x 25 cm length) on the source in the present work, the

geometries of the two works are different.

As a preliminary assessment of the

spectra, the following important points are observed.

i) the counts of the true skyshine

spectra extend upto 400 KeV on energy

scale for all the distances of observatkns.

The geometry of this set-up (Fig. 3)

is such that all photons from the source

and scattered ones from the lead-plug

emanated below the horizontal plane

passing through the source, strike the

gamma field ground or its fencing wall

i.e. photons in a solid angle 2% do not

give any sky-shine directly. Only those

source photons go straight out which are emanated from its near ground periphery

and have their azimuthal angle, <p between

45*^ and 88.5°. The source points

successively higher than this have less

and less range of angles to emanate

photons clearly into the sky. Source

photons other than the above are obstructed by the lead plug.

For the photon with <^ equal to 88.5°

which goes out just above the fencing

wall, to be detect'^jd, it should be

126
scattered vertically down by air to come

in "the field of view" of the detector

i.e. scattered to 90° with an energy

of 353 K.eV, as obtained from the Compton

formiila

! scattered E

1 + —pd-cose)

mc

1 This is the high energy limit of sky

i shine spectrum and due to poor resolution

1 of the detector in this energy region,

' the counts extend upto the channel

corresponding to ~ 400 KeV.

I

I

^

i Fig. 3. G-eometry of photon scattering by

air

The photon with <^ equal to 45°

needs to be scattered by 135° to strike

the detector from a minimum height of

150 m. above it, and the scattered photon

has 240 J£eV of energy. The mean freepath^, for 240 iieV gamma in air is ~ 70

m. This scattered gamma, therefore,

travels more than two mean free-paths

for 150 m, and more than four mean freepaths for 325 m source distance to be

detected. The photons with angles

between 88.5° and 45° when scattered at

appropriate heights by angles between

' 900 and 135° are detected.

ii) At all distances from the source

the nature of the spectrum remains the

same. There is a peak corresponding to

the channel of 72 K.eV. The ratio of

1] counts in the range 64 KeV to 80 KeY

' (taken as 72 KeY peak) with the total

counts of sky shine (Fig. 4), for both

the collimators is obtained as 0.24 + 0.02 for all the distances; however the

I effect of source distance is felt only

j in the count rates.

The 72 'B.eY peak obtained in the

sky shine is very close to the Pb

x-rays (K^^j 75 K.eV) . The spectra were

taken with and without 2.5 cm of Allining inside the detector shield at

155 m so"arce distance. Differences

observed are well within the limits of

experimental errors. Thus, the true

sky shine spectrum observed in the

present work with a pronounced peak at

72 KeV is not related in any way to the

scattering from Pb-shield.

I

1

•

£ 0?:

« 12 mm COLLJMaTOB

ii 010

0 1 . . 150 200

. . 2501 , , , , 300

1 , , J350

Fig. 4. 72 KeV peak-to-total sky shine vs. source distance.:

The inset in Fig. 2 shows spectrum

obtained with ^98^^^ jij^g ^2.2 KeV photon

in the present set-up does not contribute

significantly to the Compton continuum in

comparison to its photopeak. The con- tributions to the respective Compton

portions of lesser energy photons are insignificant. If, therefore, as a first

approximation, the Compton portion be

neglected, about one-fourth of the intensity of sky-shine in vertical direction

comprises of 72 KeV photons.

iii) The total CQ-unts under the skyshine (the intensity of the scattered

photons) follow an exponential decline

with distance from the source (Fig. 5)

The following relationship gives the best

fit with the recorded counts:

I.I X

0

• where x is the source distance in meters

and Iq is the intensity of a virtual

source, the value of which depends on the

diameter of the collimator.

iv) It is also found that the counts

spectrum of the area-skyshine (Fig. 2),

too shows a peak at 72 KeV, but ends

at

^

275 KeV. In the experimental field

wastes containing different radioactive

substances of varying strengths are buried deep in the groiind about 50 m away from the detector, in about 30 cm thick concrete cells which are covered

also V7ith the same thickness of

concrete. These sources also give

sky shine with a peak at the same energy.

Further work ia in progress

127
60 -

150 200 250 300 350 400 SOURCE-DISTANCE fMETERS)

Fig. 5. Total sky-shine counts vs. source distance.

Acknowledgements

The authors wish to thanl-L JVlr. G.H.

Vaze, Head, Electronics Division for the

help given by his staff; i»ir. R.K. Balani

supplied the 400-channel analyser, I4r. C

Gr. Chatur developed and assembled the

Pre-amplifier and matched it with the

analyser through 100 m cables. The help

in the experimentation given by M/s D.T.

Khatri, A.R. Kamath, S.H. Shirke and

K. Somanathan is gratefully acknowledged;

the latter helped in calculations also.

The facility of the source was kindly

provided by Dr. h.M. Desai, in- charge.

Experimental G-amma-Pield Station.

References

1. Swarup, Indian J. Pxire Appl. Phys.

11, 331 (1973)

2. Kinard, I.E., Wucleonics 15 {Ho. 4j,

92 (1957). "

3. Alberg, M. , Beck, H,, O'Brien, K. and

McLaughlin, Nucl. Sci. Engg. 65

(1967). [See also, E.T. Clarke, Nucl.

Sci. Engg. 27, 394 (1967) and Chilton,

A.B., ibid, 403 (1967)J.

4. Hubbell, J.H., "Photon Cross Sections,

Attenuation Coefficients and Energy

Absorption Coefficients from 10 keV

to 100 GeV'iMSRDS - NB3, 29 (Aug. 1969).

128
BACESCATTERINQ OF GAMMA RAYS BY BARRIERS

FROM VARIOUS MEDIA * D. B. Pozdneyev

Gorki State University, Gorki, USSR

Quantitative data about albedo of gamma radiation must be

known to solve some problems of radiation shielding, radiometry, nuclear instruments. Spatial - energy, differential

and integral characteristics of gamma rays albedo for the case

of the barriers of different thicknesses from beryllium,

graphite, aluminium, concrete, iron, tin, and lead were determined both experimentally and by means of Monte Carlo method.

Energies of gamma rays from the point isotropic source and of

monodirectional beam were 145, 279, 511, 662, 1000 and 1250

keV. Spectral - angular distribution of back-scattered gamma

rays escaping from various portions of the barrier surface as

a function of thickness and material of barrier, distance

from the source, geometry of the source and energy of primary

gamma radiation was also investigated. Systematized data

about differential and integral albedo of gamma rays of

various energies for the case of barriers of different thickness from various media are presented in the form convenient

for practical uses. (Albedo; angular,- backscatt ering; barrier; differentials;

distribution; gamma rays; integral; medium; Monte

Carlo)

The

backscatt

barriers

for the 8 radiation

dosimetry

exploitat

cting bac

( such as

etc. )

Introduction

quantitative data about the

ering of gamma rays from

of various media must be known

olution of some problems of

shielding, in radiometry and

, in the elaboration and

ion of some instruments detekscattered gamma radiation

thickness gauge, density gauge

Method

Let us introduce the following

current characteristics of gamma rays

albedo

a(EQ,M^ ; E, e,tf ,X , y, d) is the

probability (per one quajitum with the

energy Eq and angle of incidence vf* to

normal to the plane barrier with the

thickness d) of gamma radiation escaping

from the reflector at the point with the

Cartesian coordinates (x,y,z=0) in the

direction ( 6 ) ( 6 is polar and (f±s

azimuthal angle ) within the \init solid

angle (tne energy of such radiation is

equal to E) . In the cases of point

isotropic primary source with

the reflecting barrier, ana the mono- directional beam withH^= 0°, it is

convenient to introduce the If - coordinate

characterizing the distance between the

source and the studying region of the

reflector surface. Therefore we can write the function

a(EQ,H^ ; E, e, Cp, X, y, d) as a(Eo,y ; E, e,Cp ,r, d)

The spatial spectral albedo

a3(EQ,\p , E, r , d) =

^- //2

dCp Ja(BQ,H/;E,e,'f, nd)sin 6 dO

0 0 characterizes the integrated energy

spectriim of backscattered gamma quanta

escaped from various portions of the

reflector surface.

The spatial number albedo (distribution of reflected ganma. quanta along

the barrier surface) is characterized by

the value

ajj(EQ,v|^;y,d) =

JdE 1 dCp la(Eo,H^}E,e,9,y,d)sinede

0 0 Characteristics of backscattered

gamma rays were determined by us experimentally and by means of Monte Carlo

method

Some examples of ag( E^ ,y ; E, Ai* ,d)

for Eg = 1.25 MeV are presented in

fig. 1. For the sake of clearness all

Presented by Mr. J.H. Hubbell

129
the functions flgC Eg ,y i £,4^* , d) are nor- malized on Icm'^ of the reflector surface.

Fig. 1. Energy spectra of backscattered

photons escaped from various

portions of reflector surface.

Eo=l,25MeV.

a,b,c, - graphite point isod,e,f - iron tropic source

g,h,i - iron, monodirectional

source ( =0°) d=0, Imfp

d=0, 4mfp d=2, 5mfp

While comparing spectra for various

/IT there can be noted the following

points of principal importance: the

portion of backscattered gamma quanta

decreases with the increase of r, the

dependence of albedo on d becomes less

sharp with increase of r. With light

reflectors the increase of radius r is

followed by the enrichment of the energy

spectra with the low energy gamma quanta

owing to multiple scattering in the

barrier matter. It is easy to understand

the deformation of spectra with r increasing (fig. la,lb,lc) taking into

consideration the small role of photoabsorption in such materials as beryllium and graphite. V/ith gamma quanta

scattered at the angles nearing 180°

essential contribution to albedo was observed in the region near the primary

source[Ar=(0-0, l)mfp - fig. laj (and

in this situation the clearly expressed

peak took place in energy interval

(200-300)keV) . With the thick scatterer

essential contribution to albedo was rendered by the multiple scattered quanta

issued from the depth of the reflector.

Albedo from the thin barrier is conditioned by gamma quanta penetrating along the

reflecting surface of the barrier and

scattering at small angles (therefore

they throw down their energy insignificantly see instance the spectra for

d = 0, Imfp)

The low-energy quanta corresponding

to the multiple scattering are more intensively absorbed in the material of

the barrier. Spectra ag(EQ,v|^;E, Ar, d)

for the case of normal incidence of

primary gamma rays beam are characterized

by more finite energy field than in the

geometry of point isotropic source. This

is particularly characteristic for

heavier media. Gamma quanta with energy

lower than llOkeV (for lead lower than

l60keV) are absent in the spectrum due to

photoabsorption. The mean energy of the

spectra of backscattered gamma radiation

for the monodirectional source (normal

incidence) is lower.

In order to determine the meaning of

albedo from the local portion of the

barrier surface Ar (thickness of the

reflector equals d) - a]^(Eo»'+'; •^r, d) the

relative change of this value with d

and aj,(Eo.vV ; ^r.co) .ust be known. Example of dependence on d of

the ratio "uj^o'^ ^ ^J^»d) concrete

oJTe^TH^ } Ar,oo ) and isotropic source of primary gamma

rays is presented in fig. 2a. Fig. 2b

characterizes the change of spatial

spectral albedo ag(EQ,S';E, Ar,d) for

E = (10-160) kev with thickness of

barrier d. The accumulation of lowenergy gamma quanta due to multiple

scattering extends the range of change

of the value ag(Eo,H' ;E, Ar,d)/as(EQ,H' j E, Ar,oo). with d for greater distances

r

The analysis of the received data

shows that the dependence of albedo on

the circular regions of the semi-infinite

reflector surface ajjQ(Eo,4^; t,oo) on r can be described by the following empirical formula (with accuracy + 5a )

(1)

where aM( Eq .H^ ; cv) ) is the number

albedo from semiinfinite {6.-*°^) scatterer

with an unlimited area of the surface

(r_^oo). The values of aN(Eo,S';'^, oo

)

130
1 2 dtmfp)

Fig. 2a and 2b. Albedo from local portion

of reflector surface (in

arbitrary units) as function of barrier thickness

d. Cs point isotropic

source

a - E = (10-652)keV, b - E=(10-160) keV

1 - r=(0-0,l)nifp, 4 - r=(0,5-l,0)mfp,

2 - r=(0,l-0,2)mfp, 5 - r=(l-2)mfp,

5 - r=(0,3-0,5)mfp, 6 - r=(2-5)mfp.

Table 1

Values 0*;( Eo* H' |<M t oo) and ^

for concrete (aluminium) and 'Z^^O tS&2l^ev

,

Source geometry

Point

ieo tropic Monodlrectlonal

( y =0")

a^i 6o, ^ )CD ,00) 0,'»36+0,002 0,42+0,04 (exp) 0,242+0,002

f> (nfp)-'' 0,83 1 ,06

are given in Table 1 for concrete (aluminium) according to the results of the

experiments and of our calculation by- Monte Carlo method. The values p for

the calculation of a]^jc(Eo»H^} r, 00)

according to the formula (1) are given

in the same table. It is easy to see that a^{Eo,H^ ; ^r,oo) { Ar=r2-r±) can be

found as

The joint use of the formula {2) and

graphs which are analogous to those on

fig. 2 permitted to determine the dependence of albedo from local portion of

reflector surface on the thickness of the

barrier.

131
GAMM RAY STREAMING THROUGH AI^WLAR GYIIWDRIGAL DUCT

K.P.N. Murty, R. Vaidyanathan and

R . Shankar Singh

Reactor Research Centre

K:alpakkam-603102

Madras, India

In this paper we present the study of gamma ray streaming

through an annular cylindrical duct from an infinite plane source.

A rigorous formulation based on the ray-analysis procedure has

been developed to compute the resultant dose in the vicinity of

the duct exit, A parametric study has been carried out to

evaluate the accuracies obtained with the present rigorous

treatment as compared to the simple formula developed for handcalculations. Attempts are being made to incorporate the

scattering component to the dose at the exit, in our present study.

(Annular,- computation,- duct 5 gamma ray; integration; kernel;

radiation-, streaming)

Intro duction

Radiation streaming through ducts

is an important and difficult problem

in nuclear reactor shielding. Methods

of computing the streaming flux through

straight cylindrical ducts have been

reviewed profusely by many peop2.e-'-~5

,

Only a few attempts have been made in

the study of radiation streaming

through annular cylindrical ducts. This

problem is of importance in reactor

shielding, where one encounters

cylindrical plugs with annular gaps all

around. We present here a rigorous

analysis of the problem of gamma

streaming through annular cylindrical

ducts using Ray-tracing procedure

coupled v;ith point-kernel integration.

Formulas for Uncollided Flux

Figure 1 shows the configuration

of the duct with an infinite plane source perpendicular to the Z axis at

the duct entry. The source is divided

into 3 regions, flegion 2 is further

divided into two sub-regions, 2A and 2B.

Region 3 is divided into 4 sub-regions 3 A, 3B, 3C and 3D. Let the uncollided flux

from each region he<p^ii - 1,2,3) • 3 The

total uncollided flux is then 0 = $1 S^- L=i Assixme an axis passing through the

dose point and parallel to the central

axis of the duct. Let the separation

of the tv70 axes be 'a ' , the inner radius

of the duct RI, the outer radius of the

duct RE and the duct length L. Let the

angular distribution of the gammas from

the source be given by, S = (n+l) cosh^/4Tt

where f is the angle between the direction of the photon and the Z axis. The

spatial distribution of the uncollided

flux at the duct exit is evaluated as follows

Fig.l.

Case 1

a .

1

1

1

1

Annular cylindrical duct and the source regions.

J

rdr

%32
^,=^ fl'^expU(r^^L')^(Rl/r)i

^ n±l L fcexp ^-^(ritL^,)^(r4/r}

^2 2 (^2^^2)1+^/2 ^ 1P2A2U J J,^ (^2^j^2)i;n/2

o ^

r L"exp{-n(r2+L2)^(l+gInRl)] ^^i^ere r'^r^ when e<e

^ ' ^Re (r2.L2)lW2

r^=r„ when e>G ^ ' o Case 2 a 4Rj €t L^'exp J-^(r2+L2)^ (fi^fj^)?

^,=f±i 1^9 ' L:iexp{-.(r2.L2)i(.,/.4^ o o (r .L)

° ^1 (r'^+L^)^^^/^ J ^ ^ 2 2 4- ^_=ii±i f def L exp -^.(r ^-L")^ ^

11 Ti f ? ? 4 ^1-^? 7 5B 271 J J . 2^2Nl+n/2

fj'^J'^^ rjT27l7H72 e; y L"exp -,.(r2+L2)%+4^)

Case 3 Ri <a4IlE 6^ ^ / 2 ,2,^^ ^i:;^^::^,

2.L2)^(l.r,/r)L ~ ° (r2.L2)l-/2

o

K J "tjig above formulas

% = a cos e + (R^2_j^2 c-^y^^Q^i

p 2 2 4- = a cos e + (R-g'-a sin

= a cos e - (Rj-~a2 sin2G)^

de ln(l+(r'/L)^ n = 0 2 2

Where r' = r^ when 0^©<(eo

r^ = a cos e - (Rg'^-a^ sin 0)"^

= sin"l(R /a) - sin~l (R^a)

o 10 E

Refer to the 2A component of the

total uncollided flux at a = R^ in the

r' = rp when ®^6q duct exit plane considered in case 3.

For an isotropic source (n=0), this

component can he approximated as follows:

2

•! (r +1 j

' . u

I P'or a duct whose radial dimensions are

3r small compared to its length,

d r-li±l Iao f L'^exp{-^(r2+L2)^(l-r2/r)j „.„ ln(l+r2/L2) r2/L2 and ln( l+r2/L2 )s.r2/L2

"3 271 J^Jy ( 2 T2Nl+n/2 Substituting thd expresions fo? anQ

00 i {r +1j ) integrating, we get "4 % to f3D=^. [ddf L%xp(-^(r2.L2)^(l.^\^^ ^ ,

- Co.-lfR /R ) j J (r2.L2)l--/^ #2A=-72FR ^-R ,) Cos (R^/R^) case 4 a RE -rx, ; ^« ^^-j^ en rJ

Vexp -,(.2,,2)i(i,^^) -H, fK^2_,^2

^3 (r2+L2)lW2 -

133
Calculations and Results

Calculations were performed using

the formulas derived in section 1. The source considered was "'-'Co and the source angular distribution was considered to be

isotropic (n=0). Various ducts in lead

shields were studied. A part of the

results obtained is presented in Fig. 2.

0 3 5 10 fi

I— —-I I ^, .

I D/S TANCl (cms)

Fig. 2. Total dose-rate distribution in

the duct exit plane.

Fig. 2 shows the total dose distribution in the duct exit plane for a duct

with the parameters as follows: Rj = 3 cms, Rg - 5 cms, L = 6 to 60 cms. From

a = 0 to a = Rj , the total dose

increases; the increase is steeper for

longer ducts. It remains practically

constant in the annular region and falls

down rapidly for longer ducts

beyond a = R-g, reaching a constant value,

given by infxnite plane source and slab

shield of thickness of L cms. In the

annular region, thegdose is approximately

proportional to l/L .

:''ig. 3 depicts the relative

contribution of the various components

to the total dose for a duct of Rj = 3 cms, Rjj - 5 cri;s, L = 6 cms. These

components are denoted by Dl, D2A, D23

etc. At a = 0, D3 predominates. This

accounts for 50/. of the total dose for

L = 6 cms and 64/. for 1 = 60 cms. D2

contributes approximately the same

fraction of the total dose (25X to '55'/.) for all duct lengths. Dl contribution

falls doim rapidly with increase of duct

length (14.3/- for L = 6 cms to less than

.OOlX for L = 60 cms)

as * "

' Rj I DJSTAfJCC (cms)

1' ' -I

Fig. 3- Contribution of the components to

the total dose.

When 'a' increases from 0 to Rj-, Dl

decreases while D2 and D3 increase - D2

increasing more steeply. For longer

ducts D2 increases more rapidly with 'a'.

In the annular region D2A is the

most predominant component. This comj ponent alone accounts for about 65/- of | the total dose for a duct of length = 6 cms. For a duct of length - 60 cms, it j accounts for about 99X of the total dose.

For longer ducts, the simple formula in

section 1 which approximates the 2A

component will provide a good estimate

of the streaming flux. For shorter ducts

components 2A and 3C together, will

Drovide a good estimate of the streaming

flux. For a »R^ Dl, D2A, D2B, D3C

and D3D decrease with distance; D3A

increases slowly and reaches a constant

value. D3B also increases and reaches a constant value. Of these two components

D3B is the predominant one. It accounts

for 92*/. of the total dose while D3A

accounts for about 8% for longer distances (L = 6 cms). This shows that for

'a'^ R-g, the presence of the duct has

little influence on the total dose.

Referenc es

1. Rockwell, III:Reactor Shielding

Design Manual, McGraw Hill Book Co.,

New York (1956)

134
Price, B.T., Horton, C.C. and Spinney,

K.T., Radiation Shielding, Pergamon

Press, ::ew York (1957).

Tsuruo, -Lkira-, Shindo , i-iitsuo;

Zawabata, I-Iasahiro, Journal of

iluclear Science and Technology, 2 (4) P. 121 - 126 (April 1965).

4. Tsuruo, A., Shindo, I-I. and Kawabata,

Journal of Iluclear Science and

Technology, 2 (9), P. 325-330 (Sent.

1965)

5. Shindo, I-I. Tsuruo, A., Lliyasaka,

Shunichi et al, Nuclear Science and

Engineering 27, 450-463 (1967).

135
MULTIPLE SCATTERING OF 12 TO 40 MeV HEAVY IONS

THROUGH SMALL ANGLES

B.W. Hooton and J.M. Freeman

Nuclear Physics Division

AERE, Harwell, Didcot, U.K.

and

P.P. Kane

Physics Department

Indian Institute of Technology

Powai, Bombay-400076 and AERE, U.K.

Collimated beams of heavy ions were allowed to pass through

thin foils. The angular distributions of the transmitted beams

were measured with a position sensitive silicon detector. Oxygen,

chlorine and iron ions of energy between 12 to 40 MeV were used

in conjunction with carbon, aluminium, nickel and gold foils of

thicknesses between 12 to 250 |ig/cm2. Values obtained for the

half-angles of the distributions at half height are in fair

agreement with the recent theoretical predictions of Meyer (1971).

The data deviate substantially from the values calculated on the

basis of the Moliere theory (1948) and even more markedly from

those based on the theory of Nigam, Siindaresan and Wu (1959) • Reasons for the success of the recent Meyer theory in the

interpretation of the new data will be clarified.

(Angular distribution; foils,- ions; chlorine; iron,

oxygen; measurement; moliere theory; scattering;

multiple.)

Introduction

An experimental investigation of mul-'

tiple scattering of heavy ions in foils

is important not only for the basic

atomic physics interest, but also from

the point of view of a detailed understanding of the behaviour of ion beams in

targets used in nuclear reaction studies.

Further, since foils are used for

stripping in the high voltage terminals

of tandem accelerators, and terminal

voltages of twenty or even thirty million

volts are now considered possible, such an investigation is likely to be useful

in the estimation of beam emittance in

future accelerators. We are not aware of

any published work in relation to heavy

ion multiple scattering in the energy

range from about 5 MeV to 70 MeV. In the

literature a study-'- on multiple scattering has been found at aroirnd 4 to 5 MeV.

An investigation^ with a photographic

plate has been made of the multiple

scattering of fission fragments with

kinetic energies of about 81 MeV.

164 MeV oxygen ic. 3 and 400 MeV argon

ions have also been used in another

experiment^ using a similar technique.

Experimental Details

The experimental arrangement is I shown in Fig. 1. An analysed beam from ! the tandem, after passing (in some of thi experiments) through a 0.5 ^m Ni foil to j produce a umiform and adequately i attenuated forward beam, was collimated | by two rectangular apertures 4 mm high [ and 1 mm wide, with a spacing of 124 cm. The beam then passed through a target

foil mounted in a scattering chamber on

a moveable arm which could carry upto

three foils at a time. After multiple

scattering in the foil, the diverging

beam passed through a 202 cm length of

beam pipe to a position sensitive

silicon detector (PSD) with an active

surface of 5.0 cm by 0.75 cm mounted wit

its long axis horizontal. The amplitudes f of a pulse taken from the end of the

resistive surface layer of the detector ; was a measure of the position along the

detector at which an individual ion

impinged. From the distribution of the

scattered beam along the line normal to

the beam direction and the measured )

oi distance from the foil to the detector, ) c( the angular distribution due to multiply pj

) 5a

' 1 pe Ma

I re:

136
Fig. 1. Schematic plan view of apparatus.

scattering in the foil was simply obtained,

In order to prevent pile-up distortion

and damage in the PSD, total counting

rates were limited to 500 per second or less. The target foil could be rotated

about a horizontal axis so that its

normal moved from the direction of the

ij; coo

beam through an angle upto 70 Thus

the effective foil thickness seen by the

beam could be varied from the actual

thickness t to a value of almost 3t . The

thickness of the target foils were

measiired in a separate Rutherford type

scattering experiment. The mean thick- nesses of the scattering foils in |ig/cm

turned out to be 12 for carbon, 41 for

aluminium, 45 for nickel and 127 for

gold.

Figures 2 and 3 show typical spectra

obtained with the PSD detector. In

Fig. 2, we see spectra obtained with a 12 tig/cm^ carbon foil and an Fe beam

Fig. 2.

tf^— Soof CHAnc >u«a£R

Scattered spectrum obtained for

37 MeV Fe beam with a) no scatterer b) carbon foil placed

normal to the incident beam

c) carbon foil rotated through

60°.

of 37 MeV (calculated energy at the

center of the foil). Fig. 3 shows the

PSD spectrum obtained with 12.5 MeV

oxygen ions on 50 [ig/ cm alumini\im and a Gaussian fit attempted near the central

peak. Fig. 2(a) in fact shows the

natural width of the beam obtained in

this experiment without any foil scatterer. The half width at half height of

100 200 CHANNEL NUMBER

Fig. 3. PSD spectrum obtained v;ith 12.5

MeV oxygen ions on Aluminium with

an attempt for G-aussian fit at

the centre of the peak.

this peak is around 1/4 mm. The spectrum

in Fig. 2(b) was obtained with the plane

of the carbon foil normal to the beam.

The width due to multiple scattering in

the scatterer was obtained by subtracting

quadratically the 'foil out' width from

the observed width. Fig. 2(c) shows the

distribution obtained with the foil

rotated through 60° so that the effective

thickness seen by the beam was doubled.

The half angle of scattering ©1/2 is

defined as that corresponding to the half

vfidth at half height of the observed

distribution, after correction for the

'foil out ' width.

The overall uncertainties in the

half-angle results are estimated to lie

between + 5/. and + 20/. . The accuracy

of the target thickness measurements was estimated to be + 5/. for aluminium, nickel

and gold foils, and + 10/ for the carbon

foils.

Discussion and Conclusions

A comparison of a few typical values

of meas\ired half-widths with those^

calculated on the basis of Moliere and

NSW^theories is presented in Table I. The NSW calculated widths are larger than

the measured values by more than a factor

of two in most cases. The Moliere widths

137
Table I A comparison of measured values of ©1/2 with those

computed on the basis of the Moliere and the NSW

theories

Ion Ener^

( MeV j Targetfoil

Target

thickness

( ng/ cm^

)

Moliere

calculated

( degrees;

NSW

calculated

(degrees)

Measured

ei/2

( degrees

)

0 12.6 C 12 0.0782 0.110 0.054

0 12.6 C 35 0.142 0.200 0.110

0 12.6 Ni 45 0.470 0.162

0 21.8 Ni 45 0.262 0.099

CI 13.0 C 12 0.175 0.260 0.100

CI 21.8 C 12 0.104 0.155 0.066

Fe 37.3 c 12 0.096 0.140 0.043 ^ Fe 37.3 Ni 90 O.56I 0.820 0.241

are closer to, but substantially larger

than, the measured values. Serious

disagreement with the NSW theory had

previously been noted by Kerr et al^

in their studies of multiple scattering

of fission fragments of 81 MeV energy

from silver and gold targets {94 4 ^ 4 848).

These authors had tried successfully to

restore agreement with the Moliere

theory by the replacement, in the theoretical formulae, of the primary nuclear

charges of the ions with their effective

charges. Bednyakov et al had made a similar attempt in the course of the

analysis of their experiments with 4 to

5 MeV nitrogen and oxygen ions on aluminium ( oC:^ 30). In a study of the

scattering of I64 MeV oxygen ions and

400 MeV argon ions from zapon. aluininium,

nickel and gold (2 .9 <: 30.8) , Simon5

had noted that the NSW theory gave widths

that were upto 60/. too large.

In order to compare our data with

the Meyer theory, the experimental ©1/2

and t values were converted to 61/2

and T values. The resulting values are plotted in Fig. 4. The full curve represents Meyer 's^ theoretical calculations.

The error bar shown on one of the oxygen

on carbon points is an estimate of the

total experimental error, which was larger for carbon than for the other

foils. The overall agreement with the

theoretical curve can be considered to

be satisfactory, within the experimental

uncertainties. However, the possibility

of a z-]_ dependence is not excluded, since

the iron widths tend to lie slightly

below the theoretical curve and the

oxygen points are mostly above it.

A more detailed report will appear

elsewhere

REDUCED TMICTNESS T

Fig. 4. Comparison of experimental

values with theoretical

calculations

References

1. Bednyakov, A. A. et al., Zh. Eksperim

i Teor. Fiz. 50, 589 (1966); Soviet

Phys. JETP 2^7^91 (1966).

2. Kerr, D. et al, Zeit . Naturf. 22a,

1799, (1967).

3. Simon, W.G., Phys. Rev. 1^, 410,

(1964)

4. Moliere, G. , Z. Naturforsch. 2a., 133 i (1947).

5. Nigam, B. P., Sunderasan, M. K. and

Wu, T, Y., Phys. Rev. 115 , 491 (1959)

6. Meyer, L. , Phys. Stat. Sol. 44b, 253

(1971).

Discussion

B.K. Godwal

How do the quantiim mechanical

effects appear only after a certain

energy ? |

138
P.K. Kane

The important paramet.er is tiie ratio

of the de-Eroglie (reduced) wavelength

to the significant dimension i.e.

collision radius in this case. When this

ratio exceeds unity, quantum mechanical

theory of scattering has to be applied

of course, there is no sudden transition

from the semi-classical to the quantum

mechanical situation. V/hen the above

mentioned ratio is comparable to unity,

the problem is quite complicated.

S. Kukher.jee

1) has the scattering been considered on the basis of unscreened - or screened Coulomb field ?

2) How is the effective charge of

the ion taken into account ?

P.P. Kane

1) The ion-atom interaction

includes a screening factor.

2) The Lindhard prescription for

calculating the parameter a, the

screening distance, is supposed to take

into account the ion-atom interaction

fairly well.

If

139
CHARGED PARTICLE TRAl^SPORT IM ONE-DIMBNSIOITAl

FINITE SYSTEMS

G. Muthukrishnan , K. Santhanam and D.V. Gopinath

Health. Physics Division

Bhabha Atomic Research Centre

Bombay- 400 085

India

A semi-analytical technique for the charged particle

transport in one-dimensional finite media is developed which

can be applied to multi-energy mult i- region systems with

arbitrary degree of anisotropy in scattering. For this

purpose the transport equation is cast in the form of coupled

integral equations separating spatial and energy-angle

transmission. The spatial transmission is evaluated using

discrete ordinate representation in space, energy and

direction cosine for the particle source and flux. The

collision integral is evaluated using discrete ordinate

representation in energy and legendre polynomial approximation in the direction cosine. A computer code based on the

above formulation is described.

(Anisotropy; charged particle; computer code; energyangle; integral; legendre polynomial; scattering;

semi analytical; spatial; transmission)

Introduction

The popular method for the study of

charged particle transport is the

MonteCarlo method in which the history

of each particle is traced from the point

of its origin to the point where it is

absorbed or till it comes out of the

medium. Because of the many kinds of

interactions involved, computer time

needed will be quite considerable. To save computer time, condens edl case histories are studied where a random

walk takes into account the combined

effect of many collisions.

By solving the transport equations,

one can study the particle transport.

Barish et al^ have studied the transport

of alpha particles and protons by

solving the transport equations. In

their study nuclear reaction products

are neglected.

This paper describes a method of

solving the transport equations for the

charged particles. This is mainly based

on the method developed for gamma ray

and neutron transport studies^. To

solve the equations, discrete ordinate

representation in energy and spatial

transmission and Legendre Polynomial

approximation in direction cosines are

used. Source and flux terms are calculated at discrete angles but for

evaluating collision integral, Legendre

polynomial approximation is used.

Continuous slowing down approximation is

used to fix the meshwidthe which

correspond to different energy losses of

the incident particles as they traverse

through the medium. Angular straggling

is neglected in the studies.

Mathematical Formulation

Let S(x,E,iJ.) and if)(x,E,|i) represent

respectively the source and flux at

position X with energy E and direction

cosine p.. At equilibrium,

(|)(x,E,^) =

j Js ( x', B', iJ. ) T ( x'-^ X , e'^/, ]x ) dE'dx'

-

'

. . ... (1)

S(x,E,n) =

]J(^(x,B',tiOG(x,E^E, -^^^^)dEclXi.'

... (2)

T(x^x,E''-*E,ia) =

- :^(x-^ ^

6(2=x',f(E',E)

... (2a)

*Present Address :VEC Project, Bidhan Nagar, Calcutta-700 064

140
G and T represent the energy-angle and

space transmission kernels respectively.

The 6 function in equation (2a) represents the reduction in energy corresponding to the distance travelled. Because

of this relationship, eqn. (1), after

spatial integration reduces to

Evaluation of the flux Terms The flux ^(x-,E , [a) is given "by

r^,A) /E,^) e

0(x,E,^) = Js(f(E'),E'.n)rT-^^ ' '^ ^

... (3)

-Kx-x)

e P represents the space transmission

kernel. In the transport study the mesh

widths are so chosen that the delta

function conditions are always satisfied;

in other words, one can always find a source at x' with energy E' such that by

the time the particle reaches the

position X without catastrophic collision

its energy would have been reduced to E. If x' and E' are the initial position

and energy of the charged particle and

X and E are the corresponding final

values, then

x-oc/ _ f' - dE ... (4)

_ _ ej_NJ. U(2tn^-uyil ..(5)

where the various notations have the

usual meaning. Equation 5 can also be

rewritten as

-If = iT^(K'E') (6)

substituting this in equation 4,

'X.--X. _

KK'^ I ... (-7 As stated earlier we make discrete

ordinate representation in E and

Legendre Polynomial representation in |i as follows:

S(x^,E^,^) = "Z:^S^(x^,E.)P3_(u) .

^(x^,E.,n) = r^^^(x^,E^)P3^(u)

. (8)

the

Legendre coefficients of the source ajid

flux respectively corresponding to the

spatial position i and energy group i

3-,(x.,E.) and 0i(x.,E.) are

ire coefficients ox the som

Ei.Ev+i

. (9)

wlie

Here X represents the macroscopic

non-elastic scattering cross section.

f(E', Eg) can be linearly interpolated

between En-'s as f(E',E^) = a + bE' (12)

0-= {Ei(2lrvK'E^,)--Ei(2UK^Eg)-||[ E

1 kK'2- AEl (13)

(14)

To start with, while computing, the

medium is divided into various energy

bins and into corresponding meshes for one particular direction cosine of say

[i = 1. Thus there will be one to one correspondence between the energy bins

and the mesh vfidths, when the source term is interpolated linearly for energy

and space transmission in that direction.

But this no longer holds good at other

direction cosines. Hence the following

procedure is adopted. Fixing the energy

groups say Eg' and Eg' +1 for contributing to the flux at xj , the minimum and

maximum distances that particles have to

travel so that the delta function condition will be satisfied, are computed

using equation 7.

Thus the locations of the particles

can be calculated. They may be either

in one mesh group or in two adjacent

groups. Taking a general picture, let us assume that the locations are in the

adjacent mesh groups say between xj

and Xj ^^'^ -^j '+1 ^'^^ -^i '+2 corres- ponding respectxvely to the two energy

limits Eg' and Eg' +1. Then the linear

interpolation of the source term can be

carried out follows : , , v / \

E^g'+l-E^/ . . .(15) Using linear interpolation of

S(x',Eg'+]_, li) and S(x',Eg',!a) in

spatial co-ordinate and converting

spatial parameters into energy parameters

using 12 and after substitution in(lG)

and integrating we get

141
Zb

(16)

where A, B and C are constants, depending

on Eg's.

C alculation of Source Terms

S(x. ,Eg,!i) = Jj0(x,E',u' )G(x^,B'-^Eg,^-^^)

dE'd-O.' ... (17)

V/here G is the energy-angle transmission kernel. G can be split up into

tvjo terms and Fp, P-j. I'epresenting the

probability that the energy of the

particle changes from B' to Eg as a result of scattering and E2 I'epresjenting

the probability of the direction changing

from O.' to XI due to scattering.

.•

. G( X . , E Bg,Xl.^-n.)=Fj( E '-^E ) ^2 (-

After Tucker

''Eg)

( -a-<-=>-0-)

-ne dE

0.478656^^^0"-'-^

(18)

(19)

(20)

Where is the energy spectre of the

secondary particles and |j.o is the cosine

of the angle betv:een the emitted and the

incident particles, that is between JCI and-^- 'Sine is the non elastic scattering

cross section. Equations 19 and 20

together give the differential spectra

of the cascade particles. The evaporation process is not considered.

The angular distribution can be

represented by

e3(no-l) = Z a^P^da^)

1=0

... (21)

where a.^^ is the Legendre coefficient and

is given by

+1 ai = ^

J'e5(i^o-l)p,(,,) d^,

replacing ^(xj,E',ia')

by Z<ifex.,E') P (n') we get

Pl(^o)=Pl(n') .Pl(^i) ... (24)

Expressing S(xj,Eg,ii) in terms of

Legendre coefficients, we get

E SnvC^i'Eg) P^(^) = 0.47665 ZaJJc^^Cxj.E') . Hv(/u')

WPtHln.''al^^'^^^'^'"'...(25)

i-Iultiplying 25 by Pi(|J.) and integrating

over (i

Sj(x., Eg) =0.47865 T^a^ Jj^n^^j'^'^

X l^g ||(E')xPj_(n')P^(|i')dB'dn'

. E,, (26) = 0.478.5 IS^.I j 0J-J.E'}r.et(E'A

... (27)

<^(*j>£^and |^(E') can be linearly interpolated between Eg' and Eg'+l. The cross section is assumed to be constant

between Eg' and Eg'+l.

(23)

Substituting for ^^(x^.,E') and f|(E')

and integrating over Eg's, we get

- ^3'+'*'^a'+i/2 . •• (30a)

c. = t^''i'h')^i(^r) ... (30b)

(22)

substituting 19, 20 and 21 in 17 and
C - /a- P ^ A(dFl/d£)

+ ^(Eg,).^ ... (30c)

C 3 - ^ "Al '3 - A (aN/4t)

. (30d)

I-Iethod of Computation

Dividing the nedium into various

meshes, such that the variation in

2 W(K'Eg) is uniform, the transmitted

flux is calculated at various meshpoints,

The angular straggling is neglected in

this case. Having computed the

uncollided flux, at various mesh points

the first collision source terms are

computed analytically at these mesh

points for various direction cosines.

Then iteration is carried out .

In integrating the right hand side

of equation (4]l the relativistic correction to the dii/dx formula is not

included; however this correction also

can be incorporated in which case also

the integral can be carried out

analytically

Conclusion

This paper describes a method that

is being developed to study the proton

transport through various media. A

computer programiie is being developed for

this method.

' - References

1. Adler and Pernbach, "Methods in

computational Physics"

2. Barish, J., Santoro, R.T., Alsmiller,

F.S. and Alsmiller, E.G., Jr.

"Trapp, a computer Program for the

transport of alpha particles and

protons vrith all nuclear reaction

products neglected"ORWL-4763 (1972).

3. Gopinath, D.V. and oanthanam, K.,

rluclear Science and Engineering

42, 186 (1971)

4. Yucker, V/.R., "Empirical formulae

for secondary nuclear production

cross sections" Proceedings of the

special sessions of Accelerator

shielding. Presented at the 1965

V7inter meeting of the American

Nuclear Society AI^S-SD-3(1965 ) .

143
PASSAGE OF HEAVY CHARGED PARTICLES THROUGH MATTER

Shankar Mukherji and Brijesh K. Srivastava

. " . Department of Cjhemistry

Indian Institute of Technology

Kanpur-16, U.P., India

The energy loss of charged particles (much heavier than

electrons) at energies where electronic collision predominates

may be studied conveniently by separating the particles into

two groups : completely stripped particles and partially stripped

particles. Bethe's quantum mechanical stopping power equation

is of limited applicability for the first group of particles and

inapplicable for the second group. A general stopping equation

valid for all ions upto relativistie energies has been developed

which predicts the experimentally measured stopping powers and

ranges of partially stripped heavy ions accurately. Prom the

detailed analysis of the equation a simple formula to predict the

number of orbital electrons with velocity less than a given

velocity in an element of atomic number Z has been developed.

Assuming the above equation to be valid for all the orbital electrons

except the two K-shell electrons, it has been possible to calculate

the mean excitation potential for any medium.

(Charge; charged particle; collision; electron; ionic

charge; ionisation potential; stopping power; stripped

particle; velocity)

Introduction

For a completely stripped and com- paratively light ion like a proton or an alpha particle moving with velocity V

the energy loss per unit path length in

a medium containing n atoms per unit

volume is given by Bethe's-*- equation:

^ - 4tiZi^ e4 n 2mV^ , mV

In the above equation, I, m and e signify, respectively, the mean excitation potential of the medium of atomic

number Z2, the mass and the charge of

the electron, and Z-[_ is the atomic number

of the moving ion. Mukherji and

Srivastava^ have shown that modification

of a semi-classical stopping-power

equation of Bohr3 leads to a general

stopping-power equation valid for partially-stripped heavy ions like the

fission fragments. However, neither of

these equations holds for many ions which

are heavier than alpha particles (i.e.,

^ S, -'-"0 etc.) at energies which are too

low for the use of Eq. (1) and too high

for the equation of Mukherji and

Srivastava^. This work attempts to

present general stopping-power equations

appropriate for different ions at

energies at which electronic collision

is the predominant mode of energy loss.

Formulation

Bohr's^ semi-classical stoppingpower equation is

ff = np^{z:3(in.5ixr^.r3(in

...(2)

in which the symbols stand for:

^2nz!el ^. iV^,^,^'2,Z£ ...(3)

Further, ze is the charge of the particle, V its velocity, Ug is the orbital

velocity of the si^ electron of the

medium and Vq = e^/ti; m and e are the

electronic mass and charge. The terms

within the square brackets, if less than

unity, should be replaced by unity. The

summations were replaced by Bohr^ with

integrals

^ (in .2uj-2) (in ri^L^J"!) .

's X (In 'n^Lxj~^)dn (U ) + y (In

[^J"^)dn(U ) ...(4)

144
where n(Ug) is the number of orbital

electrons of the medium with velocityless than Ug. It has been shown^ that

in general, for a mediiim of atomic

number Z^, nCUg) is given by

n(Us) = f(Z2) Ug/V^

2/3,

...(5)

where t^l^) = 0.28 ^for Z2<45.5,

...(6)

and f(Z2) = l^^^foT Z^;^ A5 .5 ...(7)

The integrals in Eq.(3) may be written

as three integrals keeping in mind that

[x/Tig]-l = 1 for (x/rig) < 1,

j(ln n dn(U ) +

f (In Ti 2

. s s

dn(U ) =

f(Z-) u' o o

[ ;^(ln ri/[x]-2) dUg + 5

0 0 o

U " (In rig2)dUg + ln(iig3 ^-1) jiUgJ

2Vx

-1

(8)

Designating = J^(ln r^^^lx]-^) dUg.

2Vx-1

= / (m

U " s and = f (Inri 5 dU , Eq.(2)

2Vx

becomes

dE 27.^2 e^n ^^h^

dx 1,2 mV Y

( J-]_ + ^2 "^3'

...(9)

The upper limits U^' and U " must be

fixed corresponding to the actual physical

situations so that the integrals make only

positive contributions towards the

energy-loss. The following cases may be

considered:

A. x> 1

(a) V>

^2^0-

Since x> 1, for V>

Z„ V X

2 o

J, would

include all values of U upto the Velocity

of the K-shell electron which may be taken

as Z2V0. Since (il)^ = 2mV^ where Ig is

Is th the ionization potential or the s

electron, one obtains: . ... .

.

s 2 o

^1 =

ZoV, {ln(§I)2Uu„ = ^2-0

In2mV

s flZ^

...(10)

in which T stands for the mean ionization

potential of the medium of atomic number

Z^ and is defined by

s=Z2

Z In ...(11)

s=l

Z2 In I

Z V

As for J2, since , in i^)^

would be positive for all possible values

of U„. Further, since the lower limit

for Ug in is 2Vx~ and this already

corresponds to the highest possible value

for Ug(= Z2Vq), becomes redundant.

Thus

,

2Vx~-'- 7 „ 2

J r r n /2Vx2| ^2^0 -, 2mV J. = C ^ in(u-) jdU^ = In—

...(12)

= 0

(b)

^2^0^ —> V

^2^0-1/3

o . \ n 2 p \ 2 o \ 2 o Since x^l, —2 /

2 /"2 one needs to consider all the three integrals. In the case of Jn , for a given V

the term Ini^^) would be negative

s -1

for all values of Ug lying between 2Vx

and 2.2^ Hence one must use Ug'= 2Vx~-'-

145
and get For x<(l, becomes superfluous,

t.tk-;t^ t- t ^v„«^jjjg

/ while J]_ and become identical. identical,

= I

ln(§X)2 = 4VX-1 ...(13) J,=J2=j-ln(§I)2 ^^^^ _2o 2mV_ ,_,(^g^

s J s

Since 2Vx~''"<^ ^2^o' "^2 ^'^^^ (b) ^2^o

include all possible values of . Hencej,

_-]_ ,. In this case J-. or J„ requires an 2Vx appropriate upper cut-off value for U

=

) |ln(^)^jdUg = 4Vx~-'-(l+lnx) Thus,

Q which makes the logarithmic term zero.

..(14)

In the case of J . one finds that Jt=Jo= f |ln(^)^[dU =4V ...(20)

7.-V ^1/3 J-^yC u^^s

U„"= Z2V„ if V = ^2"^o 0

Hence Comparison with Experimental

' U "=Z V Stopping-power Data

s^ 2 0 = \ 3 -ll (^TT Mr') ^^'^ convenience, the various

2V I'^ s'^^J s •••^5; stopping-power equations obtained by

putting the values of J^, J 2 and in

T-.v. J.T T4.- j.T-4.- Eq.(9) are shown below:

In the actual evaluation of it is m. convenient to consider separately the

contribution of the two K-shell electrons

from that of other electrons with ^ Z^V^x ^-^ /i^„2^4^v„ 2mV^

A. xy 1

velocrtles"usy2fx-r"^Thu;7

""""

(a) V_) || = ^^^^2''^^ In- (Z2-2)Vo , • ... (21)

J,= ^r^2 ^ln(P)VlldU^ . Z.V^x, ^^Z,V^xl/5

-1

2Vx~ ^t:. o 2 4 f(Z,)

01 i'r2V_s3 -ll =

'^''^ ^ ^ L3(Z,-2)+3(Z„-2) In,, /i o\ -

+ 21n<(

^

' y

)^x

J ...(16) dx ^^2 "-^^2 ' 2 Vo(^2~^

^ 2 0 2f ( Z )

V

where the velocity of the (Zg - 2)th 6ln(Z,V )-Z„ Inx 1 ^

-f^Z^ ln(2V)j

electron, co\mting the outermost electron ' 2 0' 2 V^x ^2

as the first one, is given by U„ = ( 00)

(Z2-2)Vo , ^/ „ v— as obtained from Eq. (5). 7 v 9 a r( 7 ) ^^^2' ' ( r.) 2 0 , dj _ 4Tiz^e^n .tl^21 .

(c) V<(

Z2VQ ^'^^ 2 • dx ~mV^ - (3x-l/5^x-l)

In this case both and would ^ require upper cut-off values for U and ...(17)

has been considered by Mukherji ana Srivastava:2 A. x<^l

dE _ ilEzVn f{Z2± (3x-l/5^x-l) , , Vo . dE 4uz^e4n , , 2mV^

2 V V/ 2 • dx~ j^y2 ^2 J ° ...(17)

1. x<l, (a)

^2^0 "

. . ...(23)

146
(b) V< dE

dx

16 z en

^Tr2 V m V o fiz^) ...(24;

The term z which figures in these equations

explicitly as also implicitly through the

parameter x stands for the "effective

charge" Z^ff if the ion is partiallystripped and equals Zn if the ion is

completely stripped

that

If has been shown

Z^^^ = f(Zi) f (25)

where fCZ^) = 0.28 z2/3 for Z-l_^45.5 and

fCZn) = Zi^/^ for Zi>45.5. Thus, the

criterion for complete stripping is

,efi = Zi = f(Zi) (26;

from which it follows that the velocity

V above which the ion remains completely

stripped is

V = m

ZlVo

fTz]! ...(27)

Hence, at ion velocities above Vm

z in the above equations and in Eq.(3c)

must be replaced by Zi^ while below this

it should be replaced by Z^ff as given

by Sq^(25). Eqs(2l) and (23) contain the

term T which needs to be known for the

various media. Hukherji4 has shown that

I in eV is obtainable from

Z2 In I =|.j^ln(| mUg^) dn(Ug) = -2)V

f(Z,) ff(Zp) ( , . 2) 2 [ |ln(|mu/jdU3

+ 2 ln(13.6 Z,"^)] ...(28)

Further, it is found that the values of

I calculated from Eq.(23) are well

represented by the expressions

= (28 Z2^^^-6), for Z2<45.5

^ ...(29)

= (323+10. 33(Z-45) )for Z^^ 45.5

^ ...(30)

where I„ is the mean ionization poten-

^2

tial of a medium of atomic niimber Z2

Table I shows a comparison between

the experimental values of the stopping

powers of 19f ions in Al from Northcliffe^

along with the corresponding calculated

values using Eqs.(21), (22) and (23) in

appropriate cases. A similar comparison

is shown in Table II with the experimental

data for ^O^g ion in Al from Northcliffe5

and calculated values using Eq.(21).

Further, it is found that the energy-loss

data of Hower and Fairhall" for completely stripped ^Be ion in Au and Al foils are in good agreement with our calculated

values, as also Northcliff e 's5 values

for 14n and ^°0 ions in Al. The experimental stopping-power data of Kelley

et al .

' are also in good agreement with

the corresponding calculated values of ours in the case of 12c, 1% and loO

ions in 94.6 \im thick silicon.

Table I Calculated and Experimental Stopping

powers for ^^F Ions in Al

Ion Energy

(MeV/amu)

(dE)

Mx' exp,

/MeV cm<

^ mg '

(dE)

I '•dx'calc Appropri-

) /MeV cn^ ate

mg equation

9.60 2.85 2.89 Eq. (23)

9.04 2.98 3.08 Eq. (23)

. 7.92 3.14 3.35 Eq. (21)

7.40 3.49 3.51 Fq. (21)

2.48 6.60 6.82 Eq. (22)

Table II

Calculated and Expej

powers for

5 'imental

%e in Al

Stopping

Ion Energy

(MeV/amu)

(dEs

Mx' exp

.MeV cn^ mg

(^) Mx'calc

/MeV cue

' mg

Appropriate

equation

9.92 3.51 3.46 Eq. (21)

9.23 3.86 3.65 1

8.13 4.00 3.98 II 7.19 4.21 4.32 II 6 .20 4.86 5.02 II 5.38 5.04 5.22 1

3.50 6.51 6.74 Tl

147
References

1. Bethe, H.A, Ann. Phys. , ^, 325

(1930).

2. Mukherji, S, and Srivastava, B.K.,

Phys. Rev., B^, 3708 (1974).

3. Bohr, N. , K. Danske Vidensk. Selsk.

Mat. Fys. Medd., 18, 8 (1948).

4. Mukherji, S., Phys. Rev. B12, 3530

(1975).

5. Northcliffe, L.C., Phys. Rev., 120 . 1744 (I960).

6. Hower, CO. and Fairhall, A.W., Phys.

Rev., 128, 1163 (1962).

7. Kelley, J.G., Sellers, B. and Hanser,

P. A. Phys. Rev., B8, 103 (1973).

i48
NEUOEON THERMAIIZATION IN HTDROG-EKOUS MODERAIORS

L.S. Kothari

Department of Physics and Astrophysics

University of Delhi, Delhi-110007 , India

Ihe mechanism of neutron scattering from various moderators

is a poorly understood subject. Ezact calculations of neutron

scattering properties of commonly used moderators namely light and heavy water and graphite are extermely difficult. Calculations of neutron scattering from light and heavy water are complicated because of our imperfect understanding of liquid

structiores. Therefore one has to depend on various approximations or models for such calculations. This paper first stresses

on investigations carried out in this field for hydrogenous

moderators. A scattering kernel for light and heavy water and

its mixtures developed by us considering the low-frequency

collective oscillations in the quasicrystalline approximation

using Debye distribution has then been described. The total

scattering cross section, diffusion coefficient and various other

physical parameters calculated on the basis of this kernel has

been presented and compared with the available experimental and

theoretical results.

(Cross section, diffusion, kernel, lattice vibration,

model, moderator, neutron, scattering, thermalization)

Introduction

Light and heavy water, along with

graphite are the three important moderators. As it happens, neutron scattering

from all these three is poorly understood. Graphite has a layer structure

and its lattice dynamics is quite different from that of more isotropic solids.

Because of this, considerable difficulties arise when one wants to calculate

neutron scattering cross section of

this material, and the problem is still

far from being closed-^. For light and

heavy water, or mixtures, it is again

difficult to calculate neutron scattering cross section precisely, because

of our imperfect understanding of the

liquid state. However, a number of

models have been developed to explain

neutron scattering from these materials

and we will consider them first. Later

we will consider some other hydrogenous

moderators.

To study neutron thermalization,

one needs information about the scattering kernel, i.e. the scattering cross section for a neutron of energy E being

scattered into a unit energy interval

about some other energy S ' . Calc\ilating

this is a major problem in itself. For

water three different approaches have

been adopted: (i) gas model, (ii) sca- ttering kernel based on experimental

data of the scattering law and (iii)

quasicrystalline model.

Gas Model

This model for solids and liquids was first developed by Wigner and

Wilkins Jr. around 1944, and has been

very widely used. This model implies

the complete neglect of chemical

binding. Radkowsky5 suggested that one could partially take accoiint of the

chemical binding in liquids by treating

the mass of the scattering unit as a free parameter, and fixing its value by

adjusting the calculated values of the

total scattering cross section to agree

with the observed data. Nelkin4 developed another scattering kernel in which

he included the contributions of

hindered rotation and intramolecular

vibrational modes of the water molecules

in the harmonic approximation. The

translational motion was treated on the

basis of gas model. To obtain an agreement between the calculated values of

the total scattering cross section and

the observed data, he had to divide the

energy range into three regions and

choose different numerical values for

the parameters involved in each energy

region. This kernel, which is now

referred to as the Nelkin kernel, has

been very widely used for thermalization

and diffusion studies in water and is

able to explain the results of pulsed

neutron experiments very satisfactorily.

Recent pulsed neutron experiments

by Fujino and his co-workers^ in water

149
poisoned with non-l/v absorbers and the

measurements of temperature^coefficient

of water moderated thermal reactors has

brought out the inadequacy of the Nelkin

kernel^ . It is now generally recognized

that Nelkin kernel works satisfactorily

in cases where equilibrium neutron

spectrum does not differ appreciably from

a Maxwellian - but in such cases the calculated results are insensitive to the

scattering kernel, provided of course

that it satisfies the detailed balance

condition.

Many modifications of the Nelkin

kernel have been suggested, among others

by Kosaly and Valko', Ardent e and

GallusS, Esch et al9, Gotoh and Takahashil'-'. Using an approach very similar

to that of Nelkin, Honeckll worked out a scattering kernel for heavy water wha ch

has also been very widely used for thermalization and diffusion studies.

ScatteriniS: kernel based on Experimental

Data

Egelstaff and Schofield"*"^ were amongest the first to develop a scattering kernel for water based on the

experimental data on scattering law.

Koppel-^5 and also Haywood-'-^ have done

considerable work in the direction.

However, scattering kernels generated

by this method depend strongly upon the

accuracy of the experimental data and

have only been rarely used for thermalization or diffusion studies.

Quasi-crystalline Model

Quasi-crystalline model for water

was proposed as early as 1933 by Bernal

and Fowlerl5. Such a model is based on the idea that liquids behave as disordered crystals for times shorter than

the diffusive time. In the early 60s

considerable work, both theoretical and

experimental, was done which lent

support to this model. Larsson and

Dahlborg-^^ found that the frequency

spectrum of water at - 3°C was very

similar to that of water at +20C. Some

differenipeJ have later been reported by

Burgmann-'-' and others-'-" '-LS.

Following these and similar other

studies, a number of workers have tried

to explain neutron scattering in H2O and

DoO, particularly the quasi-elastic sca- ttering, on the basis of quasi-crystalline model for these liquids. Total

neutron scattering cross section as well

as the average cosine of the scattering

angle in the laboratory frame of reference has been calculated. However, till

recently no attempt seems to have been

made to study neutron thermalization and

diffusion using a scattering kernel

based on this model.

20-22

We have recently developed

scattering kernels for light and heavy

water and mixtxires. We treat the low

frequency collective oscillations in the

quasi-crystalline approximation using a Debye distribution function. The rotational and intramolecular vibrational

modes are taken as discrete levels and are treated in the harmonic approximation. Using these kernels we have calciilated the total scattering cross section and have studied the pulsed

neutron problem in H2O, D2O and in H2O

poisoned with non-l/v absorbers.

The total neutron scattering cross section for H2O and D2O are shown in

Figs. 1 and 2 respectively. Also shown

for comparision are cross sections based

on a pure Debye model with = 200 Z

(case A) and Q-q = 250 K (case B) and ex- perimental results due to Hughes and

Schwartz23, Neill et al24 and McReynolds

et al25.

0 0004 OCOl 001 01 OS

Energy £ CeV) I Fig. 1. Total neutron scattering cross "5 section for water at T=200C.

Curves (i), (ii) and (iii) re- j present respectively the resiilts j of present calculations based on , our model and cases A and B. Cur- ve (iv) represents the values

obtained using the gas model with

mass 18. • , X denote the experi- , mental values of Hughes and

Schwartz23 and Neill et al24 res- j^, pectively. For comparison, the

experimental values ( ^ ) of j Whittemore and McReynolds25 for j

. , 5*^C are also shown.

150
>- OOOOl

Fig.

O.Ol Energy, E (ev)

Total neutron scattering cross section for heavy water at T= 20°C. Curves , represent

respectively the results of present calculations based on our kernel and cases A and B. Curve

. . , represent the

values obtained using the gas

model with mass 20. • denote the

experimental values of Hughes

and Schwartzes. For comparison

the experimental values ( -A ) of Whittemore and McReynolds^S at

9°C are also shown.

P-ulsed Neutron Problem

The pulsed technique for measuring

neutron diffusion parameters in moderating materials was first introduced by von Dardel^o around 1954. Because of

its simplicity, it is still very widely

used. The experiment consists in introducing a burst of high energy neutrons

inside a medium and studying how it decays in time. If one waits for a sufficiently long time, the decay becomes

exponential and one can determine the

asymptotic decay constant for the pulse.

(For small assemblies the problem is more complicated and we will not go into

those details here^''^^. This decay

constant K.a is measured for assemblies

different sizes and the results are usually analysed in terms of a series

expansion^^ '^'-^

of

(i;

where B^, called the buckling of the

assembly, is a measure of its size. = 0 corresponds to infinity assembly

and larger values of b2 correspond to

smaller sizes, ^(v) is the macroscopic

absorbtion cross section for neutrons of

velocity v. It is assumed to vary as 1/v with velocity. Dq is the diffusion

coefficient and G is the diffusion coo- ling coefficient.

The value of A^can be calculated by

solving the integro-differential

equation^"* 30

[2)

where ^3 is the macroscopic scattering

cross section, D(E) is the diffusion

coefficient for neutrons of energy E,

SgCE'-^E) is the scattering kernel and

fir ,E) is the neutron fliix at T corres ponding to energy E. "

As an example we report in Fig. 3» calculated values of (curve i) as a function of B^ in at 20°C. along

with the experimental data51~33. Curve

(iv) represents calculations based on Honeck kernel whereas curves (ii) and

(iii) are based on pure Debye model with

e-Q = 200 (case A) and 250 K (case B) res pectively

Fig.

015

3. Dependence of Aoon buckling, B^

for heavy water at 20°G ( isZ^ = 19 sec"-'-). Curve (i) is based on OUT kernel. Curves (ii) and (iii) are for cases A and B respectively,

Experimental data are due to

Kussmaul and Meister^:r( O )jJones'2

(^ ) and Parks et al53(A). Theoretical results using the Honeck

kernel ( curve ( jv) ) are also shown

for comparison.

151
By fitting a polynomial in (eq. 1)

to the calculated or the experimental

data on , one can determine the values

of Dq and C. In figure 4a are given the

experimental values of Dq at various temperatures measured by different groups,

along with our calculated temperature

variation of Dq. It will be observed

that the temperature variation of Dq calculated on the basis of the Nelkin

kernel can not satisfactorily account

for the experimental results. In general

the values based on the Nelkin kernel are

larger than the measured values. On the

other hand, the calculated values of C that are based on the Nelkin kernel are

smaller than the measured values in fig- ure 4b.

20 40 60 eo ^BaosowsowToeoM

Tcmperoture 7"("C3 Pig. 4. Temperature variation of (a) the

diffusion coefficient Dq and (b)

the diffusion cooling coefficient

C for water: (i) present model;

(ii) Nelkin kernel Clendenin54.

X von Dardel and Sjostrand^S

j

a

Kuchle^O; Antonov et al^'; o Meadows and Whalen^S, « Lopez

and Beyster^9. X DlQughy and

Kvitek^'-'; A Dio and Schopper^-'-j

ooEobayashi et al^^. a Paiano

and Paiano43| ar Salaita and

Robeson44, x Jones32, Williams

and Munno^S, 8 Bret scherzo.

The temperature variation of Dq and

C for heavy water is shown in figures 5 and 6 respectively. Cvirves (ii) are based on Honeck kernel whereas solid curves are results based on our kernel.

It will be observed that the variation

in the measured values of C is very

large. This is because, to determine

accurately the value of C one must

extend measurements to large values of

b2, taut 29,30 in such assemblies interpretation of results becomes difficult.

^g20,21 Y^-^Q also calculated neu- tron spectra at different times following a bvirst of fast neutrons in various

H2O and D2O assemblies at different

2.5

2.* -

' .8 I i L_ \ I I L ] O 10 20 30 to SO 60 . 70 60

T(°C) Fig. 5. Temperature variation of diffusioncoefficient DqI (i) present model}

(ii) Honeck kernel (Honeck and

Michael^'). In this figure the ex- perimental results shown are of

the following workers: \ Ganguly et al48j5Parks et al33.^ Salaita

and Robeson44. J Westfall and

Waltner49. ^ Mala viya and Profidj

if Kussmaxil and Meister^lj ^

Raiavski and Horowitz-* •, z Silk

and Wade52. ^ Daughtry and Waltner55

8 -

2L 1 1 1 1 I I I 1 O 10 20 30 40 50 60 70 80

T(°c) Pig. 6. Temperature variation of the diffusion cooling coefficient C for

heavy water: (i) present model;

(ii) Honeck kernel (Honeck and

Michael'^')' In this figure the ex- perimental points are of the following workers! i Ganguly et al4°;

Parks et al^^j ^ Salaita and Sg^®"

son44, I Westfall and Waltner4y}

Malaviya and, Profio^O ; ^ Kussmaul

and Meister-^ .

152
temperatures. Some typical results for

are shown in figures 7 and 8 for

DoQ^in figures 9 and 10. Ishmaev et ax^^, measured time-dependent spectra

in water assembly (30x30x45 cm^) at

350c. In figure 7 is plotted the time

evolution of the neutron flux at a few

typical energies. The calculated

results account fairly well for the

approach to equilibrium of the neutron

pulse. The experimental results of

Menzel and his group55 in water assembly(7.l6 X 25.02 X 25.4 cm^) at 37.8°G

are shown in figure 8 along with the

calculated results. The agreement

between the two sets of data is good.

Menzel et al^^ found that the

neutron spectrum after 23 M-S of the

introduction of the pulse inside the

assembly was a I'laxwellian at 37.8°G.

From this they concluded that the

thermalization was complete in 23 \xs.

However, as our study shows for this

large buckling that they have used,

the asymptotic spectrum is not a Maxwell ian at the temperature of the

medium and it takes about 60 ^s for the

equilibrium to be established.

Time-dependent spectra in D2O assembly with b2 = 5.78 X 10"^ cm""^ at

20°C were measured by Poole and

Wydler5° and Wydler57 and their results

tfr 1

'lO 203O4O5OtO70 8O

Time (ps)

Pig. 7. Neutron„spectra cp (E,t) for = 0.0256 cm"^ for water at 35 C as a function of time: present model

calculations; case B calculations. The experimental results of

Ishmaev et al^^for various energy

groups are also shown for com- parison: ( A. ) 0.010 ev} ( + ) 0.015

ev, (« ) 0.025 ev} (X) 0.100 ev. (The normalization is arbitrary

and is different for different

energy groups.)

are shown in figure 9. Our calculated

results are also shown for comparison.

In fig. 10 are shown the results in D2O

assembly at 43.3°C for a 50 cm cube

assembly (B^ = 0.0108 cm~^) and experimental results of Kryter et al^°. In

puilsed neutron experiments, the effect

of adding l/v poison to the medium is

only to increase the decay constant by a constant amount f'UJIa,* However, if the

assembly is poisoned by a non-l/v

absorber, then the asymptotic neutron

energy spectrum is modified and one has

to solve the Boltzmann equation for

each poison concentration separately.

Fujino and his coworkersw) have

measured, as a function of time the

reaction rate R(t) in water poisoned

with various concentrations of cadmium:

where

"R{t)= \ Y (E)t(e,i)ciE

The experimental data along with

our calculated results are shown in

Fig. 11. As is to be expected, for

larger concentration the Nelkin kernel

gives results which are markedly

different from the experimental data.

Fig. 8. Neutron spectra 9(E,t) for B = 0.2238 cm-2 for water at 37.80C

and at different times. The ex- perimental data of Menzel et al-^

( • ) are also shown for comparison. Curves , . , —. . , respectively represent re- sults based on our model, case A and B. Curve is Maxwellian at 37.8^0. Curve XX is the asymptotic

spectrum corresponding to B'^ = 0.2238 cm~^. (The normalization

at different times is arbitrary).

153
Fig.' 9. Neutron spectra (p(E,t) for = 5.78xl0~3 cm~^ for heavy water

at 20°C and at different times.

( • ) the experimental data of

Poole and Wydler5°. Curve is

based on our kernel. (The norma- lization at different times is

arbitrary)

In Fig. 12 we have plotted (X{^)-Xoo)

/vqN as a function of cadmiixm concentration, N, at various times, where Xoo is

the fundamental mode decay constant for

the unpoisoned assembly and Vq is the

neutron velocity corresponding to an energy kgT. Experimental resl^lts of

Meadows and Whalen-^ and Larsson and

Moller°*^ are also shown. For comparison

resuilts based on Nelkin kernel are also

given. In almost the entire concentration range studied, the agreement bet-

»feen our calculations and the experimental results is very satisfactory, whereas

Nelkin kernel gives rather low values

for ( Hh)- Xoo)7voN.

Ice

Recently there has been increased

interest in studying neutron thermalization in cold moderators, with a view

of producing large flux of cold neutrons.

Moderators like graphite or berylli\im are completely useless for this purpose

since they are almost transparent to low

energy neutrons more so at low temperatures. Hence one has to rely only on hydrogenous moderators. Lot of work,

both experimental and theoretical, has

been done to study neutron thermalization in HpO, ice and also liquid

Hp and Because of possible hazards

01 explosion, some countries do not

permit the use of liquid H2 in or near

20

-

- / " 30

-

r 60

-_

- /

-

1OO

-

1 L

\*

1 1 \ 1 E(ev, Fig. 10. Neutron spectra (p(E,t) for B = 0.0102 cm for heavy water at

T = 43.3°C and at different

times. (• ) theJ- experimental data

of Eryter et al-' . Curve

present kernel. (The normalization at different times is arbitrary) .

18 I N =200 ' 10 aloms ctTJ I

20

I ( )J5) Fig. 11. Reaction rate R(t) as a function

of time for water assembly (B"^ =

0) for various concentrations of

cadmium. Experimental data of

Fujino et al^^', .. . free gas kernel (mass = 1); . _ . , Nelkin kernel} , present kernel.

154
reactor cores. Further in many ways,

H2O + D2O ice is almost as good as liquid H2 (D2 or mixtures), and the

study of neutTon thermalization in ice,

which had been neglected for sometime,

is again gaining importance.

3600

-3400

3200 -

3000

Fig. 12. ( X(t) -Xoo)/voN as a function

of cadmium concentration, at

various times. Experimental re- sults, 5 Meadows and Whalen^^j

$ Larsson and Moller"^. Theoretical results, curve , present kernel calculations-, curve . . , Nelkin

kernel, curves marked A represent asymptotic values.

Using the Debye model for lattice

vibrations of ice with suitably chosen

Debye temperature we"-'- have studied

neutron thermalization in ice down to 4" K. The results of pulsed neutron experiments

at 268° Z are shown in fig. 13 . In fig.

14 is shown the calculated temperature

variation of the diffusion coefficient

in icev along with some experimental

valuesD2-66.

Time -dependent spectra in ice ass- emblies at 77 and 21° K were measured by

Reichardt°5 and these are shown in

figures 15 and 16 respectively. Our

calculated spectra are also shown. The

equilibrium spectrum at 77° K is slightly

cooler than Maxwellian at 77° E. Further,

equilibrium is established in around 450

[iS. When ice temperature is below about

50° Z, it takes unusally long for the

equilibrium to be reached. At 21° K, even after 2 ms equilibrium is not reached . Of particular interest is the equilibrium spectrujn of neutrons in the

presence of a l/E source. This, the so called, steady state spectrum is what one would observe in a moderator block placed

near a reactor core. We have calculated

66-68 steady state spectra in ice (H2O,

D2O and mixtures) at various temperatiares

down to 4° K and in assemblies of various

dimensions. Results for ice assemblies

at 77; 21° and 4° Z of b2 = 0.1113 cm-2

26

22

^ 16

Z 1* o

10

T > 266 K (uag). 4X85 X 10^ sec

o Experimental pointsjSiWcr

(11,(111,4(111) Present calculations^'

1 1 ' ' 1

0-1 02 03 OA as 06 07

2 -2

oo

197

oo

- (a)

9* .

0^ /OK

1 1 t 1 1 173* K 193* K 213* K 233*K 253* K 273* K T

Fig. 13. ( ^^-"^^0.) vS for ice at

T=2680K ( u 2o, =4. 485x10^8 ) for different frequency distributions: curve (i)—'Debye frequency (one phonon kernel): curve (ill— ..Larsson and

Dablborgl^ which includes ro- tational modes (one-phonon

kernel): curve (iii) Debye

frequency distribution (onephonon plus two-phonon kernel)

Fig. 14. Comparison of the experimental

and theoretical results of the

diffusion coefficient Dq for

ice as a ^'unction of temperature.

6 Silvero2. O Antonqv et alo3,

XDloughy and Kvitek^O?

Salaita^^, • Reichardt^S, A

Ohanian° , —present calculations.

155
0» 17 1 6 To ti ti

Fig. 15. Comparison of experimental and

theoretical spectra at different times in ice at temperatvire

77°EandB4= 0.1548 cm-2. Experimental points are from Reichar-

(a cube of nearly 17 cm side) are shown

in fig. 17. The experimental results are

those of Whittemore and McReynolds"°

It will be observed that both experimentally as well as theoretically one gets

the same steady-state spectnim at 21° K

and 4''K. It was also observed as early

as 1961 by these authors'^ that the

effective temperature of the neutron distribution does not go below 40° K, however

much one may reduce the temperature of

ice. We'-'- have shown that this arises

because of diffusion hardening. To some

extent the situation can be changed by

adding some D2O to H2O. If we consider

a pure D2O assembly even then thermalization is incomplete in fairly large

assemblies.

The values of effective temperature.

2 E

eff - TIT,

(E is mean energy of the

distribution and kg is the Boltzmann

constant) in D2O ice at various temperatures and in assemblies of various

bucklings are given in Table I. We note

that, unlike in H2O ice, here there is a strong dependence of Tg^^ on buckling.

Fig. 16. Comparison of experimental and

theoretical neutron spectra at

different times in ice at T=2£k

and b2=0.1548 cm-2. Experiment

tal points are from Reichardt°5,

NEUTRON ENERGY (Ev) —

Fig. 17. Comparison of the calciilated

steady state neutron spectra in

ice bl6ck with b2=0.1113 cm"2

kept at 77, 21 and 4°K with the

spectra measured by Whittemore

et al'O. Experimental points

are reported by crosses.

156
Table 1

Tgf-f(°K) of Steady-State Neutron Spectra

in D2O Ice at Various Temperatures

Temperature of D2O Ice i°K)

2

(

«m-2 ^

V cm ) 77

0.0 77.2 24.1 16.9

0.005 96.5 54.5 53.9

0.01 112.5 69.5 69.3

0.0158 128.6 82.1 82.1

0.02 138.8 89.4 89.5

0.03 159.9 103.3 103.4

Figs 18 and 19 show steady-state

spectra in a 17 cube at 21* K for different HoO, DpO proportions. The vertical

lines at 0.0017 eV and 0.005 eV correspond to Bragg cut-off energies in graphite

and beryllium. For this buckling (0.1113

cm~2) we find that the proportion of cold

neutron flux is mazimum in case of a mixture with 70X H2O + 307 D2O (by weight).

Pig. 18. Steady State neutron spectra in

mixtures with 0, 5, 10, 20 and

30X DoQ s-"*^ 21°K in^an assembly

with 32=0.1113 cm~^. All the

cxxrves are normalized at the cut

off energy Also drawn in the

figure are lines corresponding

to energies of 20 and 60 kg.

(These curves are all normalized at

0.0168 eV. ) Both for lower as well as higher D2O contents, the fraction of cold

neutrons decreases. The optimum mixture

depends upon the size of the assembly.

This is borne out by figures 20 and 21,

where steady-state-spectra in an assembly

of B^ = 0.0158 cm"'^ (cube of ^ 45 cm side)

at 21 K are shown. For this assembly the

optimum mixture is 30% H2O + 70/ D2O.

The variation of Tgf-f with change in

C2O concentration, in assemblies of va- rious bucklings, is shown in Fig, 22. It will be observed that in an infinite assembly Tp^^ decreases steadily with incre- ase in BpU concentration, but it fails to

attain the temperature of the medium even in 100? D2O. In H2O assemblies, the

effective temperature hardly changes, as

one goes from an infinite assembly down

to a cube of almost 20 cm side. On the

other hand, for D2O, Tg^^ increases

rapidly as B^ increases.

For a given buckling, there is a range of optimum D2O concentration. For

large B^ values, about 20'/. D2O is expected

to give the best resiilts, whereas for

small B^ values 90'/. D2O and 10/. H2O would

Pig. 19. Steady state neutron spectra in

mixtures with 30,40,60,70 and

90/. D2O at 21 iCin an assembly

with 0.1113 cm 2. All the curves are normalized at the

cut off energy, Eq . Also drawn

in the figure are lines corresponding to energies of 20 and

60 kg.

157
E I eV) —

Fig. 20. Steady state neutron spectra in

mixtures with 0, 20, 50 and 70^

DpO at 21° K in an assembly with

B^= 0.0158 cm~^. All the curves

are normalized at the cut off

energy, E^. Also drawn in the

figure are lines corresponding

to energies of 20 and 60 kg.

give the lowest Tg^^ values. We also

note that for certain buckling values,

here '^0.05 cm~^, Tgff remains almost

constant for changes in DpO concentration

from almost 20/. to 707. . liquid Dp ^•'^^ mixtures have been

widely used as cold neutron sources in

European reactors'-'-. Considerable theoretical work has also been done on the

thermalization of neutrons in H2 and D2.

One has to take account of the existence

of the ortho-and para-spin states of the

homopolar molecules, each of which has

markedly different scattering properties.

A further complication Hp, D2 mixture

would be the formation or HD molecules.

At room temperature the para:ortho

ratio is nearly 1:3, whereas at 20 K

ortho reverts to para and the equilibrium mixture contains nearly 99. 7X

para-hydrogen

Neutron scattering cross section"^"^

for H2 is shown in Pig. 22, alongwith

available experimental result s''' 3 -7 5

The scattering cross section for para

hydrogen increases hy almost a factor

of 10 around neutron energy 0.015 eV. This is because of the excitation of the

J=l rotational level. At neutron

energies below the threshold of any rotational excitations, the ortho-hydrogen

—U 1 I I I I I

I I 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 E ( eV 1 —

Pig. 21. Steady state neutron spectra in

mixtures with 70, 80, 90 and

1007. DpQ at 21 K in an assembly

with B'=^=0.0158 cm'^. All the curves are normalized at the

cut off energy. Eg. Also drawn

in the figure are lines corres- ponding to energies of 20 and 601^

cross section is almost 30 times that of

para-hydrogen. At high energies both

cross sections tend to the free atom value

of 20 b.

Ntolror ersrty (tV)

Pig. 22. Comparison of predictions by the

Young-Koppel scattering model

with measurements of neutron

total cross sections in normal

ortho and para hydrogen at various

temperatures: A Seiffert'^ (para

at 14 K, normal at 16 Kit McReynolds and Whittemore ' ^( 21 K);

O McReynolds and Whittemore'''^

(higher resolution measurements)}

+ Squires and St ewart^^( 20. .4 K) I (ref. Moon and Beynon'-'-). .

158
Since the spin-flip interaction from

ortho to para (J=l to J=0) will result in

energy gain for the neutron, it might

appear that para-hydrogen is a better

moderator at low temperatures. In actual

practice this is not so, since the scattering cross section of para-hydrogen at

low energies is very much smaller than

that of ortho-hydrogen.

Jacrot'^5 studied neutron moderation

in H2, D2 mixttires and found, the optimum

mixture to be i H2 + £ ^2 weight (50'/

1 ortho-hydrogen ) . On the other hand Davies et al'° reported the optimim mixture

to be i H2 + 1 Dp by weight. This diff4 4 erence in optimum mixtures is attributed

to different sizes of cold neutron

soiirces used by the two groups. More

recently Carter and Jones' ' at Harwell

have studied neutron moderation in H2, D2

and mixtures at 20.4 K inside a cylinderical assembly of internal diameter 20 cm

and thickness varying from 1 to 15 cm. The effective temperatures measured by

them are reported in Table II. One will

Table II

Effective Temperature in Various Assemblies of E2, 1*2 I'iixtures at 20.4 K

Chamber Moderator Effective

Thickness Tempera-

(cm) ture (E)

1 H2 38

2 H2 38

5 H2 37

10 ^2 37

15 H2 37

1 D2

2 D2

5 D2

10 D2 29

15 D2 24

2 H2/D2(33X H2)* 39

2 H2/D2(58/. H2)* 46

5 H2/D2(25*/ H2)* 39

5 H2/D2(467. E2)* 39

5 H2/D2(74X H2)* 39

15 H2/D2(8.5X H2)* 30

15 H2/D2(18.6/. H2)* 32.5

* Atomic percent

observe close similarity between these

results and our calciilated results for

ice, presented in Fig. 23. Here too we

find that in H2 assembly the effective

temperature hardly changes as the thickness of the assembly is changed from 1 to

15 cm, and its value is almost the same

as that in the case of H2O ice at 21 K. In the case of D2, in larger assemblies

the effective temperature is lower than

in H2 and also shows some dependence on assembly size. In the case of mixtures

inside small assemblies (2 cm thickness),

Tgff increases with increase in H2 concen- tration but in the intermediate assembly

(5 cm) the temperatiire remains nearly

constant over a very wide range of H2

concentration (25/. to 74'/). This is very

similar to otir results for ice with b2 = 0.05 cm-2 (Fig. 23). In large size,

results are available only for low H2 con- centrations and here again T^ff shows

some dependence on H2 concentration.

50

55 T = 21 °K

^

50

» «

/ 0 / ^ oV

°- iO

35

30

25

20 1 11 1 1 1 1 1 1

Content of in Mixture I %l

Fig. 23. Variation of Tgff with content

of D2O in the mixture for assemblies at 21" E with different

values of B^.

Inoue et al78 have studied neutron

thermalization in methane at low temperatures. They find that because of the near free rotational modes of this molecule, it is able to thermalize neutrons

to lower temperatures than H2 + ^2

tures. This is a very promising material

and more studies may be made on this in

coming years79.

159
Neutron thermal ization has also been

studied in a nimber of other hydrogenous

materials, including zirconium hydride,

benzene polyethylene and some organic

material So Zirconium hydride has been

used as a moderator in a number of experimental reactors. In this material hydrogen acts essentially as an Einstein

oscillator, with a fairly well defined

frequency. Once the neutron energy gets

below the energy of the oscillator, thermalization will essentially stop.

Lattice dynamics of polyethylene

corresponds to that of a chain structure.

Wunderlich^ proposed a model for the

frequency distribution of this material

to explain the temperature variation of

the specific heat. More recently an alternative model has been proposed, which

in manynways, is physically more satisfactory . Neutron scattering on the

basis of this model is being investigated.

There is still considerable work to

be done on the thermal izat ion of neutrons

in small cold moderator assemblies. This

has assumed some urgency because of the

great interest currently being shown by

solid state physicists in the study of

the condensed state by the scattering of

very long wavelength neutrons.

Part of the work presented here was supported by NSF grant No. 01P72-02844

AOl", I am thankful to Mr. R.M. Bansal

for his help in the preparation of this

manuscript

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161
Discussion

M.P. Navalkar

I have done a lot of experiments and

analysis in pulse neutron technique using

moderators such as H2O, BeO, Pb etc. In

BeO we have come to the conclusion that

it is not possible to measure diffusion

coefficient because asymptotic decay

constant dose not exist below a certain

size. What is your conclusion regarding

this aspect for BeO?

L.S. Kothari

In pulsed neutron experiments one may not observe an asymptotic decay if

the buckling exceeds the critical buckling. But I did not go into that aspect

of the problem since it would have taken

one away from the line I wanted to

develop. I agree that in doing pulsed

neutron experiments, particularly in D2O

assemblies, one must be careful to choose

assemblies so that B^-^ Bq .

162
UEUTEON TRANSPORT STUDIES IN PAST REACTOR SHIELDS

R. Vaidyanathan, Z.P.N. Murty and

R. Shankar Singh

Reactor Research Centre, Kalpakkam

India

The present study alms at evaluating the relative accui^acies

ivith which the different approximations to the transport theory

represent the spatial and spectral distribution of neutrons in a typical fast reactor shield. Diffusion, removal diffusion and

discrete ordinate transport calculations, with and without the

inclusion of anisotropic scattering effects, have been performed

for the lateral and axial shield configurations of the French

fast reactor Rapsodie. The resiilts have been compared, with the

measurements made in Rapsodie and the WIOBE calculations made

earlier.

(Approximations; diffusion; neutron; NIOBE; Rapsodie; • reactor; shielding; transport calculation) "

i

Introduction

The prediction of the spatial and

spectral distribution of neutrons

through the reactor shield is a vital

requirement for shield design. In fast

reactors, due to the small size of the

core and the absence of a moderator,

there is a high leakage flux from the

core with long migration lengths in the

, surrounding material. Clearly, the

diffusion theory can not adequately

represent the asymptotic neutron angular

flux, which exhibits severe anisotropy,

especially near boundaries. Further,

the major fraction of neutrons leaking

into the reflector of a fast reactor is

in the intermediate energy range

( ^ .5 I'leV) . V/ith such scarce spectrum

and the pooily moderating materials like

sodium and steel as penetrating media,

the virgin beam should principally

I consist of intermediate neutrons. Thus, one expects that the removal treatment

1 which gives the penetration of fast

; neutrons would reduce to normal diffusion

j'. theory. All the same, it has been found-L

that the diffusion theory would yield

,t accurate resiilts with an empirically

I optimised energy group structure. But a

) practical limitation of this procedure

I is that the predictions are very

sensitive to the group structure in

regions of short slowing down lengths.

Another aspect of the neutron

ttenuation problems in fast reactor

-'ields is the marked variation in

r.eutron spectrum with propagation

through the shield. Earlier studies'^

; indicate that this effect is so severe

that few-group calculations would not

yield desired accuracy.

Scope of Calculations

The investigations ^ere carried out

with the following specifications;

a) The calculations were performed

for the axial and radial shield configurations of Rapsodie, which is a 40 MW

fast reactor at Cadara.:he, Prance. Both

axial and radial cor figurations were studied as spherical systems with the

specifications given in Table-1 with

12 energy groupsTable-la

Axial Configuration of Rapsodie

Zone Radius (Cms)

Core (Driver Zone) 16 .00

Expansion chamber 32.60

Transition Zone-5 36.95

Axial Blanket 64.60

Transition Zone.

6

67.10

Sodium 258.80

Berated Graphite •278.40

Steel Virgo 14 SB 288.40

Borated Graphite 376.40

Steel A- 42 386 .40

Borated Graphite 436.40

Steel X C-18S - 481.40

b) The transport equation was solved

with S/ approximation using DTF IV. To see the effect of anisotropic scattering

considerations, the axial calculations were again performed with the sodium

cross sections represented in 3 Legendre

moments. The diffusion calculations were performed v;ith ONEDX and a program

163
was developed here to solve the removal

diffusion scheme. A 70-group S4 calculation was performed to estimate the

variation of spectrum due to spatial

traverse in the radial shield. The

70-group cross sections were taken from

JAERI fast reactor group constants^.

Table-lb

Radial configuration of Rapsodie

Zone Radius (Cms)

Test Zone 7.07

Driver Zone 25.0

UOp Blanket-I 28.0

UO2 Blanket-II 63.5

S.S. reflector 75-5

Thermal shield 117.5

Stainless steel 121.5

2/. borated concrete 181.5

O.5X borated structural 396.5

concrete

c) V/e choose to compare here, the

different methods with measurements made

in the axial configuration of Rapsodie^

with respect to the following integral

paramet ers

i) Thermal equivalent dose in Mn:

/ \ 1 Bmax , , „

(r) = -if a(B)<p(r,B)

•^th J

dS th.eq

ii) Fission equivalent dose in Si:

1

D„. (r) lis . eq. CT

Bmax

J

a(E)9(r,E)dE.

Bmax

where a = f a(B) X(E)dE

o«' X(B) - U-235 fission spectrum

(r(E) - Activation cross section

a., - Activation cross section at ^ 2200 ms/sec.

The following approximations were made in the investigations:

a) Only coarse group fluxes (12

groups) were available at the core- reflector boundary. A white boimdary

condition was used to specify the source

for the 70-group calculations.

b) The argon cover gas between

liquid sodium surface and the rotating

plug was ignored in the axial calculaticris

Results and Conclusions

Pig.l gives the spatial profile of

the integral parameters mentioned in

Section 2, in the axial shield configuration. DTP IV is seen to agree with

the measurements within a factor of two

to three. The diffusion theory underestimates the high energy fluxes by

several orders of magnitude at deep

penetration. It is better in predicting

the thermal equivalent dose and hence

the slow flux. The removal diffusion

procedure is seen to make a feeble

attempt to improve upon the diffusion

theory resxilts. Anisotropic scattering

considerations give rise to substantial

deviations in the neutron spectrum,

though the differences are less pronoiinced in the integral parameters used

for comparison here. The neutron

Fig. 1. Comparison of the calculated

integral parameters in the axial

c onfigurat ion.

spectra at selective points, obtained by

the 70-group calculation are given in

Fig. 2. It is seen that the spectrum

within a shield zone in the present

configuration does not vary so markedly,

as to give rise to difficulties in performing few group calculations. The

present investigations indicate that -

a) The diffusion scheme can not

adequately represent the neutron distributions in the fast reactor shield.

164
s # i> i< U

HCUTRON EHER6V IH ««

Fig. 2. Spatial variation of neutron

spectrum in the radial shield.

b) The removal treatment is not very

effective and almost reduces to straightforward diffusion scheme.

c) Many group calculations should be

carried out if the shield regions are so thick that the spectral variation with

space traverse is sharp.

Acknowledgement

The authors are thankful to M.S.

Erishnan for lively discussions during

the analysis of numerical results.

Ref erenc es

1. Avery, A. P. et.al., Neutron Attenuaticn

studies in fast reactor shields,

AERE(R) 5773, (1967).

2. Sumar Sahin, Comparison of Transport

Theory and Diffusion Theory for Past

Reactor Shielding Calculations,

Atomkernenergie - Sep. 1973-

3. Eatsuragi et al. JAERI Past Reactor

Group Constants Systems Part I - JAERI

- 1195, Aug. (1970)

4. Chaplet, M. et al.. Etude experimentale

des protections de Rapsodie, CEA-R-3626.

165
SHIELDING FOR THE VARIABLE ENERGY

CYCLOTRON AT CALCUTTA

*G. Muthukrishnan, Hari Singh and

*R. Mukherjee

Health Physics Division, Bhabha

Atomic Research Centre, Trombay

Bombay-400085

India

Shielding calculations are done for the AVF Cyclotron under

construction at Calcutta. Concrete shields are designed to reduce

the fast neutron flux to less than the maximum permissible levels

outside the shields. Earth shields are designed to reduce the

fast neutron flux outside the building to less than the maximum

permissible levels for public exposure. Experimentally measured

values of half-value layer thickness are used in the calculations.

Neutron source strengths are obtained by extrapolation to higher

energies from published values at lower energies. Total neutron

spectra consisting of both cascade and evaporation neutrons are computed for the bombardment of 60 MeV protons on a Li target,

using semi empirical relations. In order to calculate the roof

shield thicknesses calculated total neutron emission spectrum due

to the bombardment of 60 MeV deuterons on a Be target is considered.

Shield thicknesses thus obtained, are comparable with values calculated for a similar cyclotron at Texas A M. University. The calculated neutron dose outside the shield agrees well with the values

predicted by Monte Carlo calculations.

(Calculation; concrete; cyclotron; design; earth shield;

neutron spectra; shield thickness; shielding)

Introduction

The AVF cyclotron, under construction

at Calcutta, is based on the design of

the 88 inch AVF cyclotron at the Lawrence

Radiation Laboratory Berkeley^. The

design specifications are as follows:

Protons 6-60 MeV

Deuterons 12 - 65 MeV

Alphas 25 - 130 MeV

Internal beam current 1.0 mA

External beam current 100 iiA. Facilities include two high intensity caves with three beam ports and two

high resolution caves with six beam

ports. Figure 1 shows the proposed layout of the experimental facilities.

The shields consist of concrete

shields outside the experimental caves

and earth shields outside the building.

The philosophy behind adequate shielding

is to limit the radiation intensity in

occupational areas to a dose rate of

5 Rem/ Year and in public areas to 0.5

Rem/Year. Shielding calculations are done for the maximum operating conditions

of the Cyclotron.

Neutron Production

Neutron production, due to the

bombardment of Protons on a Li target,

is calculated using the semi empirical

relationship, developed by Yucker^. The

program "CASCAD" calculates the total

neutron spectrum and the differential

spectra at various angles. The total

cascade neutron spectr^lm is shown in

Figure 2. Figures 3 and 4 show the

differential spectra at various angles.

The evaporation spectrum is shovm in

Figure 5. Netitron yields at higher

energies due to the bombardment of

deuterons and alpha particles are extrapolated from published values at

lower energies. Table 1 gives the

fast neutron yields due to the bombardment of alphas on Ta and deuterons

on Be3»4,5,6.

The angular distribution of

neutrons due to the bombardment of 135

MeV alphas on Ta is assumed to be the

same as that due to 80 MeV alphas. This

is justified because there is no observed

change in the angular distribution of

neutrons due to the bombardment of 40

and 80 MeV alphas on Ta^. The same was

Permanent address: VBC Project, Bidhan Nagar, Calcutta-700064.

166
167
Fig. 4. Differential cascade neutron

spectrum at 90^ , 120° and 150°,

Fig. 5. Differential evaporation

neutron spectrum.

Table-1

Neutron yields from (a,n)

(d,n) reactions.

and

ALPHAS ON Ta

Energy

MeV

Yield

ns/ sec-|iA

Energy Yield

MeY ns/sec-|iA

30

40

50

80

120

135

1.00

1.96

6.00

3.00

8.00

1.08

X 10, ^ X lolO

X lOlO

X lOll

X 10^1

X IOI2

10

20

30

60

65

3.23

6.60

1.23

1.30

2.06

1010

10

X

X 10-' X lOll

X

X 10

10

12

12

Extrapolated values.

extrapolated to 120 MeV alphas on Ta by

Wadman^

I While considering the skyshine

effect, the total emission spectrum, due

to the bombardment of deuterons on a thid

Be target, Calculated by Moyer^l using 1, Berber theory is taken as the source of

neutrons.

Shields

Concrete and earth shields are used

inside and outside the laboratory res- pectively. The concrete used is ordinarjlj

density concrete (density 2.4 gm/c.c).

Experimentally measured values of half

value layer thickness of concrete are used in the calculations. The same was extended to other shield materials,

taking into account the density effect

Table 2 gives the fast neutron fluxes

at 15 cms from the target and the

corresponding values of the half value

layer thickness. From experimental

studiesl3, it is observed that it is ] only the higher energy component of the J incident neutron spectrum that determine£|!

the half value layer thickness of the . shield material. Using these values, th(;

shield thickness are calculated.

.8

Calculations are carried out to

determine the neutron fluxes outside the;

existing shields. These results are published elsewhere^. Table 3 shows

shield thickness recommended to reduce

the fast neutron fluxes to the maximum

permissible level of 17 ns/cm^ sec.

168
Table

Fast neutron fluxes at 15 cms from

the target and the corresponding values

of the half value layer thickness for the

concrete shield.

Particles Ener- Tar- Angle Fast Half

gy get from neutron value

Tar- flux at layer

get 100 \iA thickns/cm2 ness

sec. cms. Deuteron 65 Be 0° 6.0x10^0 12.70

Deut eron 65 Be 90° 6 .246x10^ 10.16

Alphas 135 Ta 0° 1 .45x1011 18.54

Alphas 135 Ta 90° 4 .028x1010 10.16

Table -3

Recommended Conor et e shield thicknesses to reduce the fast neutron flux

to the maximum permissible level at 7.2

meters from the target for 100 iiA beam

current

Particle Energy Tar- Angle Shield thickget from ness (in

the meters)

target

Alpha 135 Ta 0° 3.90

Alpha 135 Ta 90° 2.18

Deuteron 65 Be On 2.58

Deuteron 65 Be 90° 1.92

Distance from target is 3.90 m. Earth shields are provided outside

the building adjacent to experimental and

vault areas. Measured values of half

value layer thickness of concrete are

extended^ for this shield, by taking

into account the density effect of the

shield material. (density 1.76 gms/cc)

A value of 25.3 cms is taken for the

half-value layer thickness of the earth

shield. The shield thickness is calculated to be 12.5 meters of earth.

Sky shine Calculations

Skyshine calculations have been

carried out by LindenbaumlO . Based on

this, skyshine calculations are, done,

considering the bombardment of 100 \iA

deuterons (energy 60 MeV) on a thick Be

target. The total emission neutron

spectrum, calculated by MoyerU, taken

as the source.

The attenuation properties of the

roof shield are taken into account in

the calculation. A roof shield of 1.65

meters thick concrete is found adequate

to reduce the fast neutron flux to a

level of 2'D/cm2 _ qqq at a distance of

100 meters from the source. Using the transmitted dose obtained

by the Monte Carlo Calculations^^ ,15 for

different neutron energies and shield

thicknesses the transmitted dose rate due

to neutrons produced by the bombardment

of 60 MeV deuterons on a thick Be target was computed for a concrete shield of

thickness 2.58 meters. The dose rate

thus calculated is 1.55 mrem/hr against

our computed value of 2.5 mrem/hr.

References

1. Phadke, D.Y. "Project Report on Variable Energy Cyclotron for Inter

University Centre" April, 1967.

2. Tucker, V/.R. "Empirical Formulae for

secondary Nucleon Production cross sections". Proceedings of the special

sessions on Accelerator shielding

presented at the 1965 winter meeting

of the American Nuclear Society.

ANS-SD-3 (1965).

3. Allen, N.J., Nechaj , J.F., Sun, K.H.

and Jennings, B. "Thick Target Past

Neutron yield from 15 Mev deuteron

and MeV Alpha Bombardment". Phys.

Rev. 81 (1951) 536.

4. Wadman, William W. , "Angular Distribution of Neutrons Produced by 40

and 80-MeV alpha particles on a Thick

Tantalum Target'*. Health Physics

11 (1965) 659.

5. Smith, L.W. and Gerald Kruger, P. "Thick Target Yields from the (D,n)

reaction at 10 MeV", Phys. Rev. 82

(1951) 1137.

6. Wadman, William W. , "Summary of

shielding calc\ilations based on Texas

A and M University 88. inch cyclotron

specifications" UCID 2437 (1964).

7. Tochilin, E., Ross, S.W., Shumway, B. W., Kohler, G.D. and Golden, R. "Cyclotron Neutron and Gamma-ray

dosimetry for animal irradiation

studies". Radiation Research 4 (1956) 158.

8. Wilson, Richard . "A Revision of

shielding calculations". CEA-73(1959).

9. Muthukrishnan, G. and Hari Singh.

"Summary of shielding calculations

for the Proposed Variable Energy

Cyclotron at Calcutta. BARC./I-81-

(1970)

10. Lindenbaum, S.J., "Conference on shielding of High Energy Accelerators,

Oak Ridge". TID-7545, 101 (1957).

11. Moyer, B.J., Some observations on Cyclotron Shielding, Unpublished.

12. Case, K.M., De Hoffman, F. and

Placzek, G. "Introduction to the

Theory of Neutron Diffusion".

Volume I. Los Alamos Science

Laboratory (1953).

13. Stephens, L.D. and Miller, A.J.

,

Radiation Studies at a

169
Medium Energy Accelerator". UCRL - 19386 (1969).

14, Roussin, R.W. and Schmidt, F.A.R.,

Nucl. Eng. & Design 15, 319 (1971).

15. Roussin, R.W,, Alsmlller, Jr, , R.G.

and Barlsh, J., ORNL-TM-3689 (Rev.)

1972.

170
COMPUTER CODES AND DATA AVAILABLE FROM THE

RADIATION SHIELDING INFORMATION CENTER * D.K. Trubey, Betty F. Maskewitz,

R.W. Roussin

Radiation Shielding Information Center

Oak Ridge National Laboratory

Oak Ridge, Tennessee .- 37830, USA

The Radiation Shielding Information Center (RSIC)-^'"^

is a technical institute serving the international shielding

community. It acquires, selects, stores, retrieves,

evaluates, analyzes, synthesizes, and disseminates information

on shielding and ionizing radiation transport. The major

activities include: (1) operating a computer-based information

system and answering inquiries on radiation analysis, (2)

collecting, checking out, packaging, and distributing large

computer codes and evaluated and processed data libraries.

The data packages include multigroup coupled neutron-gammaray cross sections and kerma coefficients, other nuclear

data, and radiation transport benchmark problem results.

(Computer code} data library} information; RSIC} radiation} radiation analysis,- shielding)

As an integral part of its information collection and processing activities, RSIC collects, makes operable,

packages, and distributes computer code

packages to nuclear scientists and

engineers engaged in shielding research

or design5~5. The various codes are designed for calculations related to

radiation from fission and fusion

reactors, radioisotopes, weapons and

accelerators and to radiation occurring

in space. The Center uses the word

"package" to mean all the items needed to

utilize a code effectively. The package

normally includes documentation describing the theory and code operation

(contributor's report plus RSIC abstract

and notes) and one or more reels of tape

on which is written the source program,

operating (binary or hex) program, input

and output for a sample problem, data

libraries, and auxiliary routines.

Most of the codes are written in

FORTRAN IV, which makes them nearly

machine independent. Several of the

packages actually represent coding

systems. These are represented in the

collection by prototypes, which are not

necessarily usef\il in themselves, but

which achieve generality in that they

are designed to be easily changed. Such

code systems are most useful to the

research worker who will invest a great

deal of effort in learning to use the

system. Other packages are groups of

interdependent codes which constitute a complete analysis system making use of a number of techniques.

The radiation treated by the

majority of the codes is either neutron

or gamma radiation or both, but some codes treat charged particles. The

types of geometry treated vary widely,

with many codes allowing a general threedimensional geometry.

For convenience, the available codes are grouped into two classes: (1) those

which treat radiation transport and

identified by Computer Code Collection

(CCC) numbers and (2) those performing

auxiliary data processing usefiil for

other radiation analysis purposes and

identified by Peripheral Shielding

Routine (PSR) numbers. The numerical

methods applied in the CCC codes are primarily discrete ordinates (1- and

2-dimension) , Monte Carlo (up to 3-

dimension) , and kernel integration

(generally 3-dimension) . The remaining

include removal-diffusion (Spinney),

moments, spherical harmonics, and

invariant embedding transport theory

codes and miscellaneous codes to

calculate fission product buildup,

release and resulting dose, stepping

power, optimization, sensitivity

analysis, and others.

* Research sponsored jointly by the U.S. Atomic Energy Commission and

the Defense Nuclear Agency under contract with Union Carbide Corporation.

171
The PSR codes include multigroup

cross section generation and handling,

nuclear models, experimental energy

spectra unfolding, optimization, plotting,

coupling discrete ordinate results to

Monte Carlo, random number generation, and

others

As an adjunct to the computer code

exchange, RSIC is involved in many data

activities, with most emphasis being

placed on nuclear cross section data.

Through cooperation with various agencies,

RSIC assists in improving the adequacy of

basic evaluated cross section data and

packages and distributes various types

of data libraries useful in radiation

transport analysis. The emphasis of

the effort is on the improvement of

calculational tools available to the

shielding analyst.

This work involves collaboration with

the National Neutron Cross Section Center

(NNCSC) at Brookhaven National Laboratory,

the Shielding Subcommittee of the Cross

Section Evaluation Working Group (CSBWG),

Atomic Energy Commission Controlled

Thermonuclear Research Division, the U.S.

Nuclear Data Committee, especially the CTR

subcommittee, and the Defense Nuclear

Agency (DNA).

The Center's role in the Evaluated

Nuclear Data File (ENDF) development is

to assist in the acquisition, checkout,

and review of "shielding" cross sections

in ENDF format which may ultimately be

placed in the ENDP/B file. In this

context, "shielding" cross sections are evaluations performed in the shielding,

radiation effects, or weapons radiation

transport communities which are likely

to have an emphasis on gamma-ray production cross sections, gamma-ray

interaction cross sections, and neutron

cross sections in the energy range of

interest for shielding with detailed

energy and angular distribution resolution. RSIC maintains and distributes

the Defense Nuclear Agency (DNA) evaluated

cross-section library. This is working

library in ENDF format whose content can be modified and revised as often as the

evaluator deems such changes to be

necessary. The key to this approach is a selected evaluator, the person res- ponsible for making the original

evaluation for a particular nuclide or element. He is then responsible for

authorizing changes in evaluations for

that nuclide. The evaluated data are

for those materials of interest to DNA,

whose cross-section values were originally

in a state of rapid change, and with

emphasis placed on neutron energies up to

20 MeV and on secondary gamma-ray production. Evaluations which are not being

modified frequently are found in the

ENDF/B library, which is available in

the USA from NNCSC at Brookhaven

National Laboratory.

For workaday problem solving, it has

been found useful to generate and

collect multigroup cross section sets,

and package, document, and distribute

them in a format suitable as input to

the most-used computer codes. Bach

data set, packaged as a unit, carries

a Data Library Collection (DLC) number.

As with the code packages, a particular

data package does not remain static but

is subject to revision, updating, and

expansion as required. Such changes are announced in the RSIC Newsletter. Other

data in the collection include gamma-ray

interaction cross sections, neutron

induced gamma-ray production spectra,

fluence-to-kerma coefficients, radioactive decay spectra and decay schemes,

and detailed output from transport

calculations

A continuing project, in cooperation

with the American Nuclear Society, is to

collect, edit, and publish reference

data in the form of "benchmark problems"^

The objective is to compile in conve- nient form a limited number of welldocumented problems in radiation

transport which will be useful in testing

computational methods used in shielding

analysis. The problem solutions, having

been determined by several methods,

should be representative of the state

of the art. The problem descriptions

are published in looseleaf form so that revisions and additions can be

easily made. In conjunction with

benchmark work, data sets are packaged

which allow the recalculation, with a. particular calculational method, of

already published results.

Lists of selected codes and data

packages are given in the following

table. These are typical of the most

used but not necessarily the best for

any particxilar application. Further

information on these or any other codes

or data are available from RSIC upon

request

172
Table

1. Neutron/Gamma-Ray Transport

Discrete Ordlnates

Multigroup

1-Dimension

Monte Carlo

2. Multigroup Cross Section

3. Kernel Integration

4. Spectra Unfolding

5. Fission Product Inventory

6. Multigroup Data Libraries

2-Dimensions

3-Dimen8ions

Neutron

Gamma Ray

Coupled

3-Dimensions

1.

Neutron

Coupled

References

Trubey, D.Z., The Radiation Shielding

Information Center - A Technical Information Service for Nuclear

Engineers, Nucl . Eng.Des . 2 (1969) 392-5

2. Maskewitz, B.F. , Trubey, D.Z., Roussin,

R.W. and Clark, F.H., The Radiation

Shielding Information Center: A

Unifying Force in the International

Shielding Community, Fourth International Conference on Reactor Shielding,

Paris, France (Oct. 1972), CONF721018, Vol. I, pp. 215-225.

3. Trubey, D.K. and Maskewitz, Betty F.

,

Computer Codes for Shielding Calculations - 1969, Nucl. Eng. Des. 10

(1969) 505-17.

CCC-42/DTF IV

CCC-82/ANISN

CCC-126/AS0P (optimization)

CCC-130/DTF-69 (X-ray)

CCC-204/SWANLAKE (sensitivity

analysis)

CCC-204/INAP (activation)

CCC-222/TWOTRAN II

CCC-209/DOT III

CCC-230/ TRIPLET (triangular mesh)

CCC-230/MORSE-CG (multigroup)

CCC-187/SAM-CE

PSR-I3/SUPERTOG

PSR-52/MACK (kerma factors)

PSR-51/SMUG

PSR-63/AMPX

CCC-48/QAD

CCC-94/KAP VI

CCC-213/ACRA (radioactive cloud)

PSR-17/FERDOR-COOLC

PSR-4I/MAZE

CCC-112/SAm) II CCC-233/CRYSTAL BALL

CCC-217/ORIGEN

CCC-225/REST

CCC-237/BURP 2 DLC-2/100G (lOO-group from ENDF/B)

DLC-33/MONTAGE (lOO-group activation)

DLC-23/CASK (22-n, 21-y)

DLC-27/AMPX01 (104-n, 22-y)

DLC-3l/FEWGl(37-n, 21-y ) Maskewitz, Betty F. and Trubey, D.K.

,

Computer Codes for Shielding Calculations - 1970, Nucl. Eng. Des. 13

(1970) 448-9.

Maskewitz, Betty F., Clark, Francis H., Trubey, D.K., Computer Codes for

Shielding and Related Calculations - 1972, Nucl. Eng. Des. 22 (1972) 334-341.

Roussin, R.W., Trubey, D.K. and

Maskewitz, Betty F. , Data Activities

of the Radiation Shielding Information

Center, Fourth International Conference on Reactor Shielding, Paris, France

(October 1972), CONF-721018, Vol. 4,

pp. 1191-1201.

Profio, A.E., Editor, Shielding

Benchmark Problems, 0RNL-RSIC-25( ANSSD-9) (Sup.l, 1970, Sup. 2, 1974) Oak

Ridge National Laboratory.

173
GI-AMMA RAY BUILD-IIP FACTORS FOR PIMITB MSDIA

K.John and D.Y.Gopinath

Health Physics Division

Bhabha Atomic Research Centre

Bombay-400085

Using the transport code ASFIT, energy build-up factors

are calculated for various energies and different systems. The

resijilts presented here are the energies O.O5, 0.1, 0.2, 0.4»

0.66, 0.8, 1.0, 1.25, 1.5, and 2.0 MeV. Media considered are

air, aluminium, beryllium, calcium, carbon, hydrogen, iodine,

iron, lead, magnesium, molybdenum, oxygen, silicon, sulphur,

tin, uranium and water and their thicknesses are 1.0, 2.0, 4,0,

6.0, 8.0, 10.0, 15.0 and 20.0 mean free paths. Empirical

formulae of the exponential polynomial type have been obtained

for these finite region build-up factors. Dependence of the

constants in the empirical formulae on the material property

Z has been discussed.

(ASFIT ; build-up factor ; empirical ; energy -, gamma ray ; mean free path) 1

Introduction

The build-up factor defined as the

ratio of the total detector response to

the virgin radiation' s response is a con- venient concept in radiation attenuation

calculations. In notation it can be

written as

where I = the total flux and

—LIX I e ^ = the uncollided flux

o Any given build-up factor depends

upon the material constituting the medium, the source energy or energies, the

location in the medium and the source geometry. An extensive study of build-up

factors has been done by Goldstein and

Wilkinsl using the moments method. This

method assumes the medium as infinite and

homogeneous. But in most of the shieldin;

calculations one of the important parameter is the transmitted flux. Due to the

assumption of the infinite medium moments

method does not provide this. Another

drawback of this method is that it is

^insuitable for the calculations of

heterogeneous shields.

Present Work

In this paper we present the energy

build-up factors in finite nledia for one dimensional slabs obtained using the

ASFIT (Anisotropic Source Flux Iteration

Technique) 2 transport code which overcomes the above mentioned drawbacks of

the moments method. The cross section

data used for the computation is given

in NSRD-NBS 29 . The media considered

for the calculations are Air, Aluminium,

Beryllium, Calcium, Carbon, Hydrogen,

Iodine, Iron, Lead, Magnesium, Molybdenum, Oxygen, Silicon, Sulphur, Tin, Uranium and Water. The source energies

considered are O.O5, 0.1, 0.2, 0.4,0.66,

0.8, 1.0, 1.25, 1.5 and 2.0 MeV and the

thickness are 1.0, 2.0, 4.0, 6.0, 8.0,

10.0, 15.0 and 20.0 mean free paths. We

analysed for empirical relations by

fitting the data for each media and ener- gy as a function of thickness using the

exponential polynomial'^.

Results

A very usef j.1 form for the build-up

factors has been given by Taylor^ . He

expressed the build-up factor as a sum

of the two exponentials, given by

B(^ix) = A e- °^1^^^ + (l-A)e- °^2^^^

where A, o(-j^, and are constants.

In our study we tried different types of

exponential polynomials and saw that the

funct ion

B(x) = A + A e~-^l^ (x in mean

free paths)

is the simplest and the best fit to almost all the data from energies 1.0 MeV

onwards. The constants are listed in Table-1. Table-2 gives the media in which the maximum error is above 6'/. . In all other cases the error is less than 6/. . The constants obtained are given in Figs, la to Id as a function of atomic number

(zj for energies 1.0, 1.25, 1.50, 2.0. Below 1.0 MeV we could not obtain a smootii curve for constants versus Z.

174
Table-1

C9nstant s ^ of . the , cui^-e , B( X} =^

Energy (MeV)

z l.QO

6.614+01

-6. 538 + 01

1 .363-02

2.00

1.0 HYDROGEN

AOAl

81

3.537+02

-3.532+02

3.014-03

3.353+01

-3.259+01

2.361-02

1 . 831+01

-1.725+01

3.635-02

4.0 bERYLL lUM

AO

Al

81

3.270+02

-3.265+02

3 .232-03

5 . 867 + 01

-5.788+Ul

1 .517-02

3.169+01

-3.U63+01

2 .484-02

1 . 873 + 01

-1 . 768 + 01

3 . 543-02

CARB'ON AO

Al

81

2.653+02

-2.648+C2

3 .920-03

5.680+01

-5.599+01

1.551-02

3.117+01

-3.021+01

2.498-02

1.869+01

-1.763+01

3.530-02

AIR

AO

Al

8

3.044+02

-3.039+02

3.43 7-03

5.807+01

-5.727+01

1.52 5-02

3.150+01

-3.054+01

2 .482-02

1.900+01

-1.795+01

3 . 486-02

8.0 OXYGEN

AO

Al

81

2.753+02

-2.748+C2

3 . 764-03

5.526+01

-5 .445+01

1 . 589-02

3.056+01

-2.959+01

2 .542-02

1 . 900+01

-1.795+01

3 .473-02

10.0 WATER

AOAl

B 1

3.034+02

-3 .030 + 02

3 .448-03

5.689+01

-5 .609 + 01

1 .554-02

3.099+01

-3.002+01

2 .520-02

1.891+01

-1.786+01

3.5 0 3-02

12.0 MAGNESIUM

AO

Al

8

1. 787+02

-1.781+02

5 .533-03

5.031+01

-4.947+01

1 .693-02

2.937+01

-2.839+01

2 .589-02

1. 866+01

-1.790+01

3 .431-02

13.0 ALUMINUM

AOAl

81

1.625+02

-1.619+02

6.021-03

4.908+01

-4.823+01

1 .723-02

2.918+01

-2.820+01

2 . 594-02

1.900+01

-1 . 795 + 01

3.41 5-02

14.0 SIL ICON

AO

Al

D i

1.470+02

-1.464+02

A "7 1 — n a

4.885+01

-4.800+01

1 "7 "5 n — n 9

2 .932 + 01

-2.834+01

1 .910+01

-1 .805+01

16.0 SUI.PHUR

. . ....... .

AO

Al

Bl

1.207+02

-1.201+02

7.786-03

4.591+01

-4.504+01

1 . 796-02

• ••••••••••

2.856+0

-2.757+01

2.604-02

• • ••••«••••

1.894+01

-1.788+01

3.383-02

........«•

20.0 CALCIUM

"ao" Al

B

9.243+01

-9. 172+01

9 . 70 8-0 3

4.167+01"

-4.078+01

1 .917-02

" 2.729>01

-2.630+01

2 .662-02

1.904+01

-1.799+01

3.312-02

26.0 IRON

AU

Al

B

5.92U+U1

-5.837+01

1.402-02

3.510+01

-3 .417 + 01

2 . 160-02

2.520+Ul

-2 .420+01

2.775-02

1.878+01

-1.773+01

3.272-02

42.0 MOLYBDENUM

AO

Al

B 1

2.186+01

-2.085+01

3.01 2-02

1 .991 + 01 -1 .887 + 01

3 .208-02

1 .796 + 01

-1,691+01

3 .405-02

1 .698+01

-1.592+01

3.281-02

50.0 TIN

AO

Al

81

1 .407+01

-1.301+01

4 . 12 3-02

1 .469 + 01 -1 .363+01

3 .919-02

1 .465 + 01

-1 .359 + 01

3.834-02

1. 543+01

-1.437+01

3 . 376-02

5 J.O IODINE

AO

Al

81

1 .264+01

-1.157+01

4 .389-02

1 .350 + 01

-1 .244 + 01

4 . 105-02

1.363+01

-1.256+01

3.983-02

1.469+01

-1.363+01

3.443-02

82.0 L~AD

AU

Al

Bl

5.281+00

-4 .234+00

6.285-02

6 .453+uO

-5 .401+00

5.456-02

7.453+00

-6 .398+00

4.836-02

9.283+00

-8 . 229+00

3.836-02

92.0 URANIUM

AO

Al

81

4.539+00

-3.495+00

6.023-02

5 .600 + 00

-4.551+00

5.271-02

6.607+00

-5.556+00

4.646-02

8. 301+00

-7.250+00

3.736-02

175
Table-2

Media Error {'/.) Hydrogen 13

Beryllium 13

Carbon 12

Air 13

Oxygen 12

Wat er 13

Magnesium lU

Aluminum 9 Silicon 9 Sulphur 8

1 mfp . In all other cases the error is

less than 6'/.]

ENERsy 100 Mav. COHSTAWTS OFTHf FUltCTIOK (I) - AO* A,

X lU MEAN rni PATd

4 2P0

10 30 30 40 50 60 70 z Catomic number) Pig. la

z Catomic number ) ENERGY I ZSMeV. , CONSTANTS Cf THE FUNCTION BttJ = Ao»A, e'*'*, A, . -Ao ilA Fig. lb

ENEUV V50MM.

COKSTAKTS or THe FUNCTION SCI) . Ao»At t^X

A| .-Ao-rAA

30 40 so so 70 X (ATOM/C NUMBEH) Fig. Ic

ENERiSY 2 00 Mev

CONSTANTS OF THE FUNCTION 8U) .Ao»A,

A, .-Ao'^lA

_4A_

10 20 30 « 50 60 70 JO W "W

Z (ATOMIC NUMBER) Fig. Id

References

Goldstein, H. and V/ilkins, J.E. , Calculation of the Penetration of Gamma rays,

NYO 3075 (1954)

Gopinath,!). V". and Santhanam,K. , Radiation Transport in one dimensional systems-Part I, lJuc.Sci.e Engg. 43 186-196

(1971).

Hubbell, J.H. , Photon Cross sections,

Attenuation Coefficients, and Energy

Absorption Coefficients from 10 JieV to

100 GeV 1969, ifSRDS-iJBS 29-

Buckingham,R. A. , Numerical Methods, Sir

Isaac Pitman e 5ons Ltd., London, p.329.

Taylor, J. J., "Application of Gamma Ray

Build-up Data to Shield Design" , V/APD memo BM-217.

176
PHYSICAL PRINCIPLES OF PHOTON DOSIMETRY*

Walter S. Snyder**

Health Physics Division

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

Estimation of dose absorbed in the human body is important

from the point of view of health physics as well as because of the

increased utilization of nuclear radiation in clinical and

diagnostic medicine or therapy. An idealized mathematical model

of the human body was developed and Monte Carlo calculation was applied to evaluate the photon dose. In this paper the attention

is restricted to certain physical results or principles which are

a by-product of such studies. These relate to evidence on the

validity of the reciprocity theorem, use of the build-up factor

for an infinite medium of tissue in calculating absorbed fractions,

scaling absorbed fractions for the weight of the target organ, and

the effects of non-homogeneity of the body on absorbed dose to the

organs

(Dose, dosimetry, Monte Carlo, organ, phantom, photon,

reciprocity theorem, source, target, tissue.)

Introduction

Estimation of dose is important for

medical uses of x-rays and in nuclear

medicine, whether for diagnostic uses or for therapy. Also it is of great importance for health physics since use of

nuclear energy requires careful control

of sources so that no undue exposure of

the occupational worker of the general

public results. This paper is limited

to consideration of dose from sources of

photons within the body because the short

range of electrons and alpha particles

considerably reduces the complexity of

estimation of the average dose to an

organ, and it is this concept of average

dose in an organ or tissue that is con- sidered throughout this paper. Although

many of the principles given here can be

applied to micro-dose or to the other

concepts of dose these are not considered

in this paper.

Some ten years ago the author and

his associates began to develop an idealized mathematical model of the

human body to use for Monte Carlo type

calculations of photon dose. The story

is lengthy and not without interest, but

in this paper the attempt is to focus on what has been learned about dosimetry in

a complex phantom resembling in some

Research sponsored by the U.S. Atomic Energy Commission imder contract

with Union Carbide Corporation.

**Consultant

respects the human body. In Figure 1 the

exterior form of the phantom is shown and

in Figure 2 some of the internal organs

Pig. 1. The adult human phantom.

are shown, while Figure 3 displays a sketch of a skeleton together with the

idealization of it for the phantom. All

of these organs are described by rather

177
Fig. 2

OftNL-OWG T0-4810R

Pig. 3- Idealized Model of the Skeleton

for Computer Calculations (left)

... and a More Realistic Representation (right) with Percentages of

Red Bone Marrow Found in the

Shaded Portions of the Bones.

simple mathematical formulae which are

easily adapted to computation on a large

scale digital computer. . The mass absorption coefficients are chosen for three distinct types of

tissue; namely, bone plus bone marrow

which is homogeneous with a density of

about 1.5 g/cvP, lung tissue which has a density of about 0.5 g/cm^ and the

remainder of the phantom which has ., density near 1 g/cmP. Each of these

tissues has its own characteristic

composition and while each is homogeneous, the phantom as a whole has some of

the diversity of the body. Thus the

organs of the phantom approximate actual

body organs in size, shape, composition

and density. However, there has been no attempt to reproduce minor details of

either the organs or of appendages, such

as fingers, ears, etc. which are presumed

to have a small effect on photon

scattering.

Some of the results of our studies

have been published in MIRD Phamphlet

No. 5 and more special results have been

published in Health Physics2»3 and in

ORNl report s'^~13. There have been

sixteen organs used as a "source" organ

and in each case twelve monoenergetic

sources of photons were distributed

liniformly in these organs. When a calculation is completed one has dose

to all twenty-three "target" organs of

the phantom from a uniformly distributed

source provided the statistics are good.

Frequently they are not, but this is

discussed below. An extensive tabulation

of results is in course of publication

as ORNL-5000 (in press )14 b^t here

attention is restricted to certain

physical results or principles which are

a by-product of the studies.

Variation of Dose with Organ Mass

To a first approximation, the

average dose to an organ from a source outside the organ and some distance away

is independent of the organ mass or size. Strictly, the principle cannot be

correct in all cases as is evident if the

target organ increases so greatly that

the solid angle subtended from the source is changed significantly or if

the distance from soixrce to target is

markedly changed. Except for these

extremes the dose is relatively

insensitive to the mass of the target

organs. As one example, in Figure 4 are plotted the dose per photon to three

different models of the solid bladder

which is given three different weights.

Although the weights vary by a factor

of two, the doses are so close they can barely be distinguished on the figure.

The sources are in the ovaries and in

the kidneys which are reasonably close

to the bladder. This and similar

examples provide an answer to many

questions medical people frequently ask;

"Your calculations are for a standard

man, but my patient is not standard in

many respects. What difference in dose

will result if his liver is larger than

usual?" From sources outside the liver

the evidence indicates little difference

provided the average distance from source to target remains about the same.

If the liver is both the source and target organ the answer; is rather

different. If the source is uniformly

178
PHOTON ENERCTT (M»v)

Fig. 4. Dose for Three Bladder Sizes and

Two Source Organs.

distributed in a sphere and if multiple

scattering is neglected (mean free path

much greater than the radius r) the

absorbed fraction of energy is 3t\x^I)/ A and this implies .that the dose vanes

inversely as VT^' ^ . It is surprising how

well this formxala holds for target organs

whose shape is not approximately

spherical. In Figure 5. the absorbed

fraction, AF, divided by ^^^'{^±q

ORNL-OWO 74-5131*

1

1

THYROID <— THYROID

THYROID WEIGHT (g) 0 34

4 8.5

» 11.4 1 13.4

. 15.9

• 19.6

1 1

1 1 M ml 1 1 M 1 ml 1 1

PHOTON ENERGY (Mev)

Fig. 5. Absorbed Fraction of Photons in

the Thyroid in Relation to Size

and Shape of Organ. (Source in

Thyroid)

plotted for three shapes of thyroid which are sketched at the top of the figure and

for masses ranging from 3.4 g to 19,6 g.

One can scarcely distinguish the diffe- (4 rent points they lie so closely together

and the curves do seem approximately

constant for photon energies above 0.1

MeV. Below that, the curves are still

close together but now the mean free

path does not greatly exceed the diameter

of the thyroid and so the curve is not

flat . This is only one of many illustrations which indicate the relative

insensitivity of this quotient which is,

however, only for sources distributed

uniformly in the organ. Other illustrations are given in Reference 15

The Reciprocity Theorem

The interplay of theory and practice

is illustrated by the reciprocity theorem

first stated by Mayneord, (1945)16.

This theorem states that if the same' activity is distributed uniformly in two

subregions A and B of an infinite

homogeneous scattering medium, the dose

rates produced in the other regions are

equal. In symbols, D(A<—B) = D(B<—A) where A<— B indicates the source region

B and the target region A. Now the body

is neither infinite nor homogeneous and

one may wonder whether the theorem is

useful in practice. One of the byproducts of the Monte Carlo type of

calculation is that when A and B have

each been used as a source organ one can test to see whether the equation above

holds—at least within the limits of

statistical accuracy. In Figure 6 the

resiilts of several hundred tests are recorded. The ratio D(A<—B)/D(B<—A)

is calculated, where D(A<—-B) is the larger

of the two dose rates for all choices

of A and B such that the coefficient of

variation (= 100 a/m) did not exceed 50^.

The bar graph indicates the percentage

of cases where the ratio did not exceed

1.2, 1.4, 1.6 etc. At the low photon

energies none of the ratios exceeded two,

but at higher energies there were a few

exceptions and these are indicated. In

all these cases about 60X or more of the

ratios were below 1.2, while 95/. or greater were below 1.8. Moreover, a part of this inaccuracy may be due to the

statistical scatter of the Monte Carlo

data. In fact, as the coefficient of

variation is limited to 30X and then to

20/. the exceptional cases where the ratio

exceeds 2 tend to disappear. This is

the basis for the claim- that the ratio

is, in most cases, below I.3, The data

shown are only for organs composed of

soft tissue and when bone is one of the

organs the above result no longer holds

but an adjustment can be made which is

given in reference 15. Thus, although

179
there is no doubt that the reciprocity

theorem is not exact for organs of the

body, it can still be used if one is

willing to accept a limited accuracy of

20-30/. .

Fig. 6. Distribution of Reciprocity:

Tissue Organ and Tissue Target.

The Build-up Factor

For many source and target organs

the Monte Carlo estimates are statistically uncertain and the authors have

therefore sought other methods which,

while less exact, would not involve

large errors. The specific absorbed

fraction, that is the fraction of photon

energy absorbed per gram of the target

organ, can be written as

(1)

where the integral is of the product

space AxB and \i and lig^j^ denote the mass attenuation and mass absorption coefficients for photons of the required energy

and I A[ denotes the mass of organ A and

1x-Y| the distance from point X to point

Y. This expression can be integrated

using statistical methods and when it is

compared with the results obtained from

the Monte Carlo technique a surprising

fact emerges. In effect, the build-up

factor has been tabiilated by Berger

(1969)^' for an infinite space of water

so that in effect the body is enlarged

to an infinite extent and is also

homogeneous. But this change has remarkably small effect on the value of $

obtained for the body.

In Figizres 7-9 the results are displayed, the value of $ obtained by the

Monte Carlo calculation being the

abscissa and the result of the evaluation

of (1) the ordinate. When the two are

equal the point should fall on the line

bisecting the angle. It is foiAnd that

for cases where the Monte Carlo results are reasonably exact, say with a coefficient of variation not exceeding

50/., the two results agree within a

Fig. 7. Monte Carlo Estimates of Specific

Absorbed Fractions Compared with

Build-up Factor Estimates.

2 0«NL-r)WG 7'r7£B,-R

F PHOTOM ENERGY O.OE Me^' / / .

SaF (MON~E CiMO ESTIW1T6S1 Fig. 8. Monte Carlo Estimates of Specific

Absorbed Fractions Compared with

Build-up Factor Estimates.

factor of about 2 and usually are much

closer than this. This agreement is not

due to the lack of influence of the

180
References

"O'^zz— —' 1 ,

' . . . 1

- - PHOTON EMERGY I Vev

COEFFICIENT Or viRlfiT.ON 1 / BETWEEN 20-30%

j

, , I , i

10 ' to"* ra""' SflF {MONTE CaRLO ESTIMATES)

Fig. 9. Monte Carlo Estimates of Specific

Absorbed Fractions Compared with

Build-up Factor Estimates.

build-up factor, for it has -values of the

order of 10^ at 20 mean free paths in many

cases. Only the results for photons of

energy 0.03, 0.05 and 1 MeV are shown here

but they are typical of the others. In

particular, note the values with arrow attached on the two plots for the lower

energies. These represent the ratio where

bone is one of the organs and the arrow

represents the displacement that would

occvir if one replaced p.^^ for soft tissue

with for bone. Thus this method seems

to afford a means of getting values of $

which are sufficiently accurate to bring

one within a factor of 2 of the correct

result and do not involve inordinately

i large sample sizes.

Special Studies

The Monte Carlo technique can be

applied to a wide variety of expos^ure

situations, for example, dose to the

fetus from a radionuclide in the body,

dose to an individual sujrrounded by a large cloud of radioactive material, and

I also to children. It is particularly

j instructive to note that preliminary

j phantoms have been designed for children

and the results obtained indicate that

dose per photon increases by an order of

j magnitude or more as the phantom becomes

smaller. These phantoms are now in the

. process of being refined at ORNL to

I better represent the child. The study

of dose to the bladder, an organ for

j which the dose per photon changes

greatly during the nrocess of filling,

' has been publishedl5. No doubt these

I are only a few examples of the many uses

to which the Monte Carlo method of

' calculation can provide answers.

1. Snyder, W.S., Ford, M.R., Warner, G.a.

and Fisher, H.L., "Estimates of

Absorbed Fractions for Monoenergetic

Photon Sources Uniformly Distributed

in Various Organs of a Heterogeneous

Phantom," MIRD Pamphlet No.2,J. Nucl.

Med,, Suppl. No.l, 15 (1969)."

2. Cloutier, R.J., Smith, S.A., Watson,

E.E., Snyder, W.S. and Warner, G.G.,

"Dose to the Fetus from Radionuclides

in the Bladder", Health Physics, 26,

No. 4 (1974).

3. Poston, J.W. and Snyder, W.S., "A

Model for Exposure to a Semi- Infinite

Cloud of a Photon Emitter," Health

Physics, 26, No. 4 (1974).

4. Snyder, W.S., Ford, Mary R. and

Warner, G.G. , "Estimation of Dose and

Dose Commitment to Bladder Wall from

Radionuclides Present in Urine','

Health Phys. Div . Ann . Prog .Rept . for

Period Ending July 31, 1970, ORNL4584, 206.

5. Snyder, W.S., Cloutier, R.J. and

Smith, S., "Dose to a Developing Fetus

from a Gamma Emitter in the Bladder,"

Health Phys .Div. Ann. Prog. Rept . for

Period Ending July 31, 1971, ORNL4720, p. 119.

6. Snyder, W.S. Ford, Mary R., Warner,

G.G. and Brindza, P., "Absorbed

Fractions for Internal Emitters,"

Health Phys .Div. Ann. Prog. Rept . for

Period Ending July 31, 1971, ORNi4720, p. 121.

7. Snyder, W.S., Ford, M.R. and Warner,

6.G., "Estimates of Absorbed Fractions

for Photon Emitters within the Body,"

Health Phys .Div. Ann. Prog. Rept . for

Period Ending July 31, 1972, ORNL4811, p. 86.

8. Hilyer, M.J.C., Snyder, W.S. and

Warner, G.G., "Estimates of Dose to

Infants and Children from a Photon

Emitter in the Lungs}' Health Phys.

Div. isjin. Prog. Rept . for period ending

Jvily 31, 1972, ORNL-4811, p. 91.

9. Snyder, W.S., Poston, J.W. and

Dillman, L.T., "A Model for Exposure

to a Semi-Infinite Cloud of a Photon

Emitter," Health Phys .Div. Ann. Prog.

Rept. for Period Ending July 31,

1973, ORNL-4903, P- HO.

10. Snyder, W.S. and Ford, M.R. , "Estimation of Dose and Dose Commitment

to the Bladder Wall from a photon

Emitter Present in Urine'," Health

Phys .Div. Ann. Prog. Rept . for Period

Ending July 31, 1973, ORNL-4903,

p. 115.

11. Hilyer, M.J.C., Hill, G.S. and Warner,

G.G., "Dose from Photon Emitters

Distributed UniforniLy in the Total

Body as a Function of Age," Health

181
Phys. Div. Ann. Prog. Rept . for Period

Ending July 31, 1973, ORNL-4903,

p. 119.

12. Snyder, W.S. and Ford, M.R. , "Estimates of Dose Rate to Gonads of

Infants and Children from a Photon

Emitter in Various Organs of the

Body," Health Phys. Div. Ann. Prog. Rept

for Period Ending July 31, 1973,

ORNL-4903, P- 125.

13. Snyder, W.S., Poston, J.W., Warner,

Gr.G. and Owen, L.W., "Dose to a Dynamic Bladder for Administered

Radionuclides," Health Phys .Div. Ann

Prog. Rept. for Period Ending July

31, 1974, p. 13.

14. Snyder, W.S., Ford, Mary R., Warner,

G.G. and Watson, Sarah B., "A

Tabulation of Dose Equivalent per

Microcurie-Day for Source and

Target Organs of an Adult for

Various Radionuclides," ORNL-5000,

( in press )

15. Snyder, W.S. "Estimation of Absorbed

Fractions of Energy from Photon

Sources in Body Organs," Medical

Radionuclides ; Radiation Dose and

Effec ts, USAEG report CONF-691212

(1970T7p.33-49.

16. Mayneord, W.V., "Energy Absorption:

IV. The Mathematical Theory of

Integral Dose in Radium Therapy','

Brit. J. Radiol. 18, 12 (1945).

17. Berger, M.J., "Energy Deposition in

Water by Photons from Point Isotropic

Sources," MIRD Pamphlet No. 2, J.Nucl.

Med., Suppl. No.l, p. 15 (1968).

182
TRACE THEORY APPLIED TO PHYSICAL, CHEMICAL

AND BIOLOGICAL SYSTEMS*

S.C. Sharma and Robert Katz

Behlen Laboratory of Physics

University of Nebraska

Lincoln, Nebraska 68508, U.S.A.

The conceptual structure of the 6-ray model of track effects

will be presented. Its universal applicability to a wide spectrum

of radiation detectors and radiation environments will be shown.

For 1-hit detectors, the response with LET variation is described

by two parameters, the D-37 dose for gamma-rays and the size of

the sensitive element. The role of 1-hit detectors in the measurement of radiation quality will be briefly outlined. A simple

cellular model which applies to cells whose radiosensitivity parameters have been determined experimentally yields the cellular

survival, RBE, OER etc. for heavy ions, neutrons and pions.

(Cell} delta ray; dose,- ions; LET; model; neutron; OER;

one-hit detector; pion; radiation; track)

Introduction

Studies of track effects in emulsion

and other physical, chemical and biological media indicate that secondary

electrons are the principal agents

coupling the track-forming particle to

the medium through which it passes. The

spatial distribution of ionization energy

by the secondary electrons about the path

of the particle determines the track

structure and is a relevant parameter to

describe radiation effects. Since gammarays are also coupled to an irradiated

medium through secondary electrons,

differences in the effects observed in

these kinds of irradiations arise either

from the time schedule with which the

electrons are generated or from their

spatial distribution, or both. Track

effects may be correlated with effects

observed from gamma-ray irradiation by

assuming that the response of small subvolumes of the medium near the path of an energetic particle is as if these

subvolumes are part of a larger system

irradiated with gamma-rays to the same

dose. Thus the knowledge of the doseresponse function of a medium to gammarays may be coupled with the spatial

distribution of dose from secondary

electrons to yield the spatial distribution of response about the path of a charged particle. The theory has been

applied to a variety of detectors of

interest in dosimetry, including

nuclear emulsion, scintillation

counters, plastics, glass, thermoliiminescence, and chemical dosimeters,

enzymes, viruses, and biological cells.

It is applicable to track-segment

bombardments as well as to mixed radiatian

environments including stopping

particles^.

Dose - Response Functions

The transition from gamma-ray to

heavy ions is achieved by using gamma-ray

dose-response transfer functions. Most

of the detectors display a 1 - or - more

hit response to dose. That is, the

probability P that a detector is activated at dose D may be expressed as:

P = 1 - e'^/^o (1)

where E^ (also called the D-37 dose) is

the dose of gamma-^rays at which 37%

of the detector's sensitive elements

survive (or at which 63% are activated).

At this dose there is an average of 1 hit

per sensitive element. These are on-off

detectors. If they are not activated by

a passing particle their response to the

next particle is as if there were no prior irradiation. Among the detectors,

which are classified as 1-hit detectors, are photographic nuclear emulsions.

Biological cells display a different

sort of response, described by the

mathematical form of a multi-target,

single-hit model, expressed as: P = (1 - e-^^^o)^ (2)

where m is the multiplicity of the target

structure, and it is taken that each of

the m elements of the target must be

inactivated, by a single hit, for the

cell to be killed. If some lesser number

* Supported by the USAEC and the NSF (RANN)

183
of elements than m have been affected by

the radiation, it can be said that the

cell has accumulated sub-lethal damage.

Theory

The size of a sensitive element

plays an indirect role in determining

the response of a detector to gamma-rays, as it affects the D-37 dose, but it plays

a direct role in heavy ion irradiation.

We take each sensitive element to act

collectively, and find the radial distribution in energy density 1 deposited in

sensitive elements of radius slq as a function of the elements' radial

<iistance t from the ion's path. The

result, shown in Fig. 1 as a graph of E

(z, p, t, ag). P^aQ^/z^ vs. t/a.Q, is the

basis of the calculations of the theory.

The gamma-ray dose-effect relationship

(Eqs. 1 or 2) is used as a transfer

function by applying it to Fig. 1 to find

the radial distribution of effect about

the path of an ion of charge number z, moving at relative speed p through the

medium. To calculate 1, a simple deltaray distribution formula is used, which

gives the number of rays per unit path

length per unit energy interval. The

delta rays are taken to be ejected

radially, to loose energy at a constant

rate, to move in straight line paths, to

be limited in energy where T^j^x = 2mc2p2(i _ b2)-1^ which is determined by

kinematics-^. The maximum radial penetration X has a nominal value (in water)

of about 10~^p2 cm.

Pig. 1. Radial distribution of the local

dose E, in water, deposited by

delta rays in sensitive elements

of radius a.Q whose center is at

radial distance t from the path

of an ion of effective charge

number z and relative speed

where L is the stopping power of the ion.

RBE = (o/L) (5)

At distances where both t and ag are substantially less than x, the

normalized curves of Eig. 1-lie atop one another, with the essential result that

sites for which t/aQ< 1 experience a "local dose" which varies as z^^~^aQ~ , while sites for which t/ao > 3 experience a local dose which varies as z^^~^t~^ 2. In both cases the local

dose varies as z^/p^

1 - hit Detectors

When Eq. (1) is applied to Fig. 1,

with a suitable value of Eq and a.Q, we obtain the probability P for inactivation.

Since the radial integral of the

probability is the cross-section a for

the ( in)activation of a sensitive

element by a single passing ion, we may

find the radiosensitivity of a detector

to this mode of inactivation.

04 a = j27ctP dt (3)

0 Radiosensitivity k^ may be calculated from:

ki = a/L (4)

Proiu Eqs. (1) and (3) we note that

the response of a 1-hit (m = 1) detector

may be found_£rom the two detector

parameters and aQ. We also note that

detector parameters and ion parameters are not separable variables. Dosimeters we now identify as 1-hit detectors are shown in Table-I. In most cases the

characteristic target size is only

poorly evaluated. The identification is

based on gamma-ray, or heavy ion res- ponse or both. Having the parameters Eq

and ao we can calculate the response of a detector to any radiation environment^

In Fig. 2 we show the systematic variation of RBE with an increase in LET.

In Fig. 3> we show the predictions that were made and sent to Appleby' before

his measurements of the yield of the

Fricke dosimeter in the PPA nitrogen

beam. Results are in quite good agreement .

To summarize the features and

characteristics of 1-hit detectors, we note that when energy is deposited

diffusely, it is most efficiently used

by a 1-hit detector because there is no

184
Table-I

PROPERTIES OF l-HIT DETECTORS

T

>. 6. K

erg/cm' A f/lOOeV

BidUil Production

Vtllne

Thysilne Glycine Cytosin*

S.Oxlo'

1.8

1.3 g 7.7x10?

3.0xlo'

1 5 15

8520 150

2.0

6.0 0.05

5.3 0.4

610

210

110

170

320

ln«ctl»«t1oB (enzynes)

lyio jyne Tryps In ONA-tse a-9t1«ctosUise

3.3xl0'

2.5

1.7

g 3.1x10"

14

1825

4.5

2.7 1.4

310

400 540

Inictlvttlon (viruses)

T-1 k-174 (243-252A) , T-7 (i<et)-{590-650A)

5.7x10'

5-0 c 8.5x10" 300 0.17 360

Optlcil Rotation Ar(Mnose-3I solution

51 solution

3.1x10*

5.7

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60

60 15.6 90

Lusinescence

C1tss-Ag tctivited

C«f , :Mn CtSO.:Mn

llf

1.0x10*

2.0

1.0

, l.Oxlo'

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liquid

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Cauls Ions »-2

t.O

(.2

11.5 C.5

3.0x10 2.0x10

5.0x10

1 .0 3.0x10

1200

120O

1200

1200 200O 0.\6

Pig. 2. Radiation detectors. The niimerical values of the detector parameters have been found in different ways for the different

detectors, and must be regarded

as somewhat tentative.

Fig. 3. Calculated values of the RBE of

1-hit detectors at different

values of the relative speed of

a bombarding ion, are plotted at

five ion speeds from 0.95c to

0.058c and ao=10~' to 10-4 cm. All plots are given as a functi-„

on of zS/kp'^ where k=Boao'^/2xlO~'.

By matching experimental plots

of the radiosensitivity (or RBE)

vs. z2/p2^ iQ .(jhe theoretical

curves, we can determine k.

over-kill. The radiosensitivity and RBE

decline with increasing values of the

LET and they are both multiple-valued

and non-linear. Since„RBE may be found

from the product of and the radiosensitivity, k, we note that the RBE of

1-hit detectors is always less than 1.

The role of the 1-hit detector in the

measurement of radiation quality will be

shown in the last section of this paper.

A Model for Cellular Sijrvival

When m = 1, the detector cannot

accumulate sub-lethal damage. The probability that it will survive irradiation by a beam of particles of fluence

F is e"*^^. When m>l, the sensitive

element can accumulate sub-lethal

damage. We take the gamma-ray doseresponse curve for biological cells to

be of the form as given in Eq. (2). We

follow the mathematical operations as outlined in 'Theory' and arrive at

the delta ray theory of the inactivation

of cells. Just as in the 1-hit detector, a cell can be inactivated by the passage

of a single ion, which is called ion-kill

mode, and they may be inactivated in a second mode, called gamma-kill , through

the participation of many delta-rays

from different ions. The surviving

fraction of a biological species when a dose D of the radiation is deposited is

given by

l^/N,=e-^o?Ftl-(l-e-(l-^^^/^o)"'j (6)

P=a/ao = (1-e (7)

185
where Oq, k, m and Eq constitute a set of

four fitted parameters.

D = PL

Z(l - e-125PZ-2/3

Y

(8)

(9)

(10)

where D dose in gamma-kill mode.

For biological materials there are

two size parameters which we have called

Oq and k. The first of these is nominally the cross-sectional area of a cell

nucleus. The second parameter k is

formally the value of z^/ 4p2 a,t which

plateau (or saturation cross-section) is

achieved when cells are bombarded with

various heavy ion beams. Parameters Eq

and m are extracted from the x-ray

survival curve of a biological cell.

One compact set of four parameters

describes the cell survival curves for

all track-segment and stopping particles.

The extension to the mixed radiation

environments arising from heavy ion beams,

neutrons and pions is straight forward

provided that we know the spectrum of - secondary charged particle distribution^.

In Fig. 4 the parameters for T - 1

human kidney cells and the sirrvival curves they generate are shown in com- parison with the data to which the

parameters were fitted^.

A beam of heavy charged particles

can be approximated by a simple model

incorporating attenuation and straggling,

but neglecting secondary particle production, beam contamination, energy

inhomogeneity and focusing5 . Use of the

heavy ion beam model yields cell survival

as a function of depth in a 250 MeV/amu

oxygen beam to be compared with experimental data of Roisman et al. (LBL-2016,

1973) • These results4»5 as shown in

Fig. 5 were predicted before the experiment was actually performed.

With this model, we have designed

ridge filters (to obtain iso-survival

regions of any desired width) , have

calculated survival, OER, RBE, dose as a function of the depth in a phantom for

different cell lines and have compared

some of these calculations to the

calculations of the response of different

1-hit detectors. In Pig. 6, we show the

calculated response of an alanine

dosimeter, here labelled as its RBE, in

a cross-field irradiation with a neon

beam, and compare it with the calciilated

T-1 HUMAN KIDNEY CELLS- ANOXIC -TODO-1966

Fig. 4. Calculated values of the response

of alanine, the deaerated and the

aerated Fricke dosimeters as a function of depth in a Bevalac

beam irradiated phantom having the

stopping power of water, after

Irradiation with 220 MeV/nucleon

oxygen beam. The predicted values

of the average RBE in plateau and

peak regions agree with recent

measiirements of Appleby'.

10°

—I 1

1 1

1

1 r 1

1 1—

T-1 KIDNEY CELLS (ROISMAN. 1973) OXYGEN BEAM

ENERGYj^l^lgl (MeV/nucleon) 228

170

6 8 DEPTH (cm)

10

Fig. 5. Survival data (Todd) for anoxically exposed T-1 human kidney cells are superimposed on a family of

theoretical curves from fitted

parameters^.

value of the fraction of the dose

delivered to kidney cells in the gammakill mode (Eq. 10), for both aerobically

and anoxically irradiated cells". This

demonstrates that the RBE of a 1-hit

detector must decline with an increase

with the 'LET' of the radiation. Both

S and OER show a similar decline. Thus

it is suggested that an alanine dosimeter, or other suitable 1-hit detector, can be used alongside a conventional

dosimeter in the measurement of radiatitm

quality, particularly in the case where

quality is changing".

186
DlBcusslon

A.K. Ganguly

Fig. 6. Experimental values of the sur- viving fraction of kidney cells

irradiated aerobically and

anoiically, at different depths

in a " submarine" with a beam of

oxygen ions at an initial energy

of 226 MeV/nucleon at the BEVALAC

(From Roisman et al., lBl-2016,

49, Sept. 1973) are compared with

predictions of the delta-ray

theory^ » 5

Acknowledgement

We thank Rose Ann Nelson for her

assistance in the course of these

investigations, and in the preparation

of materials for publication.

I am intrigued by the track model

you present. Can you extend the model

to deal with tracks in individual high

molecular weight systems, arising out of

single or a few radioactive atoms incorporated in them.

S . C . Sharma

The theory specifically avoids the

assignment of the microscopic interactions between radiation and matter which are ultimately responsible for the observed effects. We understand the structure

of the track common to all the detectors

rather than the individual phenomena

different in each detector. We have

simulated tracks in different emulsions

and work is in progress to understand the

parameters of significance in track

structtire. So the answer is 'no' at the

present time.

S. Mukher.ji

1. Is the theory on delta ray production tested in the single case of ionpair formation in elemental gases ?

2. The energy-loss rate for heavy

ions is not always given by Bethe's

equation.

S.C. Sharma

1. I believe there is good deal of

information on delta-ray production in

elemental gases. We use simple deltaray distribution formula and are always

interested in knowing more about the

finer details of the variation of COvalues in gases for various energies.

References

1. Butts, J.J. and Katz, R., Radiat

Res. 10, 855 (1967)

2. Katz, R., Sharma, S.C. and

Homayoonfar, M., The Structure of

Particle Tracks, in Topics in

Radiation Dosimetry . F.H. Attix, ed..

Academic Press, New York (1972).

3. Katz, R., Sharma, S.C. and

Homayoonfar, M., Nucl. Instr. and

Meth. 100, 13 (1972)

4. Katz, R. and Sharma, S.C, Nucl.

Instr. and Meth. Ill, 93 (1973).

5. Katz, R. and Sharma, S.C, Phys. Med.

Biol. 12, No. 4, 413 (1974).

6. Sharma, S.C and Katz, R., The 1-hit

Detector in the Measurement of

Radiation Quality, in Proceedings of

the Fourth Symposium on Microdosimetry, Verbania-Pallanza (Italy),

Euratom (1973)

7. Appleby, A., private communication.

2. I agree. For our computations,

we use standard tables for energy-loss

and range-energy values for heavy ions.

Although the stopping power information

is not very accurate for very low energy

and relativistic heavy ions, yet the

final results are not affected a great

deal

P.S. Nagara.ian

Could your theory predict the RBE,

OER etc. when the high LET and low LET are deliberately used, i.e. the synergestic effects ? S.C Sharma

The theory can predict the response

of any detector to any mixed radiation

environment. For cells the high LET and

low LET parts are apportioned In lon-klll

and gamma-kill modes respectively. For

details, please refer to our paper in

Physics in Medicine and Biology (1974).

187
SPECTRUM SHAPES OF LOV/-ENERGY PHOTON SOURCES

R.C. Sharma, S. Somasiindaram, IL, Unnikrishnan

and Shiv Datta

Body Burden Measurement Section

Health Physics Division

Bhabha Atomic Research Centre

Bombay-400 085

The spectrum shapes of low-energy photon (LEP) sources undergo

interesting changes in the presence of scattering media of low

atomic numbers. Two readily observed changes in the spectrum shape

are (a) downward shift of the peak energy and (b) apparent deterioration of the energy resolution of the detector. A study of these

changes is useful for in vivo assessment of LEP-emitters such as 24lAm, 239Pu, U, 210pb etc. A computer program, based on Monte

Carlo principles, has been evolved to compute the magnitudes of

these changes in piilse-height distribution. Calculations were

performed for point sources of low-energy photons located on the

axis of the detector and for different thicknesses of the scattering medium interposed betvfeen the source and the detector. The

variable parameters considered in these calculations are initial

photon energy, thickness of the interposed material and type of

detector. The magnitudes of both the above-mentioned changes in

the pulse-height spectra of LEP sources embedded under media of

low effective atomic number, such as water (Z = 7.42), tissue

(Z = 7-33) and perspex (Z = 6.47), are found to be dependent to

a great extent on the energy resolution of the detector employed,

apart from the electron density and effective atomic number of the

scattering medium. The theoretical results are presented and

compared, wherever possible, with experimental values obtained with

iNfal^(Tl) detector.

(Detector; Monte Carlo; perspex; photon energy; pulse height;

resolution; scattering media; tissue; water).

Introduction

It has been observed recently in

connection with in vivo detection of lowenergy photon (LEP) emitters (Ey<100

keV) with thin iTal(Tl) scintillation or

ilal( Tl)-Csl(Tl) phoswich detectorsl-4

that the presence of tissue produces

appreciable changes in the original

pulse-height spectrum which may be ex- ploited advantageously to estimate the

depth at which activity is located. Two

most readily observed changes in the

spectrum of a mono energetic LEP soujrce

located in a medium of low effective

atomic number ( Z2 , such as tissue (Z = 7.33) or water (Z = 7.42), are (a)

downward shift of the peak energy and

(b) apparent deterioration of the

energy resolution of the system.

Experimental work in our laboratory has

indicated that the magnitudes of these

effects are in general different for

different absorber-scatterers, which could

be explained qualitatively on the basis

of differences in the effective atomic

numbers and the electron densities

(number of electrons/cm3) of the

material4. Experimental studies with

point sources of LEP emitters embedded

at various depths in a tissue- equivalent • material have also indicated the feasibility of correlating with depth the

observed peak-shift or the change in

resolution-'-"-^. On the basis of such

correlations, it would be possible to t derive effective soft tissue thicknesses

for individuals of differing body builds

to facilitate correction of the calibration factors. Besides, in the

literature the occurrence of these

phenomena has usually been explained

qualitatively as being exclusively due to . Compton scattering in the intervening

mediiim.-'-~4 The present work describes a computer program evolved to compute the

changes in pulse-height spectra for a

v/ide range of lovj energies and depths of

sovirce in tissue-like media. The calculations provide a better insight into

the actual mechanisms leading to the

observed changes in p\ilse-height spectra

of LEP sources. The results of calculation are presented and compared with the

experimental values.

188
Computer Program

Kathematically

specified by reierr

which. C represents

of radius R and thi

of which is placed

distance t from the

intervening space b

filled with water V/ It is desired to co height response of

photons emitted by

in two steps:

the problem is

ing to fig. 1 in

the Nal(Tl) detector

ckness T, on the axis

a point source S at a detector face. The

etween S and C is

also of radius R. nstruct the pulseC due to monoenergetic

3. This is achieved

Pig. 1. Source detector geometry used in

comnutational scheme.

First, the line spectrum incident on the detector face, hereafter referred

to as the "exit photon spectrum", is

determined by the I-Ionte Carlo technique.

Scattering from the surroiindings is not

taken into account. This idealization

is quite justified since only low- energy

photons are involved. The Monte Carlo

simulation of (a) is achieved by

following the sampling techniques described by Cashv:ell and Sverett5. Fig. 2 shows the flow chart of the computer

program schematic used in the present

studies to compute the exit photon

spectrum. The relevant cross sections

;;'or water are taken from reference^.

The second step req.uired is the

derivation of the pulse-neight spectrum

resiilting from the interaction between

the exit photon spectrum and the NalCTl)

detector. A rigorous derivation would

require that each photon of the exit

spectrum be follov/ed individually into

the detector in order to compute the

actual energy deposited in C. However,

extension of our calculations for thin

Kal(Tl) detectors'? to a detector of

thickness 5 rom confirmed that below

100 keV, most of the photons incident

on the face of the crystal are completely absorbed. The presence of iodine

escape peaks would not affect the present

calculations. It is therefore assumed

that the interaction of the exit photon

spectrum with the detector could be

adequately represented by the smearing

of the former by the G-aussian resolution

function associated with the latter.

Experimental measurements at four photon

energies below 100 keV show that the

standard deviation of the G-aussian peak can be expressed as a function of energy

by the relation

a(E) = A ;/¥ + B The constants A and B are determined from

the experimental plot of a(E) vs. -fE. Smearing of the exit photon spectrum is

then accomplished by computing the

contributions from each channel to the

others, using the Gaussian distribution

function and is carried out as follows:

The contribution from the kth

channel of the exit photon spectrum to

the jth channel of the smeared pulseheight spectrum is given by

B(K,J) = ^

C(J) „

f exp[- i^=fi^%B

C(J-l)

and iLa^ 2 aj^

where A(K) is the number of counts in the

kth channel of the exit photon spectrum,

E(k) is the mean energy corresponding to

the kth channel of the exit photon

spectrum, C(j) and C(3-l) are the upper

and lower limits of the jth channel of

the smeared pulse-height spectrum and cr^ is the standard deviation of the Gaussian

peak in the pulse-height spectrum at

energy E(k). Expressed in terms of

normal probability function P(x),

B(K,J) = A(K)L?(X2) - P(Xi)

j

„ G(J-l) - E(K) wnere Xn = —^ j- ^

Thus, using the normal probability

function values and experimentally

obtained o^'s, the contribution from all

the k channels (k = 1 .... n') of the

exit photon spectrum to every jth channel

(j =1 ... n) is calculated to get the

smeared pulse-height distribution. The

location of the peak is found by using

the technique of "linearization of the

peak" . In practice five channels on either side of the peak were used for

this purpose.

Experimental Setup And Calculations

A Harshavj integral assembly (10.16 cm dia x 5 mm thick Nal(Tl) having 1 mm

Be as radiation entrance window) is

currently in use in our laboratory for

detection of Pu/Aim in vivo. The Nal(Tl)

189
I No

»,V,Z.U' 0 E- Eo

Xw,Yw At Z-Tw I

Yts X-XtU.S' Y'Ytv:S

Upt)

ColcutaW

e'

CalculoK Nfw U.V.W

No IS Torn NUMBER OF HISTORIES TO BE TRACED.

'

Iw IS THE THICKNESS OF WATER

r IS A RANDOM NUMBER BETWEEN 0 AND I . E IS THE ENEROY OF COMPTON SCATTERED PHOTON

Ndti iS THE NUMBER OF COUNTS IN THE CHANNEL CORRE SF-ONOING

IC ENEROY E OF THE EXIT PHOTON SPECTRUM

Fig. 2. Flow chart for computing

photon spectrum.

exitscintillation crystal is coupled to a 2.54 cm thick quartz light pipe and

mounted on a RCA 8055 phototube. The

output from the phototube is routed

through a FET pre-araplifier to a 400

channel pulse-height analyser. In order

to have a meaningful comparison between

theory and experiment, the computations were performed for point sources of lowenergy photons located on the axis of a Nal(Tl) detector of the available size

and for different thicknesses of the

scattering material interposed between

the source and the detector. The variable

parameters considered are (a) initial

photon energy (from 20 keV to 100 KeV at

intervals of 10 lleV), (b) thickness of

interposed scattering material varying

from 1 cm to 12 cm and (c) type of

detector - the energy resolution distinguishing each type. The experimental

results were obtained with a point source

of 241Am (60 KeV) with different thicknesses of distilled water in a thin

perspex container interposed between the source and the detector. Another

scatterer employed was perspex.

' Results and Discussion

In fig. 3 are shown a typical exitphoton spectrum as a histogram, the

resulting peak in the smeared pulseheight spectrum as a smooth curve and

the experimental values (normalized to

the smeared spectrum at the new peak

channel) as circles. The detector is a

90 100 110 Channel NO. Fig. '5- The exit spectrum (histogram) of

photons for initial energy 60

KeV and v/ater thickness 6.3 cm and the resultant peak in the

pulse-height spectrum (continuous

line) from a Nal(Tl) detector of

dimensions 10.15cm x 5 mm. The

points indicate the corresponding

experimental data.

Nal(Tl) scintillator as described above

and a point source of initial photon

energy 60 K.eV is used, the thickness of ^ the interposed water scatterer being

6.3 cm. The exit photon spectmjim and the

theoretical peak are for 20,000 source photon histories. The figure illustrates

how the peak-shift is introduced. The

exit photon spectrum does not show any

shift in the maximum photon energy and

the number of counts in the original peak

channel is still overwhelmingly large.

This would be representative of the case of an ideal detector having an infinitely

fine resolution, introducing no line

broadening. In actual practice, however,

the exit photon spectrum would be distorted due to the finite energy resolution of the detector and its variation

with energy (fwhm vs. photon energy

relation) . Since the peak-shift appears

only after the smearing of the exit

photon spectrum vrith the experimentally

determined values of fwhm, it may be

concluded that it is the energy resolution of the Nal(Tl) detector which

introduces the peak- shift in the pulseheight spectrum. Different exit photon

spectra, incident on the same detector,

would also indicate different values of

peak-shift (AE). The smeared spectrum

in fig. 3 has a peak at 58.07 KeV, i.e.

^E = 1.93 KeV. 'Ifter smoothing, the

peak-shift in the experimental pulseheight spectrum for the same case is

190
to be 1.97 KeY.

V/e may next consider some hypothetical detectors having the same f\-fhm vs. peak energy relation as the iTal(Tl)

detector but having different energy

resolutions; i.e. we consider detectors

with

otE) = Ka(S)

where aXll) is the standard deviation of

normal distribution centred at energy

E for a hypothetical detector, a(S) is

the standard deviation of normal distribution centred at energy E for the ilal(Tl)

detector and E is a constant. Therefore

and fwhm = 2.355cr^

The exit photon spectrum in fig. 3 is

smeared using several values of a' and

the peak-shifts (•^E) are observed.

Fig. 4 depicts this dependence; -^E is

plotted as a function of Z. It is seen

that when the sane exit photon spectrum

is incident on detectors having different

energy resolutions, the peak- shifts

observed are different. In the typical

case given, the peak-shift could vary

from 0 KeV to 3-09 KeV, depending upon

the energy resolution of the detector.

appears to satiirate for a detector

having an energy resolution twice as bad

as that of our detector.

Eig. 5 shows the variations of AE

and fwhm with depth of a point isotropic

source of 60 KeV photons under water

when Ilal(Tl) detector described earlier

is used. The continuous curve shows the

computed values and the experimentally

measured values are shown by the points.

The experimental values of -a E fall

close to those predicted by calculations.

The experimental fwhm values are slightly

higher than the predicted values

probably due to very little back scatter

from 1 mm thick perspex source container.

The srrall difference between the fwhm

values does not seem to introduce

significant difference in AE values.

AC (KeV)

171 u« So

1 ' "--^ 11 , 1 , , ,—

- A-o

/ *

1 > 1 1 . r

Fig. 4. •• Theoretical predictions of peakshift (AE in II eV) for hypothetical detectors having standard

deviation of Gaussion peak

Ea,- a being the parameter for

ITal(Tl) detector and K a constant.

The results are for a point source

of initial photon energy 60 keV

iinder v.'ater depth of 6.3 cms.

191

Fig. 5. Theoretical variations (conti- nuous curves) of peak shift,

F¥HI^ and ?/T ratio of the number

of photons in the 60 EeV channel

to the total number of photons

* in the exit spectrum) with depth

= . of a point source of photons of

energy 60 KeV under water. Experimentally measured values are indicated by maxked points.

Fig. 6 illustrates the variation of

AE with the initial energy of source photons when the source is located at a constant depth of 3> 5 and 7 cm of

water. These results are obtained from

our program by treating the initial

photon energy as a variable parameter . Since fwhm is a function of the

incident photon energy and increases

with energy, AE would increase. In the

initial stages this increase will be

augmented by the rapid decrease of P/T

(the ratio of the number of photons in

the 60 KeV channel to the total number

in the exit-photon spectrum) which in

turn is caused by the predominance of - the photoelectric effect in this region.

Beyond this, P/T increases slowly in

accordance with the decrease in mass absorption coefficient which works
against the increase in AE. The combined effect of all is that AE first

increases steeply with E and then falls

to a lower value.

Wl— —: . ,

Energy (KeV)

Pig. 6. Theoretical peak-shift ( AE) as

a function of initial photon

energy for point isotropic sources under constant water depths of

3, 5 and 7 cm as continuous

curves. Broken curves are for

perspex.

The dotted curves in fig. 6 are for

the same detector and perspex scatterer.

The calculations yield AE values less

than those for water, whereas the experimental values are higher than those for

water (fig. 5). We have used the cross section data in ref. 8 for perspex

(density taken as 1.0 g/cc) and in ref. 6 for water, '.'/e have not used the cross section data from any other reference to

resolve this difference.

Fig. 7 shows fwhm plotted as a function of /E, E being the observed

'peak' energy. Deviations from the

approximately linear relation observed

when no scatterer-absorber is present are evident. This deviation increases

with the thickness of the scatterer

(water) and there seems to be no significant departure from linearity below

an energy of 25 lieV.

Conclusion

A computer program using Monte Carlo

techniques has been described to calculate changes in the pulse-height spectra

obtained from detectors exposed to

low-energy photon soirrces embedded in

media of low effective atomic numbers.

The role of the detector in introducing

such cnanges has been delineated.

2

-

1 1 1 1 1 I I I 1 I •'01 2 3 « 5 6 7 8 9 10111

Fig. 7. Computed FV/Hiu as a function of VE

for the cases of point source under water thickness of 0,3,5 and 7 cms. Acknowledgement

The authors wish to express their

sincere thanks to Shri T.K. Haridasan

for his assistance in the present work.

References

1. Morsy, S.ll., El-Assaly, E.M. and

Aloush, A. A., Assessment of radioactire

contamination in man, IAEA (1972)

p. 115.

2. ilundo, J., Keane, A.T. and May, fl.A. ibid, p. 579.

3. V/renn, M.E., Rosen, J.G. and Cohen, IT. ibid, p. 595.

4. Sharma, R.G., Somasundaram, S.,

Surendran, T., Kapur, D.K. and 3arg,

S.P., BilRC report Ho.BARC-748 (1974).

5. Cashwell, E.D. and Everett, C.V.

A practical manual on the Honte Carlo

method for random walk problem,

Pergam.on Press, London (1959).

6. Sieg^bahn, K., Alpha, Beta and Gammaray spectrometry, Elsevier, Amsterdam

(1955) . 7 . Sharma , R . G . , Garg , 3 . P . and

Somasundaram, 3. iiucl. Instr. i-Ietnods,

101 (1972) 413.

8. Hubbell, J .H. , US National Bureau of

Standards report iTo. HSRDS-HBS 29.

192
DOSE FUNCTION FOR BETA DOSIMETRY

S.J, Supe and Shiv Datta

Division of Radiological Protection

Modular Laboratories, Bhabha Atomic

Research Centre, Trombay

Bombay-400085 , INDIA

The feasibility of using various shapes and sizes of field

limiting devices and collimators with beta ray eye applicators

has necessitated the study of dosimetry for these fields. A

method of obtaining dosimetry for any shaped field from the data

for circular fields is presented. The method is based on a similar procedure for X and gamma rays. The surface dose computation is done based on Clarkson's method but without splitting the

surface dose into air dose and back-scatter dose. The depth dose

evaluation is based on depth dose function which is defined as the dose rate at a particular depth for particular circular field.

The usual method of splitting depth dose into primary and scatter

doses was not found necessary. The evaluated values for the

surface and depth dose were compared with experimentally obtained

values for three non circular fields. The good agreement in these

data indicates the practicability of the method suggested.

(Air dose; arbitrary shaped field; back-scatter factor;

Clarks ' method; dosimetry; depth dose; surface dose)

Introduction

The early cases of lesions of eye were treated by X-radiation and have resulted in radiation cataract. With the use of P-ray emitters like radium D + E and radon, the eye lense dose was appreciably reduced. IvTien a pure

beta emitter, was available for use as eye

applicators, the gamma component of eye

lense dose was eliminated. This reduced

the frequency of incidence of radiation

cataract and no further attempts were

reported to reduce the eye lense dose.

These applicators were usually used

without any field limiting or collimating

devices regardless of size of the lesion

resulting in much larger doses to the

lens of the eye. Recently, use of field

limiting devices-*- as well as collimators'^'-

has been investigated and shown to be

possible for almost all cases. The feasibility of matching the field shape to

that of lesion size has raised new problems of dosimetry. As various lesion

shapes are encountered the present dosimetric data of circuJLar fields4-7 ±s insufficient for the treatment of widely

varying shapes of the lesions. Further,

it is virtually impossible to carry out

dosimetric studies for the numerous field

shaping devices of variety of sizes and

shapes. In this work a method of estimation of surface and depth dose for any

shaped field from the available data for

circular fields on the same lines as X

and Gamma fields was tried.

Clarkson® Meredith and Neary^ and

Johns and CunninghamlO described the

method for roentgen and gamma radiations

for such estimation. This method consists of measurement of air dose, use of

back scatter factor and scatter functions

for estimation of this data. The air

dose is to be actually measured for the

field size under consideration. However,

for the estimation of surface dose the

small variation of air dose with field

size is neglected and air dose assumed

to be a constant. The non-circular field

size is divided in a large number of

segments of circles with different radii

drawn at equal angles. The back scatter

factors for these are averaged to give

the effective back scatter factor for the

field under consideration.

To obtain the dose at any depth the

dose is divided into its two components,

the primary dose and the scatter dose.

The primary dose is obtained by extrapolating the central axis depth dose for

various field sizes to zero field size.

The scatter dose is evaluated by obtaining the average scatter function for the

field under consideration by the same method as used for back scatter factor.

The data so obtained are used for getting

the central axis as well as off axis

depth doses for the field under consideration. Further interpolation of this

data yields complete isodose curves. Air Dose for Beta Rays

Adoption of this procedure in case

of beta rays is handicapped by difficulties. The measurement of air dose for

betas is rather diffiCT^t-'-'-. Air dose

193
with beta rays is possible only if the

collecting electrode of an extrapolation

chamber or a flat ionization chamber is

equally thin as the upper or polarizing

electrode. If a thicker plate is used the

contribution due to back scatter from the

plate will not permit the measurement of

the air dose.

Further, the increase in air dose is

going to be very rapid with increasing

field size as a large active area would

be contributing to the dose. A constant

dose output is not possible with the beta

ray sources when used with the field

limiting diaphragms and hence it was decided to try and find out whether dosimetry at surface and in tissue could be

developed on similar lines as that of X

and gamma rays but without the help of a constant air dose.

Surface Dose

. , I —— ——^—

The variation of surface dose was studied with the field size splitting it

into air dose and the back scatter dose.

For this purpose using an extrapolation

chamber, doses were measured for a RA-

(tracerlab) type eye applicator with

increasing field limiting diaphragm

diameters. Measurements were also

repeated for 450 mCi ^^Sr- ^Oy source with a collimator of 1.05 cm length.

The surface dose rates for rectangular

shaped field sizes have been evaluated

from the dose rate for circular fields

by using Clarksonl2 method. These are presented in Table I. In addition,

surface dose measurements for the applicator with the corresponding shapes of

field limiting devices have been carried

out with an extrapolation chamber and

the results 'thus obtained are presented

in column 4 of Table I. The evaluated

values agree well within + 5/- with the

experimentally obtained ones. Depth Doses

A further difficulty was observed i calculating the dose at any point in

tissue on similar lines as those for X

and gamma rays. In the case of beta rayS;

obtaining the value of the primary com- ponent of dose was found to be rather

difficult. The central axis depth dose

data for beta rays are available from the

maximum field size of about 8 mm down to

about 2.00 mm and would not yield by

extrapolation the primary dose with the

required accuracy. Any attempt to measure doses for field sizes smaller

than about 2 mm diameter is handicapped

with inaccuracies introduced in making

electrodes of extrapolation chamber

smaller than this diameter^^ and the

primary component of beta dose at various

depths cannot be obtained with sufficient

accuracy

Close scrutiny of the procedures for

calculating the dose at any point within

the field and at any depth revealed that

such separation of scatter dose from

primary component is not necessary. It was noted whether primary dose is determined separately and added to the average

value of scatter function or whether the

average of the total dose is estimated,

the same results are obtained. Thus it was decided to use dose function for beta

rays rather than scatter functions. The

dose function is defined as the dose rate

at the particular depth on the central

axis of a circular field. The dose functions were evaluated in the following

manner. The surface dose rate for a particular field size was multiplied by

the percentage depth doses at different

depths for the same field. These dose

functions for various field sizes and

TABLE

, '

'

SmFACE DOSE RATES FOR VARIOUS FIELD LIMITING DEVICES & COLLIMATORS

Sr. j No.

1

Collimator/

field limiting

device aiEe(iixm)

Source to

I surface

! dlstanoe(oa8)

Dooe rate(rad/8) | Doee rateCrad/s)

Extrapolation ; evaluated valuea

' cbflBber neasurfflnents V

1. 6x6 0 117.0 116.2 !

2. 6 x4 0 , 77.5 81.2 i

I

3. 6 X 3 0 65 62.1

1

4. 6.6 X 6.2 1.05 19.2 18.7 i

5. 6x8 1.05 20.1 19.5

6. 6x6 1,05 14.5 13.8

194
Using the surface dose rates and

the dose functions for circular fields

as basic data for Clarkson's method, com- putation of depth dose in the space around the source could be easily carried

out. This has been done for three

fields and the depth dose data thus obtained are presented in Table I and II. Non-circiilar field limiting diaphragms were constructed and using the

experimental method already described

dose data were obtained for these fields

which are also presented in the same tables. It can be seen that the depth dose data obtained by the computation

and those obtained experimentally are in

fairly agreement for the three shapes.

This agreement indicates that the pro- cedure suggested here is practicable

enough for therapeutic purpose. The

computation can be carried out within a period of a few hours with some practice.

A computer programme can also be easily written for this purpose.

Acknowledgements

We are indebted to Shri G. Subrahmanian for his keen interest in these

investigations. Gratefiil thanks are

also due to Shri S.M. r.ao for his help

in experimental measi^rements

a) RA-1 applicator with field

limiting devices.

b) 450 mCi source with collimators.

TABLE- I

EXPERIMENTAL AMD EVALUATED DEPTH DOSE DATA

RA-1 Applicator with field shaping devices .

D«ptb F»re«nta«* depth dose data toe oollinatora sizes of 6x8 ' 6 X 6 6 X 3 £ixp«rlsental Syaluattd ExperljB*ntal Evaluated Experlaeatal Evaluated

0. 100 100 100 100 100 100

100. 49.0 45.3 46.5 44.9 46.0 45.7

200 26,5 22o7 24.5 21 .7 23.5 20,6

300 13.3 mm mmmmm mmmaamm^i

11.3

1 wM mm »mmm^

12.2

naawKfli mmm mmmm

10.2 11 ,0

mm mm mmm

9.0

mm«a»aia«a

450 mCi Soureewlth oolllaatcars

8 X t) mm 6 X 6 ssn

0 100 100 100 100 100 100 100 64.9 71.7 66.6 73.0 64.9 69.0

200 40.9 41 .8 46.7 43«0 38.7 38.7

300 26,1 25.1 29.0 26.0

1^ 24.4 22,3

195
4.

References

Supe, S.J. and Cunningham, J.R., Am.

J. Roentgenol, and Rad. Therapy , 79 . 570 (1965).

Supe, S.J., Am. J. Roentgenol, and Rad.

Therapy , 11^, 24 (1972)

Supe, S.J. and Rao, S.M., Brit. J. Radiol., 786 (1974).

Krolimer, J.S., Am. J. Roentgenol and

Rad. Therapy, 66, 791 (1951).

Jones, C.H., and Dermentzoglou, F.

,

Brit. J. Radiol. 203 (1971).

Mc Taggart, W.G., West, W.D., Claypool,

10,

11,

12,

H.A., and Collins, V.P., Radiology,

76, 278 (1961) . Sinclair, W.K. and Trott, N.C., Brit

15 (1956).

R., Brit. J. Radiol, 14,

J. Radiol.

,

Clarkson, J 265 (1941).

Meredith, W

J. Radiol.,

Johns , H.E.

,

J. and Neary, G.J, Brit,

12, 75 (1944).

and Cunningham, J.R.,

Springfield, Illinois, Chas. C. Thomas (1969). The Physics of Radioloar.

Sheppard, C.W., and Abele, R.K.,

AECU-655, (ORUl-265) (1949).

Supe, S.J., Int. J. Appl. Radiat

Isotopes, 24, 545 (1972).

196
ACTUAL PROBIEMS IN PHOTON DOSIJ-ISTRY*

D. F. Regulla and G. Drexler

G-esellscliaft fiir Strahlen-und Umweltforschung mbH Hiinchen

D-8042 Neuherberg, Ingolstadter Landstrasse I Germany, F.R.

A brief review of the evolution of quantities and units

in dosimetry is given, and the relevance of the dosimetry

concept to applications in medicine, technique and health

physics is pointed out. IVhile radiation dosimetry seems to

have, from a phj'-sical point of view, achieved an adequate status,

handling of the physical fundamentals as well as practical application of quantities, units and measurement methods to

operational dosimetry appears to be limited mainly to the level

of highly competent authorities in dosimetry, such as IGRU or, on a national basis, to primary standard laboratories. This

consequence is based on the authors' experience, that there is

hardly a country, in which the numerical value of a dosimetrical

quantity can be determined reproducibly through the different

institutions engaged with practical dosimetry. WHO and IAEA,

for this reason, started to establish a net-work of secondary

standard laboratories, recently, with the aim of an improvement

of dosimetry in medicine, radiation protection and radiation

research. Details of this joint international effort on standardization are given, results already evident in some countries are presented. Recent advances, particularly in solid state dosimetry, are discussed together with the scientific aspects of physics in

diagnostic radiology. To the authors' opinion almost every

effort in the field of diagnostic radiology is worthy and

promising for reasons of reduction of population dose and amelioration of information but also due to the broad interdisciplinary

possibilities, the immediate output of applied research and, last

not least, the benefit to mankind. Some examples on new results

of medical physics as well as an outlook to future developments

are given.

Introduction

From literature study we found keynote addresses to be often characterized by

two formalities: On the one side, the

speaker wishes to express his gratitude

to the responsibles of the conference for

the honour of invitation - which practice

we should like to join - and, on the

other side, he searches for a concept of

the lecture by interpretation of the term

keynote. Following this example we found

the term keynote defined in the dictionary

as "fundamental tone of a scale".

Seeking for a relationship between this

definition and the subject of the present

session "Radiation Dosimetry and

Instrumentation" one is inclined to

correlate the term fundamental tone merely

v/ith the physical basis of dosimetry

vfhich could function as a connecting link

between the diverging topics, such as

microdosimetry , calculation of stopping

power, solid state dosimetry etc.

Doubtlessly, at this place a keynote

address could exceptionally be presented

on the basic physical aspects of

dosimetry.

However, to the authors' opinion it

should be pointed out, that dosimetry

even after its physical definition and

interpretation in terms of the respective

quantities and units is gaining importance

and justification only by imbedding it

into the matrix of the manifold applications. Thus, dosimetry is loosing the

character of ending in itself and

becomes a tool for a relevant qualitative

and quantitative description of the

radiation field and its interaction with

the absorber medium. On the basis of

*bedicated to Professor Dr. F. Wachsmann on the occasion of his 70th birthday.

197
this approach one has - by returning to

the dictionary definition of the keynote

- to see the fundamental tone of dosimetric physics in connection with the

scale of applications, at least, in

biology, medicine industry, agriculture,

health physics and research.

The dosimetric procedure selfevidently practiced today by starting

from the physical fundamentals and

adapting them to the respective field of

application has not been common as far

as to the beginning of the sixties. For

a long time, any quantification of the

radiation effect was performed by

description of type and intensity of the

effect under consideration. The early

biological dosimetry methods to be

designated as "analog technio^ues" such

as the erythema dosimetry, the epilation

dosimetry or even mouse-dead dosimetry

become understandable by the lack of a relevant dosimetric philosophy and

physical concept of measurement . Time was not yet ripe for a detailed application to photon fields of the fundamental concepts of particle fluence,

flux density and energy spectra - familiar from the kinetic theories of

gases—because theories of the dual

corpuscular and wave nature of photons were still evolving. It was the

application of ionization as a physical

pre-condition for a dosimetric digitalization of the measuring procedure

that first made a definition of physical

quantities possible in dosimetry and

established a connection to the exact

natural sciences by introducing welldefined and reproducible units.

Nevertheless, the concepts of exposure

and fluence are philosophically rather

close: They both attempt to define the

radiation field independently of its

interaction with matter.

The importance of, and the state

of art achieved in modern dosimetry

may be measured against the fact, that

dosimetry and its aspects are discussed

within the frame of physical symposia

and conferences, today. Nevertheless,

there has up to recently been much

discussion of the fundamental concepts

and quantities employed in radiation

dosimetry. This has arisen partly from

the rapid increase in the number of

individuals using these concepts in the

expanding field of science and technology, partly because of certain

obscurities in the existing formulation

of the quantities and units themselves.

For instance, a serious source of

confusion has been the failure to

define adequate, and that in time, the

radiation quantity of which "roentgen"

was said to be the imit^. As a consequence of this ommission the roentgen

had gradually acquired a double role:

The use of this name for the unit had

become recognized as a way of specifying

not only the magnitude but also the

nature of the quantity measured. This

practice conflicts with the general

usage in physics, which permits, within

the same field, the use of a particular I unit for all quantities having the same dimensions

A number of dosimetric quantities * and units have been introduced in course

of time, but only those that are of

importance in the framework of the ;i dosimetry concepts discussed here, will

be reviewed. '

Ob.jectives of Dosimetry

The term "dose" is biologically -\ oriented and originating from the early

medical use of X-rays. In order to

reproduce medical and biological '| radiation effects, compare different

radiation effects among each other and

estimate the amount of ionizing radiation for any application one needs an

effect caused by and related to the

dose, which can well be defined,

measured and quantified along a scale.

This, however, is no more a medical or biological problem but a physical one. Therefore, dose has at least been

defined in terms of physically measurable

quantities

The ideal unit of dose from the

standpoint of radiation protection and

biophysics would be the one which would

produce the same biological effect

independent of the kind and energy of

radiation. Such an ideal is, parti- ^ cularly on biological basis, probably f unattainable because of the extreme

complexity of radiation-induced damage ' in living systems. For realization, a ^ physical dose unit is applied which ' gives nearly the same biological effect ^ independent of the energy of a given ' kind of radiation. i

Thus, it is the aim of dosimetry to J determine a physical quantity to which » the chemical, biological and medical

effects can be related. In this conne- ction particularly those quantities will

be of importance, v^hich describe the 1 physical interaction of radiation with i matter. ' I

198
Radiation Quantities and Units (DE) = D(QP).(DF)

Prom results of radiobiology it is

obvious that local radiation effects can

well be correlated with local energy density. Therefore, it appears logical to

choose the energy absorbed (or alternatively imparted to) a mass of matter for

dose description. The energy imparted by

ionizing radiation to the matter (AWp)

in a volume is the difference between the sum of the energies of all the directly

and indirectly ionizing particles which

have entered the volume (AW-g) and the sum

of the energies of all those which have

left it (AWj^), minus the energy equivalent ( A W^) of any increase in the mass

that took place in nuclear or elementary

particle reactions within the volume

On the basis of "energy imparted to

matter", the concept of absorbed dose D

has been defined and recommended by ICRU

ll'^ as "the quotient of dWj) by dm', where

dWj) is the energy imparted to the matter

by the ionizing radiation in a volume

element dV, and dm = pdV is the mass of

the matter with the density p in that

volume,

^ _ dWg ^

1 dW^

dm p* dV

By this definition the absorbed dose has

the dimension energy per mass which in

terms of the SI units refers to J kg~^.

The special unit of the absorbed dose is

the rad.

1 rad = 0.01 J kg"""", formerly

1 rad = 100 erg

g""'"

The definition of absorbed dose is

valuable for all types of radiation and

radiation energies in all kinds of matter.

However, the indication of absorbed dose

is only useful if the conditions of irradiation and the material, in which the

absorbed dose has been determined, are

reported. Moreover, the definition

appears incomplete without specification

of the size of the volxme element3.

Apart from the absorbed dose, additional quantities and units common in

dosimetry should be mentioned here:

i) For protection pxirposes it is

useful to define a quantity which will be

termed the "dose equivalent", (DE) . (DE)

is defined as the product of absorbed dose,

D, quality factor, (QF), dose distribution factor, (DF) ,and other necessary

modifying factors.

The dose equivalent is a rather

hybrid quantity compounded of three

elements, the first consisting of physical

data, the second concerning factors

derived from radio-biology and the third

consisting of administrative factors.

Thus, dose equivalent is by definition

immeasurable

The unit of dose equivalent is the

"rem". The dose equivalent is numerically

equal to the dose in rads multiplied by

the appropriate modifying factors.

ii) Recently defined is the quantity

"kerma" which represents the kinetic

energy transferred to charged particles

by the uncharged particles per unit mass

of the irradiated medium. This is the same as one of the common interpretations

of a concept- 'first collision dose', that

has proved to be ol great value in fast

neutron dosimetry. The concept is also

closely related to the energy equivalent

of exposure in an X-ray beam.

Per definition, the "kerma" (K) is

the quotient of dV/ by dm, where dV/r^ is the sum of the initial kinetic energies of all

the charged particles liberated by indirectly ionizing particles in a volume

element of the specified material, dm is

the mass .of the matter in that volume

el enent dV

dWj. 1 dWg. ^

' .

^ dm" " p' dV"

Kerma can be a useful quantity in

dosimetry when charged particle equilibrium exists at the point and in the

material of interest and bremsstrahlung

losses are negligible. It is then equal

to the absorbed dose at that point. Prom

the more specific definition K = "^-^^^/p

(v7here Y = energy fluence of the photons;

[io-jo = mass energy transport coefficient)

io becomes evident that it allies the

primary and secondary components of the

radiation field for mathematical treatment of dosimetrical problems. The unit

of kerma is equal to that one of absorbed

dose

,iii)V/hile for photons, the reduction of

fluence or energy fluence is primarily

caused by a reduction of particles, the

energy fluence in case of charged particles decreases mostly by energy losses

of the particles with practically constant particle flux density. For characterizing these energy losses, the mass stopping power S has been introduced.

199
The mass stopping power of a material with the density p for charged

particles with the energy E is the

quotient of dE and the product of p and

dl

^ - p.dl

where dE is the mean energy loss i^ithin

the path length dl in material v/ith the

density p.

iv) A quantity closely allied to stopping power is the linear energy transfer,

abbreviated LET. This is defined as the

linear-rate of loss of energy (locally

absorbed) by an ionizing particle

traversing a medium and may conveniently

be expressed in keV/fj,. The use of the

concept of LET concentrates attention in

the transfer of energy to the material,

rather than on the loss by the particle

as does mass stopping power.

Physical Concept of Radiatiori Dosimetry

So far, the concepts of some dosimetric quantities and units and their

definitions have been revievzed; it is

pertinent to examine physical concepts

and practical techniques currently used

in operational dosimetry.

Implied in the term radiation dosimetry is the central problem of the

radiation field characterized by

specific field parameters. V/ithin the

radiation field there are interactions

between the ionizing particles and the

atoms or molecules of matter. The

absorbed dose refers to such interactions.

Though absorbed dose does not give a final answer on the kind of expected

biological effect, it is that dose

quantity which corresponds with the

observed biological reaction in the

most promising way. It seems important

to point out this fact, in particiilar, as the opinion can be heard that it is

sufficient to refer chemical or biological radiation effects solely to, for

instance, particle fluence. Nevertheless,

field quantities such as particle flux

density, particle fluence, energy flux

density and energy fluence are reDated

to dose quantities by physical laws via

the interaction coefficients dependent

on radiation energy and matter for the

different types of radiation, for

instance, the attenuation coefficient,

the energy absorption coefficient,

stopping povrer as well as capture and

scattering cross sections.

V/e shall distinguish betvreen the

two basic approaches to radiation dose

determination at a specific point of

interest in matter:

a) The first approach gives primary

attention to the radiation field itself;

in concept, measurements of energy-angle

distributions of particles in the field are carried out to specify the radiation

at each point in terms of physical

quantities, giving rise to direct

absorbed dose calculations.

b) The second approach characterizes

the field primarily in terms of its

interaction with matter in local vicinity

of the point of dosimetric interest, by

appropriate measurements. This approach

is of great practical value and has

formed the basis of almost all radiation

dosimetry

The distinction between the two

approaches is somewhat arbitrary in that we know the radiation field only through"

its interaction with matter.

Calculation of Absorbed Dose from Field

Parameters

I, The calculation of absorbed dose

provides the term energy imparted to ( matter, W-^. The concept of energy

imparted will be considered from the

point of view of a macroscopic field

theory.

A complete specification of the

field can be made in terms of (i) the

nature of particles, (ii) the spatial

density of particles, (iii) the energy

of the particles and (iv) the direction

of the particles. This can conveniently

be expressed by n (r, E.iX, t) d"^r i dEdH, which is the number of particles

at time t in the volume element d"^r around r with the energies between E and

E + dE and v/ith the velocity vectors in

the solid aiigle element of dO-around the

unit vector-ft.. Other parameters, such

as polarization"' v;ill not be regarded.

In the present case of a field of

photons and electrons, '.1-^ on the basis

of ICRU definition is given by the

general expression, in which the

temporal variations are neglected.

Wj, = jK(r) pdV-]"dVj"dri .diV[A .Je®I®

(r,^E®) dE®J

200
where: u (eP'

The absorbed dose D in the point r is

then calculated by

I . P (?,^,eP) d^

The indices p, e refer to the photon or electron component the radiation field.

l(r,A, E)dBdX^- the fluence of the res- pective radiation component in the energy and

angle range under consideration

E the energy of electrons

or Dhotons

dV

dXI

jKpdV

the volume element

the solid angle element

mass energy transfer

coefficient

the total kinetic initial

energy of electrons of

the volume dV, V7hich

have been released by the

photons through photo and

Compton effect

For the calculation of the electron

fluence I® of the first generation of

photo or Compton electrons one can proceed

as follows

Ej)dDjdXl = lJ.jP(?^,ri^,EP).

— dH dUdEPdE? .

In this equation is

11

da/dS^dil^

the number of electrons

per unit volume of the

absorber

direction of primary

photons

differential cross section for the generation of photo or Compton

electrons

direction of photo or Compton electrons of trie first generation r_^lative

to the direction jQ.^

energy of photo or Compton electrons

Calculati

for dose

a limited

principle

paramet er energy sp

physical

cation of

by utiliz

technique

lim D

V-»0 JpdV

on alone is rarely sufficient

determination but will provide

number of measurements. In

the determination of field

s such as particle fluence and

ectra are well-established

concepts and permit quant ifiunperturbed radiation fields

ing highly sophisticated

From this, any absorbed dose may be

calculated using the fluence (r,^,Ej

distribution for each kind of radiation

incident on the medium. However, to

make thorough determination of field

parameters in, as is normal, an imknown

radiation field is complicated and timeconsuming; in most cases it may even be

impossible and, moreover, not all input

data concerning interaction with matter

will be knovm with sufficient accuracy.

Particularly, the respective interaction

coefficients for a certain material

change with the particle energy thus

providing knov/ledge in its spectral

distribution. This distribution may

change v/ith penetration depth for reasons

of interaction with matter, and that both

for photons and secondaries. Moreover,

the consistency of most absorbers is

normally not homogeneous causing serious

discontinuities in the field parameters

and requiring differentiation of the

interaction coefficients.

After this short analysis of the more theoretical approach of absorbed

dose some actual problems in photon

dosimetry shall be pointed out. At first, basic field parameters, such as low energy photon spectral distributions,

still look for an intensive investigation.

The evident output of those investigations influences the largest field of

X-ray application, the X-ray diagnosis.

As a high proportion of the ionizing

radiation received by the population is

due to medical X-ray diagnosis it is

essential that the necessary diagnostic

information shoiild be obtained v/ith the

least possible amount of radiation.

In the range where the energy

dependence on the mutual effect of

patient and detector systems is great, as is the case with the usual polycliromatic X-ray spectrum. X-ray spectrometry is indispensible in answering the

201
questions which arise. From the spectra

of a diagnostic X-ray tube (operating at

120 kV) monitored in front of and behind

a phantom it can distinctly be seen, that

the low-energy component of the primary

radiation merely contributes to the

exposure of the patient but is hardly

noticeable any more in the image forming

radiation (Fig. 1). Different filtration

at the tube strongly affects the spectral

distribution of the primary radiation

whereas the spectrum of the image forming

radiation is mainly influenced by the

object and the tube voltage. Hence, the

necessity for higher filtration to reduce

radiation dose to the patient is evident.

0)

no

K

60

to

1-

b) — 2mmAI

1 — 2mmAl — immAI i

/'/

—im

QlnmAt* vnCu —£ mmAt* | / VmmCa \ fj

^

[i] A IY|I f

1 1

Photon Entfgy

Fig. 1. Primary radiation (a) in front of

and (b) attenuated by a 20 cm water phantom for different tube

filtration. Tube voltage 120 kV.

However, comparison of the spectra

of the image forming, attenuated primary

radiation, and the scattered radiation

both incident at an image point clearly

showLS the limits of scatter elimination

(Fig. 2). The spectrum of scattered

radiation includes a large portion of the

same energy range as the primary radiation spectrum thus hardly rendering

feasible an energy-selective filtration

of the scatter component behind the

patient. Furthermore, a strong increase

in scatter proportional to the increase

in volume irradiated can be recognized.

Problems of adaptation of the spectral

sensitivity of the image recording

system to the available radiation qualities as well as those relating to the

improvement of grids can also be solved

by spectrometric methods.

For measurements of the spectroscopic field quantities, semiconductor

detectors represent state of art since

the interpretation of their pulse height

spectra into polychromatic spectral

fluence is feasible with the well-known

characteristics of the detectors. In

particular, the constant resolution over

the areas of interest simplifies the

calculation of true spectra. By contrast.

-f—

v

/

/ \

1

Photon energy (keV)

Fig. 2. Comparison of an attenuated primary radiation ( , measured)

to the integral scattered

radiation( , calculated) at an

image point. Phantom thickness

20 cm HgO, tube voltage 120 kV,

field size 10 x 10 cm*^. the widely used scintillation spectrometer with limited resolution depending

on energy would yield serious problems in

unfolding the pulse height spectra.

Fig. 3 shows the deterioratim of an assumed but typical test spectrum by the

inherent qualities of two spectrometric

systems (ciystem I : fwhm=const. System

II: fwhm=f(E)). Thus considering the

exposure of patient quantitatively the

determination of fluer.ce together with

geometric data must only be regarded as the first step for solving the above

introduced fundamental integral equation.

Fig. 3- Influence of energy resolution

of a detector on the pulse

height spectrum.

I'lany attempts

out to determine a electron spectra w

est together with

energy absorption

a considerable lac

those data exists,

Konte-Carlo transp

with an appropriat

ntion of the human

have been carried

ttenuated photon and

itnin organs of interthe interaction and

coefficients. Since

k of information of

approximations by

ort codes together

e mathematical describody's shape and of

202
its dimensions have been carried out . Problems arise from considering all

interactions possible as well as their

mathematical treatment. From results

already available agreement vfithin a factor of 2 is supposed to justify those

extensive calculations, in principle.

Determination of Absorbed Dose by

Measurements

Absorbed dose evaluation and calculations are generally verified by an experimentally determined description

of the field parameters in terms of its

interactions with matter. The objective

of this approach of absorbed dose is to

avoid the complete field characterization

by taking into account that the dose

quantities are integral quantities providing integration over the different

spectral field components. Thus, instead

of using integration procedures on a calculative basis and the application of more or less knovm coefficients, one can alternatively apply selected measuring

techniques which are able to appro ximatively perform the intended integration

experimentally

In order to perform such a measurement, one must use an effect caused by

irradiation which is easy to measure

and, moreover, in magnitude proportional

to absorbed dose. Since the medium to

which the radiation dose is applied does,

in general, not yield a proper measurable

effect, a radiation sensitive detector

is brought to the point of dosimetrical

interest. It is the detector material

in which the dose-proportional effect is

measured. For certain pre-conditions,

i.e. charged particle equilibri\im, CPE,

or the fulfillment of the Bragg-Gray

conditions, one can - by means of the

measured dose effect - perform the

determination of absorbed dose generated

in the irradiated medium as if it were

there instead of the substituting

detector. A suitable measuring effect

is the ionization of gases. As pertinent

dose qiiantity the "exposure" (X) has

been introduced, for air as a detector

material

The "exposure" is defined as the

Quotient of dQ by dm, where dQ is the

Sum of the electrical charges on all

the ions of one sign produced in air

vrhen all the electrons liberated in a volume element of air with the mass dV, are completely stopped in air.

The special unit of exposure is the

roentgen (R) ; 1 H = 2.58 x 10"^ C kg"-"-.

With present techniques it is difficult

to measure exposure when the photon

energies involved lie above a few MeV or below a few keV. The principal quantity

in the relationship betv/een exposure and

absorbed dose is the average energy

required to produce an ion pair (w-value).

The "exposure" is measured v/ith ionization

chambers which in dimensions and wall

material must fulfill the conditions of

CPE or Bragg-Grray

CPE is achieved v/ith chambers walls

consisting of air equivalent materials

so that

en ] S /wall

_en S air

and a linear extension d>R max of the

secondaries

The BRAGG-GRAY principle describee

the possibility to express the absorbed

dose Dm in a material by the specific

ionization J in a small air filled cavity

imbedded in the material by use of the

equation

(S/p) (S/p; M

(S/p) air

air (S/p)

= W.J

air

provided the following pre-conditions are

fulfilled: (i) the cavity dimension must

be such that particle flux density is not

changed, i.e. ^^^y. = ^jvj* (ii) for non- ionizing radiation the ionization in the

cavity must be small against the secondaries of the material, i.e. (M-en)M'^

) . , (iii) the cavity wall d^^-^R,

vj-hich^ii the range of secondaries, or is

made of tissue equivalent materia.l in case of biological measurements.

Determination of absorbed dose (Dj^j) in an arbitrary material from exposure

(X) measured in air by means of the

BRAGG-GEAY principle is characterized, as mentioned above, by

(S/p)^

^^(S/P? air

air

For conditions of CPE, defined by the

conditional equation WqJ^)^^ =

(^^en'^^kr one obtains with '

_ dQ _ 1 da

^ ~ dm ~ p

' dV (s/p)h

rSTpT^air

203
the special form of the BRAG-G—G-RAY-principle for X and y-rays:

" ^^^en/P^air air

By using [rdj = 0.869. X [r] which

is the absorbed dose in air one receiv

the .^reneral formula:

es

Dj,.[rdJ = 0.869 \

'/'Jy . Z[Rj-f.XLRj

en The f-fact or implying measurements

of exposure under conditions of CPE

converts exposure values to absorbed

dose} another conversion factor, g, implies measureuents of ionization under

Bragg-Gray conditions. Usually, the

factors f and g are calculated from the

ratios of the mean values of the mass energy absorption coefficients and tue mass stopping pov^er of the tv;o media,

respect ively

f = 0.869

, da ,„p

, „Pn -In — dii-^ ^en^^^P hi dE^

f/ /-,Pn -In i®

-1.

0.869 M dE^

I(S(2')P~')air

^

—da j-ne dB

approximately equivalent materials this

ratio will change much less with the

spectrum than the single coefficient.

Therefore, the radiation spectrum does

not affect the dose determination so significantly as in case of dose calculations from the field parameters.

The concept, as well as the methods

and tecliniques in dose measurements are well established, thus meeting the

requirements of a high accuracy standard

But problems may arise from field

application and control of procedures

and equipment. This is shown at the

determination of a basic property of a radiation detector as is the energy

dependence of its signal response

in Fig. 4. Even for the same detector

different energy calibration factors may

be achieved at different labs for reasons of differing calibration spectra

applied. It is obvious that these

discrepancies refer to different approaches of effective energy with non-compatible spectra since monochromatic X-rays

are, up to now, not common in the range

of low energy photons. In other terms,

it appears possible to produce any

response curve which you are asked for, even a flat response, by use of an adequately filtered bremsstrahlung. The

resulting serious problem may only be

solved sufficiently by standardization

of calibration procedures. This was

lirgently called for at the IAEASymposium on Advances in Physical and

Biological Radiation Detectors in fall

1970, however, without leaving a sound

effect.

It can be shown that the dose conversion

factors f and g are not dependent on geometrical factors, such as depth in

water or the field size, i'urther detailed parameters of interest can be taken

from the respective ICRIJ-Reports

For soft tissue ;sue 1.1

air

approximately energy independent between

O.i and 10 MeV; the resulting absorbed

dose D, . [rdj = 0.97. X [rJ. tissue^

Obviously, also the above shown

way of dose determination is dependent

on interaction coefficients which

provide prior knowledge of the quality

of radiation or making assumptions as to

its composition. However, it is the

ratio of interaction coefficients for

the medium of interest and air as detector material v;hich influences the

calculation. Particularly, in case of

/ \ / >

/

'

/ / ^

/' " f-T^ ^

rrgelK ^ \

=30 •/.

Fig. 4. Response of a dosimeter for

different qualities of calibration

radiations (The curves are fitted;,

to unit sensitivity a 120 keV)

1. Assumed response to monoener- getic sources

2. Calculated response to calibration set v;ith AE/Emax = 30j- 3- Calculated response to a cali-=

bration set with AE/Emai = 60*/f

204
Operational Dosimetry and Problems

From a recent directory published

by the International Atomic Energy

Agency one can find that the high energy

radiotherapy eqiiipments are concentrated

in advanced centres of preferably developed nations. This inequity certainly

has created a separation of the level of

dosimetry as practiced by the countries

involved. The need for constant development and improvement of new, reliable

dosimetric techniques has no doubt thrust

the advanced institutions into the front

line in the field of radiation dosimetry.

Radiotherapy centres in some of the

developiftg nations certainly cannot

afford to catch up with this trend due to

the lack of both equipment and trained

personnel. Moreover, facilities in such

parts of the world have frequently ex- perienced neither the \irge nor the need

for new techniques while other pressing

problems claim higher priority.

In general, the most observable

deficiency in these centres is the lack

of some of the equipment considered

essential for basic dosimetry work. This

includes various types of ionization

dosemeters but, equally, education and

dosimetric joining to reference labs.

The necessity for transferring ra- diation quantities between different

labs has become evident bv multinational

surveys for cobalt-60 radiation therapy

dosimetry, by means of a postal dose

intercomparison service. These surveys,

based on a joint V^HO/lAEA^ project,

pointed out that more than 40X of the

participating institutes exceeded by

partly significantly more than + 5/. the

reference dosimetry value.

These findings for cobalt-60 gamma

dosimetry which dosimetry somehow is

simple to proceed, give a certain imagination upon the dosimetric problems in

that practice where X-rays are applied and

where, in addition, the accuracy of dose

distributions is of interest. In this

case all uncertainties of an X-ray generator application must be taken into

acco\int. In this connection one again

laust point out the need of establishing

characteristic field parameters, i.e., at

least, the penetrability or the HVl of

the X-ray quality imder consideration.

However, as can be seen from Fig. 5 v/hich

shows the spectra of two calibration

qualities with the same HVL, even this

first approximation to the radiation

energy by its penetrability characteristics, is a doubtful value.

Fig. 5. Spectral distribution of two

X-ray qualities of the same HVI

(0.75 mmCu) achieved with different tube voltages and filtrations.

As a result, one has really to be in

doubt, if the problem of the establishment of absorbed dose or exposure measurements with an ideal uncertainty of around

+ 4/. is further on of exclusive priority.

Eventually it should be of preference to

direct main effort to the proper definition and application of radiation fields

in terms of the respective parameters.

A IAEA panel on the activities of

Secondary Standard Dosimetry Laboratories

(S3DL), taking place at Rio de Janeiro

still at the end of this year will try

to balance both the aspects of calibration

and education in order to overcome those

problems, world-wide. The installation

of SSDL's by '.ffiO/LlEA has already encou- raged improvement at many institutions

and thus, in turn, has increased the

standard of medical dosimetry practices.

Standardization of procedures and

techniques in these regions, however,

seems to be a difficult task at the

present tine.

A useful tool in the field of

applied dosimetry, supplying standard

ionization techniques can be the solid

state dosimetry, which is based on

meas\rrable changes of, at least, one property of the solid body as a fimction

of interaction with radiation. Some newer solid state dosemeters, for

instance thermoluminescent or photoluminescent dosimetry, have proved particularly suitable for special problems such

as storage of dose information, use in

very confined spaces or measurements of

extremely low or extremely high doses.

Further, for certain detector materials

there is a relatively small to neglegible energy dependence of the relative

mass stopping power compared v;ith water or soft tissue. The geometrical and me- chanical features of the detectors are outstanding together with a reasonably

good reproducibility of the radiation

induced signal, whicn has just again been

205
roven for thermoliiminescent dosimetry

TLD) on the occasion of an I.nternational Buratom Intercomparison on Nov, 11

to Nov. 15, 1974 at Bologna, Italy.

The results of that meeting, clearly

point out the necessity for a new generation of read-out devices to achieve

higher precision and that more reliably.

The new readers shoiild be automated in

cycliig \:±th a multi-step temperature

program and diminish the influence of

planchet reflectance on the signal, f.i.

by using hot gaz heating. Nevertheless,

TLD is worthwhile to be shortly reviewed

on its possibilities and the problems

still to be solved. Multiprobe TLD

measurements in medical physics can be

recommended as routine procedure for the

determination of dose distributions,

surveys of radiation burden in critical

organs during radiation treatment as well as for equipment checks . Problems

of sterilisation or handling of the

detectors can be overcome.

In the large field of radioecology

,

a number of surveys and an equal number

of different results due to inadequate

dose assessments can be found in literature. These surveys involve investigations of radiation burden from natural

sources ( t errestrial and cosmic radiation,

radiation resulting from building

materials) and sources caused bjr civilization and technical progress (medical

diagnosis, nuclear power plants). Of

particiilar interest will be exact data

on the medical radiation burden causing

around 95/. of the artificial radiation

burden as well as routine dosimetry in

the popula,ted environment of nuclear

povjer stations for permanent control of

the radiation level. The importance of

quant it itative information on the effect

of radiation on human beings justifies

any effort

In all these application fields of

radioecology TLD could be of major importance. However, sensitivity and

energy dependence are still lacking

improvement. Basic features of the

detectors would be a lower limit of

detection of jirad and particularly, an

energy independent response down to

around 10 keV. At the moment, there is,

to the authors' knowledge, no detector

material fulfilling both requirements.

In occupational monitoring the

possibilities of dose assessment with

TLD meet, in general, the requirements

of modern health physics trends for

higher possible accuracy and that to

better respect the I'-IPD values and

determine also lov/ doses for an amelioration of the working conditions.

However, there are still fundamental

monitoring problems due to discrepancies

between the objectives of radiological protection measurements and its physical

practicability. As a common basis of

understanding, the principal objectives

of personnel monitoring are the demonstration that the level of radiological

safety meets appropriate standards, and

the provision of information that allows

improvements of working conditions if

necessary. In more specific terms, the

objectives are to achieve compliance with,

the recommendations of ICRP as reflected

to national legislation. These specific

objectives can only be met if measurements of the personnel dose allow estimation of the mean dose in various

organs, since this is the basis of ICRP

recommendations. In practice, however,

the radiation field will neither be

locally nor temporally constant for

simple straight-forwar_d I measurements,

i.e. each point of the body surface will

be exposed to a radiation field different

in intensity, spectral distribution and

incident direction. For these reasons,

the relationship between measured

personnel dose at the surface and required organ dose is rather complex and

ambiguous

Because of the lack of physical

realization of the measurement of organ

doses an appropriate philosophy has been

installed declaring the surface dose

measured at a representative place of

the trunk to be equal to the respective

body dose. This philosophy is valid for

external radiation coming from directions

predominantly within one hemisphere, i.e.

the direction towards which the individual

is facing.

In order to meet the requirements

of this philosophy, the dosimeter should

be approximately tissue-equivalent

between photon energies from 10 keY to

3 PleV. For discrimination between the

radiation burden of the skin, due to p's

and low-energy photons and of organs in

the depth due to higher energy photons a simple dosimeter system should be sufficient consisting out of two detectors

differently shielded - in compliance with

recommendations of ICRP publication-^^ ,15

In this dosimeter-system one detector

behind 10 - 20 mg/cm^ filtration would

differentiate the non-penetrating radiation, the second detector behind 0.5 - 1

g/cm^ tissue equivalent filtration would

give a measure of radiation of higher

penetrability vihich could be set equal

to the organ dose.

TLD is able to meet the requirements

of this philosophy, within the error

206
limits acceptable of a factor 1.5 in

Fig. 6. However, there still remains

the problem of more specific data interpretation in case of doses in the

vicinity or in excess of i-EPD's.

V/hile personnel dosimetry is well

installed in developed nations, using

partly highly sophisticated dosimeters

and discussing problems of philosophy as mentioned above^^, more than 30X of

occupationally exposed personnel in

developing coimtries is not monitored.

2ven in countries vrith monitoring

ser^rices which I got to know as an IAEAexpert, this service was partly done

quite unsufficiently. For instance, one service applying a four-filter badge,

evaluated only the open-window field for

all kinds of radiation vrorkers. Further,

the calibration has been done only v/ith a 70 kV radiation X-ray quality using no additional filtration to the inherent

filter. It is obvious, that energy

independent TLD introduced to personnel

monitoring in these countries will be of

major help and effectiveness in radiation

prot ection.

o < KhfVi I •c^i I. >iao kiV

' "r 1 1 1 iiJi 1 1 1 1 1 Mil J

1 1 1 Mill 1 1 M 1 III

A

. c

• a

1 o

> »

1 1 1 1 IIJI I 1 I It 111 1 1 1 1 III! 1 1 1 1 >iii B 100 xm UOOD atlSXfi

' Expcsura X,,fTiR

Fig. 6. Reading of TL dosimeter shielded

with 300 mg/cm in dependence of

the dose applied (Parameter:

photon energy)

For the understanding of radiation

mechanisms in radiobiology and radiochemistry it is important to intruduce

further parameters for field description

in addition to the absorbed dose.

Particular interest is given to the

density of energy imparted along the

path of a particle (LET concept), to the

energy deposed in a certain object size

' or to the statistical distributions of

these energy amounts deposed in certain

object sizes. The quantities and

.methods important for the studies of

reaction nechanisms and describing

microdosimetry shall not be further

discussed, here.

Modern solid state dosimetry techniques eventually matching the requirements of microdosimetry, such as thermally

stimulated exoelectron emission (TSEB), are still under elaboration. TSE3

promises a detector depth around some loci ngstroem. Hov/ever, at the moment,

the investigations deal still with the

interpretation of the TSEE mechanism

prior to dosimetry application. Results

of unexpected high exoelectron energies

in Fig. 7 are first steps of betjer

understanding of the phenomenon-^ ^

Particularly for measurements in vacuo,

high reproducibility and linearity has

been foimd for TSEE output versus alpha

or gamma fluence for different grades of

ceramic beryllium oxide in Fig. 8.

Relarding potential IV

Fig. 7. Integral exoelectron energy distributions for ceramic BeO (Beryllium Consolidated) during the

heating and cooling cycle. Parameter glow temperature.

/-fiuence fcm-^J

^ a tffl660i-ev ft

a - fluence lan-'l

Fig. 8. Integral TSEE output of different

ceramic BeO versus a- and yfluence.

207
Conclusion

illthough the concept of energy

absorption in matter represented a philosophical departure from the idea of

quantifying the radiation field per se, the absorbed dose probably is, at present, the central physical dose quantity,

while other dose quantities are auxiliary

quantities supporting, for instance, the

determination procedure of absorbed dose

(exposure) or requirements of health

physics (dose equivalent). But, reviewing all the dose quantities existing and

having in mind, that even the main

quantity, the absorbed dose, cannot be

measured simply in practice^ ^one is

inclined to think of DENNIS exclaiming:

Once upon a time we had the Roentgen,

which we could measure but didn't want,-

then we had the rad which we wanted but

couldn't measure; and now we have got

the kerma which we don't want and can't

measure"

Both the approaches of absorbed dose

pointed out above, i.e. starting indirectly, from the determination of field

parameters or from direct measurements

of the radiation interaction with matter, are still lacking further and more exact

data concerning basic parameters of

interaction. For instance, there are serious doubts as to the adequacy of

%if-values, there is a need for stopping

power data and spectroscopy of secon- daries in matter-, further there are problems in measuring compatible characteristics of field instruments for

bremsstrahlung due to the absence of

standardization of calibration conditions.

Thus, care has to be given to the

correlation between the measurement

output and the absorbed dose. In applied

dosimetry there is the further problem

of data interpretation which often are measured at a point different from the

one of dosimetric interest. Further,

absorbed dose cannot be seen isolated

from considerations of LET and microdosimetry in the fields of radiobiology

and radiotherapy.

However, emphasis should be given

to the importance of ensuring that the

Inevitable imprecision of data

measiirement , estimation and transfer is

not reflected in a corresponding

imprecision of concept.

References

1. Franz, H. and Kobner, V/. Proc. 2nd

Int. Conf. on the Peaceful Uses of

Atomic Energy, Geneva 1958,P/971

21, p. 101.

2. ICRU-Report 11, 1968, Radiation

Quantities and Units.

3. Rossi, n.H., Mcroscopic Energy

Distribution in Irradiated tiatter,

Radiation Dosimetry, Vol. I, Acad.

Press, New York (1968) . 4. Rindi, A. and Thomas, R.K. Health

Phys. 23, 715 (1972).

5. Fano, U., Spencer, L.V. and Berger,

K.J. Penetration and Diffusion of

X-Rays, Handbuch der Physik 38/2,

660 (1959).

6. Jones, T.D., Auxier, J. A. and Snyder,

v/.S. Health Physics 2±, 241 (1973).

7. ICRU-Report 10 a, 1962, Radiation

Quantities and Units.

8. ICRU-Report 14, 1969, Radiation

Dosimetry: X-Rays and G-ainma Rays with

Maximum Photon Energies between 0.6

and 50 HeV.

9. ICRU-Report 17, 1970, Radiation

Dosimetry: X-Rays generated at

Potentials of 5 to 50 kV.

10. ICRU-Report 19, 1971, Radiation

Quantities and Units.

11. ICRU-Report 23, 1973, Measurement of

Absorbed Dose in a Phantom Irradiated

by Single Beam of X- or Gamma-Rays.

12. Moos, V/.3,, Balamutov, V.G. and

Abedin-Zahed, R., National and

International Radiation Dose Intercomparisons, IAEA-PL-479/18.

13. ICRP-Report 12, General Principles

of Monitoring for Radiation Protection of V/orkers.

14. Dunster, H.S., Symposium Radiation

Protection - Philosophy and

Implementation, Aviemore / Scotland,

June, 1974.

15. Ecker, E.H., Wittmaack, K., Regulla,

D.F. and Schulz, F., Proc. 4th Int.

Conf. on Luminescence Dosimetry,

Krakow (1974)

16. Dennis, J. A., Personnel Dosimetry

Techniques for External Radiation,

p. 207, EiiTopean Nuclear Agency,

i'ladrid (1963) .

208
NEUTRON DOSIMETRY BY TJEERMOLUMINESCENCE DOSIMETER

Yutaka Furuta and

Japan Atomic Energy

Tokai Research.

Tokai-mura , Naka-gun

,

Shun-ichi Tanaka

Research Institute

Establishment

Ibaraki-Ken, Japan

In this report, a historical survey of neutron dosimetry

by thermoluminescence dosimeter (TLD) is made to begin with

and then, as the basic problems for neutron dosimetry, the

energy response to neutrons, gamma-ray discrimination perfor- mance in gamma neutron mixed fields, and sensitivity improvement are described. Furthermore, two types of conversion

efficiencies are introduced to obtain the integral glow value

of TLD from its kerma value. These efficiencies are given

for any charged particle and may serve not only to estimate

neutron energy response of any TLD but also to study the

energy transfer to material from charged particles. As

applications of these studies, the possibility of development

of a rem response TLD or absorbed dose measurements for

neutrons by TLD are also described.

(Charged particle, dosimeter, dosimetry, efficiency,

gamma ray, kerma, neutron).

Introduction

Because of its many superior characteristics, studies of the thermolumi- nescence dosimeter (TLD) have rapidly

increased during the past ten years.

Especially, some of TLD's have an effective atomic number similar to that

of air and most of the studies have been

devoted to gamma-ray exposure measurements. Therefore, the studies of TLD as

a gamma-ray dosimeter are considered to

have proceeded fairly well at present.

On the contrary, investigations on neutron dosimetry can not be considered

as sufficient and there are many problems

yet to solve.

In the present report, the authors

will survey the historical development

of neutron dosimetry by TLD and v;ill

show the approaches to develop a new dosimeter or dosimetry to neutrons.

Historical Survey

The discovery of radiation-induced

thermoluminescence goes back to the

beginning of the present century. It

vfas reported recently that Mme. Curie

wrote in her thesis her discovery of the

phenomena in the course of studying the

various physical and chemical effects

produced by exposing various substances

to radium^. Rapid development of the

studies, however, may be considered to

have started in 1950.

2 Daniel et al had introduced wide

feasibility of the thermol-uninescence

(TL) phenomena including radiation dosimetry as a research tool. In early days,

studies were mainly made for X or gamma

rays, but in later 1950s considerable

effort was concentrated on the practical

means of measuring neutrons with TL

materials

Haring and Schoen^ tried to detect

neutrons by a CaF2 film with or °Li

film held in front of the CaF2 film.

The CaF2 TLD responds to alpha particles

produced by (n,a) reaction of ^^B or °Li

with neutrons of a high reaction cross section. These materials serve as the

radiator of alpha particles. They

described that the lower limit of neutron

detection in the case of using -'•^B film was 3 X 10^ neutrons, and besides, °LiF

film was more energetic and found to be more suitable and 5 x 10^ neutrons could

still be detected. Furthermore, they

used simultaneously a second GaF2 film

without the radiator film in order to

eliminate the contribution of gamma rays

to the TLD. In their report, it was also

suggested that the utilization of protons

recoiled by neutrons in radiator was a disadvantage because of their rather small

energies, but the utilization of neutrons

to be moderate, which could possibly be

done by the human body, was promising.

We see in their report many fundamental

concepts for neutron dosimetry by TLD

used in these days.

A neutron dosimeter using TLD in

conjunction with a fast neutron moderator

and a radiator was reported by Surjadi^.

His dosimeter consisted of a layer of

CaF2 '^-^^ enveloped by a LiF film and a

209
paraffin ball surrounding the detector

device. He studied the relation between

the sensitivity and the ball radius from

4 to 12 cm and the energy response to mono- energetic neutrons of 1,2 and 14 MeV.

The sensitivity to fast neutrons

can be considerably increased by suspension of LiF TLD in alcohol, and the

method was practiced by Karzmark et al^.

In this case, alcohol serves both as the

moderator for fast neutrons and as the

radiator of recoil protons. Furthermore,

it is convenient to use a volatile

liquid like alcohol because it is readily

evaporated at room temperature prior to

read-out

At that time, Harshaw Chemical

Company (Cleveland, Ohio, U.S.A.) had

developed activated LiF crystals specifically for TLD in cooperation with the

University of Wisconsin. These materials

were identified as TLD-100 (natural Li

containing LiP TLD) and TLD-700 (^Li

enriched LiF TLD) . Cameron et al° of the

university studied the characteristics

of these TLD's and showed that thermal

neutron dose in gamma neutron mixed

fields may be estimated by subtracting

the light output of TLD-700 from that

of TLD-100, because of the response of

TLD-700 to thermal neutrons was less than

0.5/. of TLD-100.

The 1st International Conference on Luminescence Dosimetry was held in 1965

at Stanford and many papers were submitted. In this conference, the major

reports concerning neutron dosimetry were

as follows:

7 1. Wingate et al. reported the TL

response of TLD-700 to thermal and fast

neutrons at energies from 0.26 to 14 MeV.

From the results, they concluded that

TLD—700 made a convenient gamma-ray

dosimeter in mixed gamma neutron fields

because of its low neutron sensitivity.

Furthermore, they indicated that the

thermal neutron fluence may be conveniently measured witii normal LiF( TLD-100)

with linear relationship between light

output and neutron fluence up to about

10-'-^ neutrons/ cm^ , and also pointed out

from their results of glow curve that a higher read-out temperature was required

than gamma-dose measurements.

2. A pair use of TLD-100 and TLD-700

was proposed by Simpson to obtain

gaimna-ray dose in gamma neutron mixed

fields of a reactor environment utilizing

the characteristic of the same response

to gamma rays and different response to

neutrons. He also obtained the linear

relationship between light output and

thermal neutron fluence similarly to the case of Wingate et al.'.

3. Endres^ reported a pair of

capsules of LiF TLD's used at Hanford as

a neutron dosimeter, of which one was filled with a phosphor alone for measurement of gamma-ray exposure and the other

filled with the same phosphor and alcohol

(or other hydrogenous material) for

measurement of the gamma-ray plus neutron

exposvire.

4. At Brookhaven National Laboratory,

a neutron dosimeter system has been

developed by using LiF TLD within a Bonner sphere. In the report by Distenfeld et al. a 12" diameter polyethylene

sphere modifies the neutron response

characteristics of the LiF TLD to reaso- nably resemble the dose equivalent

response characteristics of neutrons in

tissue from thermal energies to approximatelj'' 20 KeY . Evaluation of the gammaray response is made by using "LiF TLD

(°Li enriched LiF TLD) and ^L±F TID ('Li

enriched LiF TLD) pair simultaneously in

the system.

To evaluate experimentally the neu--,

,

tron shielding performance, Gayton et al.

reported several methods using LiF TLD.

One of them was a new type of spectrometer, the DELTA spectrometer, which

used LiF TLD's along the axis of a cylindrical moderator irradiated on one

face. The spectral information was

obtained from the thermal neutron ! fluence distribution by an iterative

solution to a matrix equation. The

report described that the device covered [ nine decades of energy and was suffici- ; ently^sensitive to measure fluence levels j of 10° neutrons/cm^

Kuz'min et al. studied the relation

between sensitivity and phosphor layer

thickness of TLD with recoiled proton

radiator, and obtained a flat response

dosimeter to neutrons having energies of

0.2 to 4.5 MeV.

Stolterfoht and Jacobi^^ also obtained energy response of ^LiF TLD with and

without alcohol using two kinds of

capsule made of teflon and polyethylene

to fast neutrons of 3 to 15 MeV.

In 1968, the 2nd International

Conference on Luminescence Dosimetry was held at G-atlinburg. In this conference,

energj' responses were reported by Endres

and Kocher-^ • to neutrons of several

types of TLD's (TLD-lOO, TLD-600 (^Li

enriched LiF TLD made by Karshaw

Chemical Co.), Li2B40Y, CaF2, and BeO)

placed on a polyethylene phantom with and

210
without Cd or shield.

Use of a TLD with neutron activation

material was proposed by Kocher and

Endres-^5 as a personnel neutron dosimeter,

of which TL is induced by radiations

emitted from the material activated by

neutrons. In their dosimeter, Rh was

used as a neutron activation material.

A pair of ceramic BeO discs, of

which one was covered with a non- hydrogenous material (graphite) and the

other with a hydrogenous material

(polyethylene) was reported by Becker

and Crase-'-". For read-out, thermally

stimulated exoelectron emission (TSEE)

technique was used.

17 Busuoli et al. showed that the

ratio of the main peak (210°C) and the

high temperature peaks (250 - 300°C) of

the glow curve of TlD-100 is 24.5 for

gamma rays and 2.4 for slow neutrons, and

suggested that this characteristic makes

it possible to use LiF TLD for measuring

neutron dose in gamma neutron mixed

fields.

Falk-'-^ reported a personnel neutron

dosimetry system consisting of three

pairs of LiF TLD's (TLD-600, -700) shielded with Cd. In his system, one of the

pairs is shielded from the front, one pair from the back, and the third pair is

shielded from both front and back.

An application of the LiF-teflon

discs using °LiP and 'LiF TLD's pair

laminated between the plastic layers of an identification card was reported by

Nash and Attiz^S as accident dosimeters.

In July 1971, the 2nd AEC Workshop

on Personnel Neutron Dosimetry was held

in New York^*^. In this meeting, many

researchers participated from main establishments in the United States. It was then reported that most of the establishments employed the albedo type TLD

neutron dosimeter, and the following was concluded at the meeting.

1. Neutron dosimeters utilizing the

albedo neutrons require a fixed or well

known spacing between the dosimeter and

the body of the individual.

2. Energy dependence is still an

important problem, but the dosimeters

can give good results when properly worn

and when calibrated with neutron spectra

approximating those to which they will

be exposed.

The 3rd International Conference on Luminescence Dosimetry was held in

October 1971 in Riso. In the conference,

a new idea was reported by Mayhugh et

al.2-^. They tried to apply the activation of TLD composite material for

thermal neutron dosimetry. That is,

after exposure of a TLD in gamma neutron

(thermal) mixed fields the TLD is annealed. When a constituent nucleus has

an activity by thermal neutrons, the TLD

landergoes self-irradiation (self dose)

from the internal radioactive nucleus.

A period of time after, the TL is read.

The read corresponds to the neutron

exposure, independent of the gamma-ray

contribution during exposure in the mixed

fields. They suggested 44Ca or ^

Dy as suitable isotopes contained in the TLD.

In November of the same year (1971)

,

a Symposi-um on New Development in

Physical and Biological Radiation Detectors was held by IAEA in Vienna. In the

symposium, Attix^^ discussed the neutron

Ixminescent dosimetry problem and proposed a TLD system to obtain the

neutron tissue dose by BeO TLD for thermal neutrons, for intermediate neutrons

by a mixture of some TLD-lOO powder with

TLD-700, and for fast neutrons by TLD-600

and TLD-700 combination.

Neutron dosimetry technique utilizing TLD self dose proposed by Mayhugh^-^

for thermal neutrons was extended for

fast neutrons by Pearson et al'^^. They

used phosphors such as MgFp TLD which

contain two activating nuclei with

different threshold energies and different decay times, and suggested some neutron spectrum analysis.

Efforts to utilize TLD's for personnel neutron monitoring are continuing

at several major laboratories. At the

Savannah River Laboratory a prototype

badge had already been developed'^'^, and

further development have been made by

Hoy^^. The newly developed dosimeter

consists of a 2" diameter polyethylene

hemisphere which is divided into two

parts at I/4" from the roiinded end, and

only a large part is covered with Cd

plate. Both parts have recesses for a pair of ^LiF and .'LiP TLD's and the

whole placed in a stainless steel

housing and attached to a belt. The

report concluded that it has limitations

in certain energy regions of the spectrum, but the dosimeter provides a reaso- nably acciirate method of integrating

personnel exposures from unknown spectra

at installations where neutron sources are contained or sufficient scatter is

present . . . The response of LiF and Li2B40Y TLD

to thermal neutrons has been investigated by Ma j born et al.^° primarily with

a view to using them for personnel moni211
toring in areas with mixed gamma neutron

fields. The investigations include: 1)

measurements of TL response vs. thermal

neutron fluence, 2) measurements of TL

response vs. dosimeter thickness, 3)

measurements of TL response vs. isotopic

abixndance of °Li and -'-^B, and 4) measurements of backscattering and gamma-ray

contribution from a phantom in a collimated-beam geometry.

Blum et al.^'^ reported a usage of a mixture of highly sensitive CaSO^ TLD

(CaS04(a/]V28) ^nd glucose (3 parts of

glucose and 1 part of CaSO^CTm) powder)

for fast neutron dosimetry. The same

authors'^" also reported the results of

fast neutron dosimetry by CaFp TLB in

pair use with hydrogenous (polythene) and

with non-hydrogenous (lead) screens.

They concluded that lead was a convenient

material for the latter and recommend

microrod type TLD rather than disk type

because of the directional dependence of

the former dosimeter.

Attix et al.-^*^ reported that an attempt was made to determine the gammaray dose component in the neutron beam

from a cyclotron by CaFp and 'LiF TLD

(TLD-700) at U.S. Naval Research Laboratory.

Kocher et al.^"'" reported a fiveelement TLD using LiP blocks for beta

particles, photons^ and neutrons used at

Hanford, of which 'LiF block is shielded

to provide interpretation of the 1 cm tissue depth dose, and a second '''liP block is xmshielded to provide the kerma

dose interpretation, and two "LiF and

one 7LiF blocks are used for fast and

thermal neutron dose interpretation.

Calculated response of several

albedo neutron dosimeters using °LiF TLD was reported by Alsmiller and Barish52

for neutron energies lower than 400 MeV.

They obtained the results for each of the

dosimeter geometry considered, which were

presented for both mono-energetic and

continuous incident neutron spectra and

for both normally and isotropically

incident neutron fluences.

The 4th International Conference on Luminescence Dosimetry was held in

Xrakdw this summer (1974). The present

authors have not acquired yet the proceedings except manuscripts of a few

papers. In these, there is a paper on composite dosimeters using CaS04 and

BeO phosphors for x-ray, gamma-ray,

beta-ray, and neutron dosimetry reported

by Iga et al.33 in their dosimeter.

CaSO.(Tm) powder and Won-TL °Li or 'Li

compound mixtures in a weight ratio of

1 : 1 are used.

Basic Problems

If we wish to use TLD for neutron

dosimetry, some basic properties must be

taken into consideration. These are the

energy response, gamma-ray discrimination,

and sensitivity. We will describe about

these problems.

Energy Response

In any case, one of the most basic

requirements for radiation detection is

to know the energy response of the

detector to objective radiations.

Figures 1 and 2 show the energy res- ponse of typical TLD's to neutrons. Experimental results were obtained to monoenergetic neutrons produced by Van de

G-raaff accelerator. In the same figures

the energy responses obtained by calculations are also shown. These were obtained

as follows:

S V

S 8

6 icV

1C5"

I I I I 1 1 M| I

i

I I 1 1

1 1| I , , T1lll| I If

®LiF(Mg)'

"1

• ' ' 1 1

1 ill

eKp.(F irut« & Tanaka)

I I 'I'll I"

icT* id"' I 10 to' neutron energy (MeV)

a { K l/IO) -

^ i exp. (Wlngate et al.) j^j- a ' (Goldatoln et "l-jl^, ' o " (Furuta i TanaXaCj.

cal. ( " )

Kf« tcr' I )o 10' nautron energy (MeV)

Fig. 1. Energy responses of ^LiF and "^LiF

therraoluminescence dosimeters.

When the TLD is calibrated by ^"^Co gamma rays, the integral glow value to

neutrons is obtained by the kerma

calculation

= ?^(i)-^(i) (i;

212
K(i) = C.e(.).(E^ + Q(i)).cr(.)(E^)

.$(Ej,),N^^ (2)

where

^(i)

K

(i)

(i)

'(i)

(i) n'

'(i)

integral glow value (R

Co equivalence/neutron.

cin-2) , incident neutron energy

(HeV), mean conversion efficiency for i-th particle

produced or recoiled by

incident neutron to

obtain integral glow

value from kerma value

of the particle (R "^Co

equival enc e/ erg . g~-^

)

,

kerma value of i-th particle (erg-g"-*^),

conversion factor to

obtain erg unit from MeV

unit

,

fraction of energy transfer to i-th particle from

incident neutron,

Q-value of nuclear rea- ction concerning i-th

particle production (MeV),

reaction cross section

with neutrons of energy

E concerning i-th particle (cm )

,

fluenc e of neutrons

having energy E^ (neutron.

cm~2 )

,

number of atom concerning

i-th particle in unit

weight of TLB {g~^)

i I

9 8 g

. S >

I 1

1-1 8

*^

If we know the value of the mean conversion efficiency for each particle

produced or recoiled by incident neutrons, we may estimate the energy response of any

TLD to neutrons by the above calculations.

Therefore, it is clear that the conversion

efficiency is also very important in

developing a new TLD, and we will describe

the efficiency further in a later section.

We may also estimate the energy response of the moderator type or the albedo type dosimeter by this method in

conjunction with the calculations, such

as the I-Ionte Carlo calculation, of

neutron spectmim at the TLD set position.

10'

r- 1 "

I mil III I I T

CoSG4(Tm)

I'll'l' ' ' ' 111! iii|"^f I—

I I I Hill f

I I << I"' I I I I mil Kf' icf 1 . 10 neutron energy (MeV)

I I llllj I 1 I Mil

( X I/IO)

V -!xp. (Goldstein at al.)?^' _ A " (Tochilin et a'.r*"* O ' (Taraka t Furuto)-"' —.cal. (FuT'ita' 4 Ta.iakaJ''^'

I ^

I I I mill , ,1. 1 I III .1 I ml I I I I mil

JO 1 10 neutron energy (MeV) Fig. 2. Energy responses of CaSO^ and BeO

thermoliiminescence dosimeters.

Q-amma-ray Discrimination

In most cases, neutron fields are accompanied by gamma rays, and to obtain

the neutron dose in these gamma-neutron

mixed fields gamma-ray discrimination

must be taken into consideration. As seen in the historical survey, the following methods have generally been used.

i) Utilizing a pair-use of two types

of TLD which show the same responses to

gamma rays but different responses to

neutrons; for example, °LiF and 'LiF

TLD's.

ii) Utilizing the difference of glow

cuirve shape; for example, °LiF TLD.

iii) Utilizing the reaction caused

only by neutrons; for example, the self

dose induced by neutron- activated nucleus.

213
These methods are also usefiil for

future development of a new TLB's.

Care must be taken in the facts

that any TLD has non-negligible response

to the fast neutrons as seen from the

energy responses to neutrons, and that

^LiF TLD is sensitive to thermal neutrons

because of large cross section of ^Li(n,a)T

reaction to thermal neutrons inspite of

small contents of ^Li in '''liF TLD. Therefore, as described in the literature, it

is not suitable to use TLD in fast neu- tron fields.

Sensitivity

As seen from the energy responses of

TLB's, the sensitivity of TLD to neutrons

generally is not so large except for some TLD's containing elements of high reaction

cross section with neutrons. On the

whole, it is about lO'lO r dOcq eguiva- lence for 1 MeV and about lO"? R °°Co

equivalence for 10 MeV to unit neutron

fluence in rough estimation. For the

moderator type or the albedo type dosimeter, incitement of the sensitivity by

several digits may be expected. The

sensitivity of them, however, shoiild be

changed by geometrical conditions of the

moderator, and the energy response must

be obtained for each geometry.

The development of new phosphors of

high sensitivity or new method to readout the luminescence should be expected.

The photon counting or the TSEE method

is considered to be promising.

Recently, new phenomena were found

by Podgorsak and Moran.59 phenomena

concern the electrical polarization

phenomena in dielectic solids which can

be induced by ionizing radiation.

According to their report, radiationinduced thermally activated depolarization (RITAD) effects are quite different

from radioelectret effects, and for

normally pure CaF2 sample, the RITAD

signals showed a signal-to-noise power

advantage of 40 decibels. They suggested

that the phenomena will be a great

potential for use as a dosimetry technique.

Conversion Efficiency

To develop a new TLD having desired

response to neutrons, its energy response

must be estimated. As seen in the preceding section, it may be done by calculation if we know the mean conversion

efficiencies for all charged particles

produced or recoiled by neutrons. We may

consider two types of conversion efficiencies for the TL phenomena. They are

the mean conversion efficiency and the

differential conversion efficiency. The mean (conversion) efficiency is defined

as "the ratio of the integral glow value,

say the whole luminescence, Gq to the

initial energy Eq of a charged particle

which induce the TL (Gq/Eq)." The

differential (conversion) efficiency is

defined as "the ratio of the partial

glow value dG to the differential energy

loss dE by which the partial glow is

induced (dG/dB)." In general, both the

efficiencies are not necessarily equivalent.

The response of TL material to

neutrons provides much information with

many applications for radiation physics

including health physics and reactor

physics, which could not be obtained from

the investigation for gamma rays. The reason is the response resulting from

the migration of many kinds of charged

particle composing TL material, which is

considered as a fundamental phenomena in

radiation physics. The differential

efficiency may serve to theoretical

treatment of these phenomena and the mean efficiency may serve to practical use for

estimating the energy response of TLD

to charged particles or neutrons.

The mean efficiency (relative to

that for electrons) as a function of the mass stopping power for the initial

energy of charged particles is shovm in

Fig. 5 (upper), and the differential

efficiency (relative to that for electrons] as a function of the mass stopping power i of a charged particle for the energy at j each instant during energy loss in materia^

is shown in the figiire (bottom). 3!hese were obtained for a chain of particles

one after another from experimental data

of electron (for LiF and other TLD),

proton (for LiF TLD), triton (for °LiF

TLD), alpha (for LiF and CaF2 TLD),

berylliim (for BeO TLD), oxygen (for

CaSO^ TLD) and so on. The story of

obtaining the efficiencies should be

interesting. It is describedju however, more fuUy in another report. 55

In Fig. 3, the ranges of the mass stopping power which must be considered

to reactor neutrons are shown for several

types of particles.

New Approach for Neutron Dosimetry by TLD

Dose Equivalent Measurements

As seen in the historical survey,

the TLD dosimeters already developed may

be mainly classified as follows or a combination of the following:

1) moderator type,

214
2) albedo type,

3) self dose type.

At present, all of them do not

necessarily satisfy the desired conditions for neutron dosimetry. Especially,

it is difficult to obtain a significant

value by moderator type dosimeter to

neutrons because neutron spectrum is not

well known usually. The same thing may

be said for albedo type dosimeter. The

self dose method is rather hopeful in

estimating neutron spectrum reasonably

using many types of TID as threshold

detectors. It is unsuitable for personnel monitoring, but, though only rough

estimation of fast neutron dose can be

obtained, it may serve an accident

neutron personnel monitor even if single

TLD is used. For example, CaSO^ TLD,

which is usually used as a gamma-ray

personnel dosimeter, can be used as a fast neutron monitor utilizing ^'^S(n,p)

32p reaction.

O p(Lll I 7 5 (CaFj/ O o(LiF) A a(LiF)

X 0(CaSO,)

Lucas t Ralnbolt^l) Harvey I Townsend*2)

J»hnert<0) Furuta t Tanaka35)

_l I I "III Iff'

_i I I I mil

10 for initial energy (MaV/mg • on'^)

o

• 1

I I I n ii| I—I I II I I I I 1 1 ii| I I I 1

'Cor

o p(LiP) - J»hnert<0) V a(CaFj) - Lucaa ( Rainbolt*'.' a a(LlFT - Harvey t TcJmaend*^' H a(LlF) - Jlhnurt<0) _ x OCCaso )- Furuta t Tanaka^o)

to 10

from the TLD is too simple. If we can

make, however, a new TLD which shows a neutron response similar to that of dose

equivalent, the defect becomes no longora

problem and it may be applied to neutrons

having any spectrum. Hence, we will call

hereafter the TLD having such property as the rem response TLD, and will introduce

our approach to develop the TLD.

As described in the preceding section, we already obtained the conversion efficiency for any charged particles and the

energy response to neutrons of any TLD

may be estimated by calculation.

The rem response TLD now considered

is consisted by a pair of two types of

TLD having almost the same response to

gamma rays and one type sensitive to

neutrons while the other is not. Fig. 4

shows an estimated neutron response of

the TLD. It was obtained by subtraction

of the integral glow value of the neutron

insensitive TLD from that of the neutron

sensitive TLD. In the same figure, the

maximum dose equivalent for monoenergetic neutron of unit fluence incident normally on a 30 cm thick tissue

equivalent phantom43 is also shown. From

the figure, a fairly good agreement is seen between both responses.

0 C3X

Fig. 4. Energy response of a newly developed rem response thermolumi- nescence dosimeter.

Absorbed Dose Measurements

Fig. 3. Mean conversion efficiency and

differential conversion efficiency . One of the reasons for the difficulty in obtaining the significant value

by moderator type or albedo type dosimeter is that the information obtained

In reactor physics or engineering,

including fusion reactor, we often en- counter the necessity to obtain the

absorbed dose or energy deposition by

neutrons for any material. Estimation

of radiation heating in shield materials

or damage of structural materials are considered as the example. These problems

215
are very important in reactor physics or engineering, even at present, and the

importance will rapidly increase in the near future especially in fusion reactor.

Recently, applications of TLD in

gamma-ray. heating estimation have been

reported. por neutrons, however,

applications, in absorbed dose or energy

deposition measurements are not reported

yet. In this report, we will offer a suggestion of the feasibility of TLD in

neutron absorbed dose or energy deposition measurements.

As described previously, . we had

obtained experimentally the energy res- ponses of several TLD's. From the

results it was seen that the responses

of some TLD's very much resembled the

calculated kerma of some material.

We will show two examples from the

results in the present report. Fig. 5 is a comparison between the energy

response of 'LiF TLD to neutrons obtained

by experiment and the calculated kerma

of aluminujn, and Fig. 6 is also the

energy response of UD137N TLD (made by

Matsushita Electric Industrial Cq., Ltd.)

(CaS04(Tm) and non-TL '^LiP TLD) 53 and

the kerma of iron. Good agreement may

be seen from the figures.

CM

I -« a 'Of o

neutron energy (MeV)

Fig. 5- Energy response of ^LiF thermoluminescence dosimeter and kerma

of aluminum.

It may be concluded that if the

neutron field is not disturbed by

positioning a TLD, and if the contribution of gamma rays to the integral

glow value of the TLD may be estimated,

the absorbed dose of some material may

be estimated by TLD.

Mutxu «iur9y (MeV)

Fig. 6. Energy response of UD137N thermoluminescence dosimeter and

kerma of iron.

At present, the following combinations are considered as giving good

results

material TLD f

Aluminum '''LiF 1.0 X 102

Sodium UD137N 2.7 X 102

Iron UD157W 5.0 X 10

The value of f shows a fitting

factor to obtain the kerma of a material

Kjjj in erg. g"-'-/ unit neutron fluence from

the integral glow value Gmj^-Q of the

corresponding TLD in R "'^Co equivalence/

unit neutron fluence for each neutron

energy E^ i that is

Conclusion

Recently, the necessity of a neu- tron dosimeter having high sensitivity

and accuracy is increasing at rapid rate

in health physics and in reactor physics

and engineering.

As may readily be seen from the

historical survey, personnel neutron

dosimeters practically used at present are not necessarily sufficient to the

purposes. For neutron absorbed dose or energy deposition measurements the same may also be the case. The thermolumi- nescence dosimeter, however, has many

superior characteristics CQJOgajced with

other dosimeters, and it should be

216
utilized in various fields. The authors

believe it has the ability, and they

feel honoured if some suggestions described in this report might be of service

to the development of new neutron dosimeters or dosimetry.

Acknowledgement

The authors express their thanks

to the Organising Committee of this symposium and to Professor G-hose for their

kind offer of a chance to deliver this

Key-note address in this symposium.

One of the authors, Y.Puruta, is

also indebted to IA3A for making his

attendance to this symposium possible.

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,

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217
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Discussion

A.K. Ganguly

What is the highest energy of neutron upto which you feel you can use the

TL dosimetry?

Y Furuta

It may be considered that the problem depends on the size of TLD used.

Vi'hen most of the lost energy of the produced or recoiled particles is absorbed

in the TLD, good results may be expected.

W. S. Snyder

Are the comparisons with dose based

on the "air-dose", that is the dose to a small dosimeter, or are they based on the

maximum dose within the body?

Y. Furuta

Our rem response TLD introduced in

this symposium has a neutron response

similar to that of the maximum dose equivalent when it was used in a free space.

We are also considering now another TLD

which shows similar response to the maxi- mum dose equivalent when put in front of

a human body.

S.Makra

Adding a small-size polyethylene

moderator to a paired TLD detector which

is located on the body improves the response very slightly . I think there is

very little point in doing so.

I feel that the delta-spectrometer

has a poor resolution thus the practical

importance of this instrument is limited.

Hydrogeneous radiator - TLD combination is a very promising device, I hope

it will be used more widely.

Y. Furuta

In our rem response TLD, hydrogeneous

material only use for the purpose to slight compensate the slope for 10" 1 MeV

region neutron energies to the MADE response .

I also think so, but for some purpose

it may be useful.

I also think so.

218
EFFECT OF HEAT TREATMENTS ON THEEMOLUMINESCBNCB

OF PURE Al20^

A.S. Basu and A.K. Ganguly

Health, Physics Division

Bhabha Atomic Research Centre

Bombay-400085

Six TL glow-peaks at the temperatures 100°C, 150°C,

200"C, 275°C, 310^C and 415°C are observed in pure AI2O3

after gamma irradiation. For higher exposures ( > 1000 R)

the 275°C TL glow-peak is masked by the lower temperature

peaks and is not seen. Thermoluminescence of this pure

AI2O, is investigated after different thermal treatments.

The overall sensitivity increases with annealing temperatures and reaches a maximum at about 1200°C. The results

are explained in terms of the structural change in alumina

during these heat treatments.

(Aluminium oxide; glow; heat treatment; impurity;

temperature; thermoluminescence)

Introduction

Rieke and Daniels-'- have shown that

gamma ray induced thermoluminescence of

aluminium oxides depends on the extent

of hydration and the crystal form

produced by different calcining treatments. A peak at 236°C depends on

sodiujn impurity. They have used different samples of AI2O3 with varying

impurity contents and prepared with

different calcining treatments. In the

present paper thermoluminescence of

A120-J is studied with one sample of spec

pure quality alumina (with impurity

contents in ppm level) after different

thermal treatments.

Experimental

Phosphor Characteristics and Preparations

The starting material of spec pure

AI2O3 used in the present investigation

contains the following impurities (data

supplied by the manufacturer)

Chloride - 0.05/.

Sulphide - 0.01/

Fe - 0.01/.

Loss on ignition - 1/

The general method of preparing AI2O3

consists of precipitating A1(0H)3 which

after repeated washing is fired at

llOQOC to remove the last trace of H2O.

Hence it can be presumed that the above

sample had been fired at about 1100°C

For studying the effect of thermal

treatment on alumina, the sample is

heated at temperatures ranging from

700°C to 1400°C. The heating is done for

two hours in air at any given temperature

and cooled in the switched off furnace.

The sample so prepared are referred to as treated AlpO^ at that temperature and are

stored in light tight containers.

TL G-low Curve Recording

For studying the TL output , the

samples Here given gamma exposure of

3.3 X 10^ R from a "^Co gamma irradiation

facility. The glow curves were then

recorded at a linear heating rate of

25°C/mln using 2 mg of irradiated powder,

in the temperature range of 25°C to

500°C. The details of the TL Reader set

up used is fully described elsewhere . Results

Fig. 1 shows the TL glow curves of

AlpO^ treated at temperatures as indicated and also of untreated AI2O3 (virgin

sample without giving any heat treatment)

after gamma irradiation.

From the figure it can be seen that

AI2O3 exhibits six peaks in its TL glow curve at temperatures of 100°C, 150°C,

275°C, 310°C and 415°C. The 275°C and

310°C peaks are not easily discernible

from a visual inspection of the TL glow curves but can be distinctly seen by

partial bleaching techniques. If an irradiated powder is heated at 220°C for

half an hour, the TL recorded, it

exhibits clearly the 275°C peak.

Similarly TL glow curve of irradiated

powder after heating at 280°G for half an hour exhibits clearly the 310°C peak.

219
" I400*C

1300'C

\ iioo'c \

80O°C,9OO''C, lOOO'C

700*C

UMTREATEB

Fig.

50 100 150 200 ;5? 310 330 400 450 500 TE),fP£«ATUP5 (°C)

TL glow curve of AI2O5 heated at

different temperatures for two

hours and cooled in the furnace.

The total thermoluminescence output

(area under the TL glow curves) increases

as we go from untreated KL20-z^ to 1200°C

treated samples as in fig. 2. As the

treatment temperature is increased from

700°C to 12000c, the area goes to a maximum and then falls for any further

increase in the treatment temperature.

Figure 3 shows the glow curves of AI2O3

when the sample is quenched i.e. when it

is removed directly from the indicated

temperature to the room temperature from

lOOOOC onwards. The TL glow curve of

quenched as well as fxjrnace cooled AI2O5

is the same for treatment temperatures

upto 900°C. Figure 4 shows the glow

curves of A120-5 when it is heated under vacuum (atmospheric pressure of

(1-I.5)xl0~'^ Torr) at a few indicated

temperatures. Table 1 gives a comparative study of the relative TL outputs of

AI2O2 when it is heated under these three

conditions. From the above table is is

clearly seen that the TL output of

quenched AlpO^ is less than that of

furnace coolea AI2O5 from treatment temperatures of lOOQOC onwards. The TL

output reduces still more when it is

heated \inder vaccum.

tI iKPOO'C

3

2

1

, . "»

200 250 300 350 TEMPERATURE IN "C Fig. 3. TL glow curves of AI2O3 when at

different temperatures for two

4

3

2 2 1

^2

hoiirs and quenched.

1400*C

2

1300*C

TOO 800 900 uoa noo taw 1300 TEMPERATURE OF lEAT TMATMENT X

no 200 210 300 TEMPERATURE IN 'C

Fig. 2. Relative TL sensitivity of AI2O5

at different temperatures and

cooled in the furnace.

Fig. 4. TL of AI2O3 samples heated at

different temperatures in vacuum

for two hovirs.

99n
Table-1

Comparative study of relative TL sensitivity of AI2O5 when heated under different conditions.

Temp, of Relave TL Relative Relative

treatment output TL out- TL

for two when cooled put when output

hours in the the when

furnace sample is heated in

( C) quenched vacuum

700 33.2 33.2

800 42.5 42.5

900 42.5 42.5

1000 42.5 21.5

1100 43.2 21.9

1200 50.5 25 .2 1300 26.17 17.6 7.32

1400 21.4 3.3

Relative TL output for untreated sample

- 30.65

Discussions

The different modification of AI2O5

obtained on annealing^ at different

temperatures are

150OC

AI2O3 3H2O - AT n nn n 300°C ^Al20j IH2O >

Y AI2O3 -

°Q°°> a AI2OJ

Y-AI2O3 is a face centred close packed

oxygen lattice which transforms into a hexagonal close packing - the a form on heating at 1000°C. This transformation

Y to a is complete when heated at 1200°C

in air. Annealing temperatures below

1200°C is likely to produce a mixture

of y/a.

It is known from Low Energy Electron

Diffraction^ that a alumina undergoes a change of surface structure upon hea.t treatment under vacuum above 1250°C

accompanied by a change in the chemical

composition of the surface by the loss

of oxygen. This structural change is

reversible and can be changed back to the

initial stage by heating at 1200°C in

presence of oxygen ( 10"^ Torr of oxygen

pressxire) . In the light of the above discussions, our TL results can be interpreted to

indicate that a alumina is the most

sensitive TL emitter among various forms

of alumina and presence of oxygen during

any heat treatments to aliimina helps to

preserve the TL sensitivity. For temperature of treatments higher than about

1000°C, fast cooling of the sample

reduces the TL sensitivity perhaps

because the s\irface structural changes

oc curing in a alumina get frozen.

References

1. Ricke, James K. and Daniels,

Farrengton, J .Phys .Chem. , 61, 629

(1957)

2. Sunta, CM., Ph.D. Thesis, Agra

University, 1970.

3. Holzapfel, G. and Chrysson, E. , Third

Internat .Conf . Luminescence

Dosimetry, Riso, Oct. 11 - Oct. 14,

1971.

4. French, T.M. and Somorjai, G-.A., J. Phys. Chem. , 74, 2489 (1970).

221
THERKOLUMIIIESCENCE MBCHATTISMS IN LITHIUM FLUORIDE

; r 1 S.P.Kathuria,V.N.Bapat,C.I'I.Sunta and V.K.Jain

Health. Physics Division

Bhabha Atomic Research Centre ,.„;,.

, Trombay, Bombay-400085 , India '

' '

Five glovj- peaks upto 200°C are well known in lithium

fluoride after gamina irradiation. Seven new glow peaks above

200°C are reported in the present work. They are designated

as I to XII in the ascending order of temperature of appearance.

Activation energies are determined by initial rise method for

five glow peaks, which coiold be well isolated by partial

annealing from the lovier teiiiperature glow peaks. TL emission

from the prominent glov/ peaks is similar and contains four bands

with maxima at 370nm, 390 nm, 415 nm and 470 nm approximately.

The ispectral distribution of the total TL emission and emission

from glow peaks V (195°G) and ZII (400°C) are obtained also by

plotting the integrated intensities of individual glow curves recorded at every 5 nm interval from 250 nm to 800 nm. The TL

emission spectra obtained in this way are corrected for the

instrument response. Optical absorption spectrum of lithiiAjn

fluoride crystal is recorded after garmaa. irradiation. Distinct

absorption bands are observed at 225 nn, 250 nm, 310 nm and 380 nm. Absorption spectra are recorded also after various thermal

annealing treatments. The spectral similarity of individual glow

peaks and the continuous bleaching of F band (250 nm) with the

annealing of individual peaks, shows that F centre takes part in

recombination process at each stage of glow peak emission. The

thern^ly released carrier at individual glow peaks is therefore

of hole type.

(Irradiation; gamma rays,- LiF; optical absorption;

spectral distribution; tiiermoluminescence)

Introduction

Thermoluminescence of lithium fluoride has been studied extensively by a number of worker sk"-' Five glow peaks upto

200°C have been observed by all workers

but observation of TL emission at temperatures higher than 200°C has varied

from worker to worker. Sunta et al°»

observed ten glow peaks upto 400°C.

There are conflicting opinions

regarding the natvxe of charge carriers

released on heating and also about the

thermoluminescence mechanism^ >

'

Christy et al8 proposed the recombination

centre as the impurity centre absorbing

at 196 nm. TL emission occurs when a hole freed by thermal heating is

captured by this centre. The crystal is

restored to its initial state by an . electron tunneling from a nearby F

centre, to the impurity ion v;ith the

emission of a second photon. However,

Claffy-^-^ observed thermoluminescence in

the absence of 196 nm absorption band

also

I-Iayhugh et al-^^ found that trapped

charge carriers responsible for TL are electrons. On heating the irradiated

LiF phosphor, electrons from their

respective trap centres are liberated and

captirred at V3 centres containing tvro trapped holes 12, This would result in

a single hole centre (V^j- centre) which

is unstable at room temperature. The

indirectly produced mobile hole then

undergoes recombination at an impurity

site with electron from F centre resulting in light emission. In the present

work, a study of optical absorption

spectra and TL emission spectra in LiF

after gamma irradiation is undertaken to

identify the luminescence centres and

nature of charge carriers released on heating.

1

. Experimental

Lithium fluoride samples used are

(i) LiF (T) powder (I40 to 200 mesh) from

crystal grov/n in the Technical Physics

Division of this centre and (ii) TLD-100

of Harshaw Chemical Co., USA. Before use

the povfders were annealed at 400°C for

1 hour and cooled to- room temperature by

leaving in air on a block of aluminium.

Irradiation was carried out in °^Co

gamma cells having dose rates of 2.3

ICR/min and 7.0 KR/min. TL measurements were carried out using 5 mg of powder

at a linear heatirg rate of 25°C/min with

a reader system described by Sunta-'-^.

222
Experimental arrangements for recording

optical absorption spectra and TL emission

spectra have been described elsev/iiere-^4

Res^olts and Discussion

G-low Curves

TL glow curves of five LiF samples

are shown in Fig. 1. Qualitatively all

the five glov; curves are similar. It is

also evident from the figure that while

the general structujre of the glow curves remains the same, the relative peak

heights may vary from sample to sample,

-he TL of LiF obtained from whatever

source, does not seen to depend, critically on the impurities so far as the glow curve structure is concerned Kovrever,

it does depend upon the impiarity and

preparation parameters if one looks at

the sensitivity, relative peak heights

and response characteristics of various

peaks. In the sample TLD-7C0 (Batch 48

DZ) there are ten distinct glow peaks

seen at the temperature 62°C , 102°C',

142°G, 175°C, 195°C, 215°G, 232°C, 257°C,

287°G and 403°C . In other four samples,

glow peaks at the temperature 215°G, 232°G,

and 287°C are not clearly seen but there

exists a presence

Fig. 1. Til 31ovr curves of iiiF samples for

the gamma exr)osure 7.05 x 105r

(aj TLD-lOO (48 LV/) (b) TLD-lOO

(IJL; (c) TLD-6C0 (26 EAD) (d) TLD- 700 (48 DZ) (e) LiF (T)

To ascertain the exact number of

glow peaks beyond 200'-'G one of the LiF

samples (TLD-lOO) was annealed at 160°C

for 30 minutes after gamma irradiation

so as to erase the first 5 glow peaks

and then quenched to room temperature.

The glov; curve recorded after this

annealing treatment shov/s a clear glov;

peak at 220°C which was not seen before

the annealing treatment. (Fig. 2 curve

b) . This peak was obviously submerged

below the 195°G glow peak. Aliquots of

the irradiated sample were then successively annealed at higher temperatures.

These annealing temperatures and tirae are chosen in such a way that the glow peaks

preceding the one under examinations are completely eliminated during each anneal.

The glow CLirves recorded after each such

thermal annealing are given in fig. 2 (cujrve b to h) . Following this procedure, seven more TL glow peaks above 200°C

which v/ere not obvious (curve a) are observed at 220°C, 237°G, 260°G, 295°G,

312°G, 337 C and 405°C. Following the

similar procedure, these new peaks

clearly shov/ed up in other samples also.

Thus, a total of twelve glov; peaks are observed in all the Li? samples studied.

They are designed as I to XII in the

ascending order of the temperature of

appearance. • •

Thermal activation energy of glow

peaks II, V, VIII, XI and XII are determined by initial rise methods for LiF (T)

and TLD-lOO samples and are given in

Table-1.

: Table-1

Thermal activation energies of glow

peaks II. V. YIII, IX and XII deter- mined using initial rise method

Glow peak Thermal activaG-low Temperature ( G) tion Energy (eV)

peak

IIo. LiF(T; TLD-lOO LiF(T) TLD-100

II 102 103 1.36 1.25

V 195 195 1.63 1.5

VIII 257 260 2.10 2.08

XI 332 337 1.97 1.97

ZII 402 405 1.54 1.37

TL Emission Spectra

The annealed TLD-lOO samples are irradiated to lO^H and 10°R and the glow curves with 10 mgm of each of these

samples are recorded at intervals of 5 nm

from 250 nm to 800 nm. The area under

each glow curve is determined and

plotted against the respective wavelength

after correcting for the system response

( curves a of figs . 3 and 4} . Gurves b

of figs 3 and 4 show the Tij emission

spectra of glov; peaks V and XII respectively recorded in a similar v;ay with 105r

and 10°Pl irradiated TLD-lOO samples. It is seen from these figures that there

223
are four emission bands appearing at

370 nm, 390 nm, 415 nm and 470 nm and

qualitatively all the TL enission

spectra are siiuilar. However, there is

variation in relative intensity of

emission bands.

5

-

4 -

a »100 3 -

2 -

0 /

JTig. 3. TL emission spectra of TLD-100

(IJL) after lO^il gamma irradiation (a) Total TL emission (b) TL

emission from glow peak V.

100 200 300 400 TEMPERATURE °C Pig. 2 . TL glov; cijirves of TLD--100 (IJL)

(a) After 7.05xlO'^'-R of gani-ia irradia

tion

(b) •a followed by 30 rain amiealing

at 150°C

(c) •a followed by 20 min annealing

at 180°C

(d) •a followed by 10 rain annealing

at 22C°C

(e) 'a follovred by 20 min annealing

at 240OC

(f) •a follovred by 30 min annealing

at 260OC

(g) 'a follovfed by 10 min annealing

at 300°C

(h) •a followed by 2 hrs annealing

at 330°C 250 300 350 400 4 50 500 550 600 WAVELENGTH (nm) Similar results were obtained when

emission spectra were recorded at the

temperatures 85°G, 135°C, 180°C and

380°C^ . At these t emperatiires prominent glow peaks II, III, V and XII are emitted respectively. This shows that

the same luminescence centres are involved in the therraoluminescence

process at all temperatures. The change

in the relative intensity of TL emission

bands is possibly because of the change

in the configuration of the luminescence

centres with temperature.

Pig. 4. TL emission spectra of TLL-100

(idL) after 10 R gaima irradiation (a) Total TL emission (b) TL

emission from glovf peak XII.

Optical Absorption Spectra

Fig. 5 shows the absorption spectra

of LiI''(T) crystal after gamma irradiation and annealing at 100°C, 150°C,

200°C, 250°G and 350°G for 30 minutes

each. After gamma irradiation three

absorption bands at 250 nm, 310 nm and

224
380 run are seen clearly and. there is a suggestion of another absorption band at

225 nm. 250 nm absorption band is a well

knov/n ?-band and is due to the electrons

trapped at the negative ion vacancies.

M,

I

Fig. 5. Optical absorption spectra of

LiP(T) crystal after

(a) 7. 05x10^3 gamma irradiation

(b) 'a' followed by 30 min annealing at

(c)

100°C

'b ' followed by 30 min annealing at

150°C

(d) ' c ' follov/ed by 30 min annealing at

200°C

(e) •d' followed by 30 ain annealing at

250°C

(f) 'e' follov7ed by 30 ain annealing at

350°C.

The F-band decreases progressively

after each thermal annealing (curves a to f ) . After annealing the crystal at

350°C , the absorption at 225 nm and a part of the F-band only are left (curve

f) and in the corresponding glow curve

there is only one glow peak present at

402°C. Both the absorption bands, 225 n:n and F-band disappear together with the

4C2°C glovf peak after annealing the

crystal at 400°C for 1 hour. If it is

assumed that an electron and hole centre

are required for TL emission, it would

appear that the 225 nm absorption is due

to hole centres and is correlated with^

402°C TL glow peak (XII). FJLick et al^

have suggested that the absorption at

225 nm arises from a centre v/hich traps

two holes. Such a centre has been identified in KCltCa^'.

All the glov/ peaks are regenerated

by irradiating the LiF sample, having

glov7 'oeak ZII as residual to Hg lamp UY

light^^. UV light photons release the

charge carriers from the peak XII traps

which are captured by the trapping sites

corresponding to lower temperature glow

peaks, emptied during thermal annealing.

The glow peak XII has been correlated v;ith the optical absorption found at

225 nm vrhich is due to hole centres.

Therefore charge carrier involved in the

transfer process from peak XII traps are

the holes which are being captured by the

trapping sites corresponding to lower

temperature glow peaks.

The progressive decrease in F-band

optical density after different thermal

annealings (fig. 5 curves a to f) shows

that F-centres take part in the recombination process. The exact configuration

of the luminescence centre is not identified in the present work. Thus on heating the gamma irradiated LiF sample,

holes are released from traps of different thermal stability which recombine

with electrons of the F-centrea - part

of the luminescence centres. Energy is

supplied to the luminescence centre by

the recombination of the hole with an electron which appears as light. The

emitted TL emission bands correspond to

the energy states of the luminescence

centre modified by the crystal field.

Acknowl edgement s Autho^rs are grateful to Dr. A.K.

Ganguly, Director, Chemical Group for his

keen interest in tne v;ork and many helpful

discussions

References

1. Daniels, F. , Boyd, C.A. and Saunders,

D.F., Science 117, 343 (1953).

2. Daniels, F. , Lum. Dosimetry, AEG Symp

Ser. Vol. 8, G05fF-650637 , Stanford

(1965)

3. Claffy, B.v/., Lum. Dosimetry, AEG

Symp. Ser. Vol. 8, GOUF-650637

,

Stanford (1965).

4. Cameron, J.R. and Daniels, F. Science,

134 . 333 (1961).

5. Cameron, J.R., Zimmerman, D.V.'., Kennqy,

G. , TJuch, R., Bland, i1. and Grant, R. , Health Physics, 10, 25 (1964).

6. Sunta, CI-I. and Kathuria, S.P. Advances in Pnysical and Biological Radiation Detectors, SM-143/24, IAEA,

Vienna (1971)

7. Sunta, G.I-I., Bapat , V.H. and Kathuria,

S.P. Proc. 3rd Int. Conf. Lum. Dosimetry, Oct. 11-14, Riso (DAEC and

IAEA), (1971).

8. Christy, R.V/., Johnson, iJ.H. and

i/ilbarg, R . R . , JJlppl . Phys . J^, 2099

(1967)

9. laick, CO., Claffy, E.V/., Gorbies,

S.G., Attix, F.ii., Schulman, J.H. and

Allard, J.G., J. Appl. Phys. 28,3867

(1967)

10. Kayhugh, M.k. , Christy, R.V/. and

Johnson, K.I-i., J. Appl. Phys. 41 , 2968 (1970)

11. Claffy, E.W., Phys . Stat . Sol . 22, 71

(1967).

12. Viinter, S.i'i. , V/olfe, D.ft. and

Christy, R.V/., Phys. Rev. 186, 949

(1969)

13. Sunta, C.il. Ph.D. Thesis, Agra Univ.

(1971).

225
14. Kathuria, S.P., M.Sc. Thesis, Bombay

University (1974).

15- Jones, D.S. and Burt, A.K., Lum.

Dosimetry, ASC Symp . Ser. Vol. 8,

COiJF-650637, Stanford (1965).

16. Kathuria, 3. P., Indo-Soviet Conference on oolid State Material, Dec. 11-

16, Bangalore (1972).

17. Crawford, J. H. Jr. and Nelson, CM.,

Phys. fiev. Letters ^, 314 (i960).

18. Kathuria, S.P., Bapat , V.N. and

Jain, V.K., Presented at the Fourth

Int. Conf. Lum. Dosimetry, Aug. 27-

31, 1974, Krakow, Poland.
THERMOLUMINESCENGE RESPONSE OP LiF TO GAMMA RAYS

V.K. Jain and S.P. Zathiiria

Health Physics Division

Bhabha Atonic Research Centre

Trombay, Bombay 400085

India

The thermoluminesc enc e of lithium fluoride shov?s twelve

peaks, of which II (lOOOQ), III (135°G) and V (190°G) grow

linearly first and then become nonlinear, eventually

saturate and finally show decreased response or damage.

Peaks beyond the Vth peak on the other hand seen to grow

supralinearly right from the beginniiig. None of the available

explanations for the supralinearity of the dosimetry peak (V)

is entirely satisfactory. Similarly damage too is not

understood. In this paper it has been shovm that the radiation

induced sensitisation is linked with the Xllth peak (400°C).

It is postulated that this peak is created as a result of

irradiation and hence is supralinear right from the beginning.

The other high temperature peaks, though supralinear, are

not found to be responsible for radiation induced increaf^e

in sensitivity of lower temperature peaks. It is shown that

the trap centres (TC's) responsible for the Xllth peak are generated as a resiilt of the break up of complex centres

TCLC's on irradiation. This break also causes the addition

of luminescence centres (LC's) which leads to increase in

sensitivity. The complex centres (TCLC's) themselves are

formed due to the 400^0 annealing. Decreased response or damage after saturation is the result of loss of luminescence centres v^hile the traps remain unaffected.

(Dose; gaEima rays,- LiF; response; sensitivity,

supralinear; thermoluminescence)

Introduction

Many aspects of TL response to Xand gamma rays of LiF dosimetry phosphor

are vaguely understood. For example, the

complicated annealing behaviour-'- » 2 and

radiation sensitization^ » 4, 5 are not

satisfactorily explained. Similarly,

radiation damage in LiF is quite critical

and needs investigation.

The glow curve of LiF has many more

I peaks than are generally reported in

j' literature". In this paper the TL res-

! ponse of some of these peaks is reported.

' The model proposed earlier^, to explain

radiation sensitization and supralinearity in LiF is elaborated. Some aspects of

the lowering of response, due to radiation

1 damage are reported and the involvement

of luminescence centres in this is

liscussed.

Experimental

Lithium fluoride samples used were

(i) LiF (T) powder (140 to 200 mesh) from

! crystal grown in the Technical Physics

Division of this Centre and (ii) TLD-100

of Harshaw Chemical Co., USA. Before use

the powders were annealed at 400°G for

one hour and cooled to room temperature

by leaving in air on a block of aluminium.

Irradiation was carried out in Co-60

gamma cells having dose rates of 2.3 'i^B./ min and 7.0 feU/min. TL measurements

\iere carried out using 5 mg of powder at

a linear heating rate of 25°C/min with a reader system described by Sunta°.

Results and Discussion

Thermoluminescent Response of Some Peaks

Fig. 1 shows the glow curves of

lithium fluoride after gamma irradiation.

There are total of tvrelve glow peaks

present in the glow curves of LiF

samples^. But for the first peak v;hich

decays rapidly and Xlth peak which is

hidden under Xth peak, ten peaks can be

clearly seen. In Fig. 2 the response

of some of the peaks viz. II, III, V,

VIII, and XII is sho\m. From .the growth

pattern it appears that the TL peaks in

LiF fall into two groups: one group

comprises peaks upto the Vth (dosimetry

peak) and the other of peaks beyond the

Vth. The first -group peaks initially

rise linearly and become supralinear at

higher exposures. The second-group

peaks seem to respond supralinearly right

227
from tne beginning (VIII and XII in

fig. 2). 2\lso snovm in this figure is

sensitization by gamu.a irradiation and

annealing at 350°C for 15 niin for peaks

V and VIII. The well known sensitization

procedure enliances the response of not

only the Vth (dosimetry) peak but also

of the VIII peak as shov/n and other peaks,

not shov^n. Sensitization is shown for two

ganna pre-exposures and it can be seen

that when the sensitization is incomplete

the phosphor still responds supralinearly

though at a higher exposure.

iT

J L- I "XL

Fig. 1. TL glow curves of LiF TLD-100

exposed to 2.3xlO''R and LiP(T)

exposed to o.gxlO^R and 2.3x105r.

One of the reasons for the therrnolurainescence peaks to be supralinear

throughout could be that they are created

by irradiation as has been suggested by

Ilason and Linsely^*^. The Vlllth peak

and the Xllth peak both are supralinear

but v;ith a difference. Tne Vlllth peak

is radiation sensitized but not the

Xllth. In fact radiation sensitization

is dependent on the Xllth peak vfhich is

'created' (see next section). If the

Vlllth peak were due to traps whicii

captured more than one charge carrier,

its grovjth would be supralinear*.

!iupralinearity and Sensitization

The ratio of the response to 100 R

of gamma rays of TLL-100 sensitized by

4.0x104r of gamma rays and subsequent

annealing ( S ) and that of the unsensitized TLD-lOO ( So) gives the sensitization

factor (S/So). Also the area of the

glow curve remaining after the gaimna

Pig. 2. Response of peaks II, III, V, VIII

and XII in LiP(T). Peak V and VIII

(1) LiF(T) annealed at 400^0 for 1

hour (2) 1 followed by 1.15x10%

of sensitization exposure and

annealing at 350°C for 15 min (3)

1 followed by b.gxlO^R of sensitization exposure and annealing '- as in 2. Peak XII as in above.

exposure and subsequent annealing gives

the residual theraiolumine sconce (RTL) . How S/So varies with RTL remaining as a result of annealing at different temperatures for various periods is shown

in Fig. 3- From these curves it is

apparent that S/bo does not depend

criticalljf on RTL except when the latter

has decreased to a negligible proportion

which corresponds to peak XII. Sunta

et al concluded tliat glow peak XII

alone is responsible for sensitization.

A model was proposed earlier" to explain

supralinearity and sensitization. The

model postulated the formation of a complex centre (TCLG) consisting of a trap centre (TG) and a luminescence

centrelO. Initially the number of such

complexes is s.aall. .By annealing at

high temperatures (400 C), trap centres

and luminescence centres are brought

togetuer to form more complexes'^. On

irradiation this complex breaks up into

its constituents (TO and LO) . As irra-

* The fact that for densely ionizing radiations like

alpha rays the relative response of the high temperature peaks is more, suggests this.

228
diation progresses, more and more luminescence centres are added which, cause increase in TL response leading to supralinearity. Annealing the irradiated

po'.^der at a lov/er temperature say 35C°G

does not reform the complex and the added

l-jiiinescence centres continue to be

available resulting in sensitization.

8 S/So .ig. 3. Change in sensitization factor

with annealing at different temperat'ores for different times.

As has been indicated by Zimmerman , v;e postulate further an association

between the TL trap and the luminescence

centre. Thus when the luminescence

centres increase on irradiation as a result of break up of TCLG, they get

spatially associated with the nearest

trap available. I'ow on release of the

charge carrier from the trap there is

greater probability of recombination with

:-e luminescence centre. I'hen this

mxTiber has increased sufficiently, as

l.appens after an exposure of about

5xio4il for glow peak V, there is no -urther increase in the probability of

recombination and maximum response is

reached. iJiaiilarly after a pre-exposure

of the 3a_'.e order followed by 230°C

annealing for 1 hour, though the trap

responsible for lower temperature peaks

-.ave been enptied, the recombination

centres continue to be associated with

the respective traps. The 280°G annea- ling does not destroy this association.

The TL response of the powder is therefore

that enhanced by radiation (radiation

sensitization) . At 400°G however, the

"created trap", TG and the added luminescence centre, LG , combine to form the

complex (TCLG). The increased sensitivLty

is thus removed.

Radiation Damage

The response curves of fig. 2 show

decrease beyond the saturation point.

The decrease depends upon the total

exposure given to the phosphor (order of

graphs 1,2 and 3 reverse to 3>2 and 1

beyond saturation) . This decrease in

response is due to damage effects (13)

and is a general feature of LiF thermoluminescence. This is presented in

fig. 4. Prom these graphs as well as those of fig. 2 it appears at least for

the first group of peaks, that even after

dainage the saturation exposure does not

alter indicating no change in trap

population. This has been verified for

various initial exposixres. The thermoluminescence output, however, decreases

tfiroughout indicating less recombinations.

Thus damage to TL in LiF can be attributed

to loss of recombination or luminescence

centres. This is also indicated by the

change in tne TL emission spectrum of

LiF after damage-'-'^.

Fig. 4. Damage effect in LiF (T) for

8.3xlO°R. For each peak (Wot

marked) , upper curve is without

damage and lower with damage.

229
Conclusion

The main characteristic required to 6. be seen for LiF in dosimetry is sensitivity. The radiation sensitization in 7.

LiF is due to the break up on irradiation

of a complex centre (TCLC) into TO and

LC which itself is formed while annealing 8.

at 400°C.

9. References

1. Cameron, J.H.., S\mtharalingam, N. and 10.

Keney, G.U., Tnerrnoluminescent Dosimetry, University of V/isconsin Press,

iladison, V/isconsin, U.S.A., (1968).

2. Zimmerman, D.V/., Rhyner, C.R. and

Cameron, J.R., Health Physics 12, 525, 11.

(1966)

3- Suntharalingam, N. and Cammeron, J.R.

Phys. I'led. Biol. IJ-, 397 (1969).

4. Cameron, J.R. and Zimmerman, D.W.,

Modifications of the Kathematical 12.

model reported in COO-1105-102' . and

Report COO-1105-113, (1966). 13-

5. Claffy, E.W., Klick, C.C. and Attix,

F.H., Proc. 2nd Int. Conf. on 14.

Luminescence Dosimetry, G-atlinburg,

eds.J.A. Auxier et al . (CONF-6S0920,

WBS, Springfield, Virginia, USA (1968)

Kathuria, S.P., M.Sc. Thesis. University of Bombay, Bombay (1974)

Jain, V.K. , Kathuria, S.P., and

Ganguly, A.K., J. Phys. C (Solid St.

Physics) 8, (1974)

Sunta, CM., Ph.D. Thesis, Agra

University, Agra, (1971).

Kathuria, S.P., Bapat , V.N., Sunta,

CM. and Jain, V.K., Paper in this

conference

Mason, IS.V/. and Linsley, G-.S., Proc.

3rd Int. Conf, on Luminescence

Dosimetry, Riso, ed. V. Mejdahl,

(Riso Report i-lo. 249) (Riso: Danish

ASC and IAEA) (1971)

Sunta, CM., Bapat, V.N. and

Kathuria, S.P., Proc. 3rd Int. Conf.

on Luminescence Dosimetry, Riso, ed.

' V. Mejdahl, (Riso Report No. 249)

(Riso:DAEC and IAEA) (1971).

Zimjnerman, J., J. Phys. C (Solid St.

Physics) ±, 3277 (1971).

Marrone, M.J. and Attix, F.H.,

Health Physics 10, 431, (1964).

Jain, V.K., Bapat, V.N. and Kathuria, | S.P., J. Phys. C (Solid St. Phys .) 6,L343

(1973). ~

E

230
CHANGE IN TL SENSITIVITY OP QUiRTZ DUE TO STRESS

M. David and A.K. Ganguly

Health Physics Division

Bhabha Atomic Research Centre

Bombay-400085

Stress and strain caused by progressive and impact pressure

loading can change the TL sensitivity of natural quartz. Stress due

to progressive loading enhances the TL sensitivity considerably. It is found that sensitisation increases as the amount_uf stress

increases and reaches a maximum at about I4OO kg cm . The TL

sensitisation obtained is correlated to 'strain hardening' by the

dislocation nets produced by stress. In the case of stress caused

by impact loading, TL sensitivity is reduced. This may be due to

the conversion of quartz to a glassy state at a high stress.

(Quartz; sensitivity; stress; thermoluminisum)

Introduction Results

TL of quartz has been observed to be

affected by the stress to which the

crystal is subjected prior to irradiation.

The effects of stress on the TL output of

quartz have significance in both

understanding and applications of TL

phenomenon in (i) archaeological and

geological datings^"-^ and (ii) radiation

dosimetry^.

This paper reports the results

obtained in the studies carried out on

the effect of stress on TL of natural

quart z

Experimental Methods

Thin plates (0.5 cm thickness) were

cut from naturally available transparent

single crystal of quartz along the

directions perpendicular to c-axis.

These plates were then polished very

carefully to obtain flat s-urfaces to ensure uniformity of stress all over the

crystal

An Instron Universal Tensile

Testing Machine was used to give various

stresses to the samples.

Two kinds of stresses were applied

to the crystal plates: (i) stress by

progressive loading along the c-axis and

(ii) stress by impact loading along the

c-axis. These quartz plates were then

powdered using agate mortar to sizes

less than 0.151 and were used for TL

studies.

All the irradiations to gamma-rays

were done in ice bath at a rate of

6.9 X 103 R/min.

Effect of Stress by Progressive Loading

The crystals were subjected to

stresses of different peak loadings. The

desired stresses were developed on the

sample by loading at rate of 500 kg/min.

The sample was kept in the state of peak

stress for three minutes and then the

stress was released at the same rate as loading. The stresses given to different

plates were 308 kg.cm~2. visible

deformation was found in the samples for

stresses upto I4OO kg.cm~2. por stresses

above 1400 kg.cm~2 extensive cracks

developed in the crystal.

Natural thermoluminescence (NTL, the

TL signal naturally present inside the

sample prior to any ajrtificial irradiation) glow curves were recorded using 5 mg of the samples. A linear heating

rate of 25°C/min was employed over a temperature range of 25°C-500°C.

Figure 1 shows the NTL glow curves obtained from all the five samples. Two

TL peaks were observed, one at 260°C and

'1 1 1

1

Pig. 1. TL glow curves of unirradiated

quartz samples after giving

different amounts of stress by

progressive loading.

231
another at about 350°C. No significant

difference in TL output was observed

between the stressed and unstressed

samples

The stressed samples were subjected

to a heat treatment of 400°C for 90 mins.

along with an unstressed sample so as to remove the NTL completely. These samples

were then given an artificial irradiation

(test dose) of 2.4 x lO^R from a Co-60

gamma source and the glow curves were

recorded. There were mainly five glow

peaks present in all the samples viz: at

75°C, 110°C, 180°C, 235°C and 320°C

Areas under glow ciirves are plotted

against stresses in Figure 2.

Table-1

Effect of stress on thermal activation

energy of different TL glow peaks of

transparent quartz

Activation energy (eV)

Peak Natural Sample after stress

t emp . sampl

70°C

110°C

180°C

255°C

320°C

.658

.298

.718

.831

308 1436 2873

.658 .732 .621

.653 .675 .582

.784 .843 .814

.873 .906 .829

.865 .911 .878

1000 2000 3000 STRESS iKg.Cn?) Fig. 2. Effect of stress (by progressive

loading) on Thermoluminescence of

Transparent quartz.

TL output is enhanced very slowly

with the increase in stress till 600 kg

cm~ beyond which it goes through a stress

developing maximum sensitivity in the

crystal and falling back to almost the

value obtained with the unstressed

crystal at 2875 kg.cm"'^. The fall in the

TL output beyond 1400 kg.cm~2 appears to

be associated with plastic deformations

occurring to the samples at heavy loads.

The sensitisation produced is by

overall enhancement of the entire glow

curve. Even though the change in sensitisation is observed no change in

behaviour in respect of linearity of

response to gamma dose was observed. The

glow peaks of the samples subjected to

stress, saturate at the same dose as that

of unstressed sample.

Activation energies of the glow

peaks of the stressed samples were ^ calculated using the initial rise method''

(see Table-l). Average activation

energies of the glow peaks of the samples

are plotted against the stresses in

figure 3. It is seen that the activation

energies increases in the cases of all

the peaks and reaches a maximum at 1435

kg.cm" . It is to be remembered that TL

emission also was maximum around this

stress

1 - 70 C Pt«»

2 - 1'0'c PtAR 3-180*0 PEAR

4 - ZWC PtAK

5 - 320* C PEAK

I 9M 1436 len

STRESS CKj Cm')

Fig. 3. Effect of stress on Thermal Activation Energy of different glow

peaks of transparent quartz.

Effect of Stress by Impact Loading

Stress by impact loading was done

by dropping a load of 200 kg from a height of 20 cm on a (10 x 8 x 5 mm)

plate. The sample got crushed and was further crushed to a standard mesh size

(0.151 mcs) . This sample was heated at

400°C for 90 minutes and thpn given a test gamma dose of 2.4 x lO-'R and the TL was measured. It was found that the

sensitivity was reduced considerably.

The glow curves of the stressed and

Tinstressed samples are given in Figure 4.

TEMPERATURE 'C Fig. 4. Effect of stress by impact

loading on TL of transparent

quartz

232
The activation energies of the TL

glow peaks of the sample subjected to

impact loading were also found to have

reduced considerably.

Discussion and Conclusion

Mc Dougall^ explained the effect of

stress on the TL output of quartz as due

to variation in free energy associated

with trapped electrons of the crystal,

which in turn is related to the formation

and annihilation of lattice dislocations.

The initial increase in the observed

TL (cf. fig. 2) after giving different

stresses can be correlated to the strain

hardening due to the development of

dislocation nets in the crystal. If the

argument is valid, the stress induced

sensitisation should be initiated at the

elastic limit of the crystal and should

reach a maximum during the early stage

of permanent deformations. The sensitisation of the sample starts around a stress of 600 kg cm" . This means that

the 'hardening' due to the development

of dislocations starts at about this

stress. It is possible that the TL

sensitisation by stress is associated

with 'strain hardening' in quartz

crystals and that the elastic limit for

this sample is at about 1400 kg.cm~2,

beyond which the crystal damage occurs.

The fall in sensitisation may be due to the plastic deformations in the lattice

and annihilation of dislocations during

the recovery from strain hardening.

The reduction observed in TL output

after impact loading of the crystal may

be due to the conversion of quartz to a glassy state at a high stress. Short"

gives data showing the conversion of

quartz to a glassy state at a load of

300 K.bars. It is to be noted that in our studies the stress given to the

crystal by impact loading was also well

above the suggested pressure for the

conversion

In archaeological and geological

dating of the samples, natural TL and its

calibration against artificial TL is very

important. The present investigations

bring out that in these types of applications of TL, the geological stress

that the sample might have received,

should be taken into consideration.

References

2. Aitken, M.J. TL Dating in Archaeology,

in TL of Geological Materials (Mc

Dougall, D.J.J Ed) Academic Press,

London and New York, p. 369 (1968).

3. Zeller, E.J. Geological Age

Determination by TL, in TL of

Geological Materials (Mc Dougall D.J.j

' Ed) . Academic Press, London and New

York (1968)

^. Mc Dougall, D.J.; Some TL Properties

of quartz and its potential as accident radiation dosimeter. Paper

presented in 3rd International Gonf.

on TL (1971)

5. Randall, J.T. and Wilkins, M.H.F.

Proc. Roy. Soc . , A-184 . 366 (1945).

6. Short, M.N.; J. Geology, Jd 705

(1970)

Discussion

D.V. Gopinath

Does this enhanced sensitivity

change with time or is it permanent ?

If permanent, does it mean that by

pounding it in different ways, one can obtain different sensitivities?

M. David

Yes, it is a permanent sensitisation

in the sense, it will not be desensitised by itself with time. The

sensitisation produced is not dependent

on the method of powdering,- it depends

on the amount of stress to which the

sample was subjected.

1. Ichikava, Y. and Higashimura, T. Application of TL of quartz, paper

presented in conference on TL at

Tennessee (1969)

233
ESR-TL CORRELATIOIT STUDIES IN Cab04(RE) PHOSPHORS

K.S.V. Nambi

Health Physics Division * "' Bhabha Atomic Research Centre ' ' Bombay-400085, INDIA ' - •

ESR and TL glow curve measurements were done after gamma

irradiation at room temperature of CaS04 samples doped individually with all the lanthanide series rare earth (RE) elements, an yttrium doped sample and a few undoped samples of different

origins. Samples were prepared in the laboratory using

standardized techniques and concentration of the dopant in

individual doped samples was maintained at a typical value of

O.iy. by weight in CaS04. ESR as well as the TL glow curve patterns of all the sixteen samples were almost identical

excepting for relative intensity differences. By observing

the build up of these signals with increasing gamma dose and

also by following the decay of these for storage at room temperature, it could be inferred that the nature of the trapping

species indicated in the ESR ajid TL glow curve patterns are the

same. The behaviour of these patterns for various thermal

annealings at different temperatures have revealed that the

trapping species might have configirrations like SO4, SO3, O3

etc. having different thermal stabilities and these are res- ponsible for the observation of the multi-peak TL glow curve structure involving a variety of thermal activation energies.

The increased intensities observed in the ESR and TL signals

of the differently doped samples indicate that presence of

various RE impurities in CaS04 enhances to different extents

the stabilities of these trapped species after gamma irradiation.

(CaS04; correlation; dose; ESR; gamma ray; glow

ciirve; irradiation; TL)

Introduction

In thermoluminescence, trapped

electrons and holes either at an impurity

ion or at a host lattice ion or at a complex involving both, play the key role

and if any of these are paramagnetic in

nature, it is evident that ESR technique

can be effectively applied to determine

the structure of these trapping

centres. This paper presents the

results obtained in an attempt to

correlate ESR-TL characteristics of

rare-earth doped calcium sulphate

[CaS04(RE)J phosphors after gamma irradiation at room temperature (RT)

Experiments "

CaS04 (polycrystalline) samples

doped individually with all the rare

earths of the lanthanide series and an yttrium doped sample were prepared in

the laboratory by the simple technique

of coprecipitation and evaporation.

The dopant concentration chosen was about 0.1'/. by weight. A blank CaS04

sample without addition of any dopant was also prepared.

A varian dual cavity X-Band ESR

spectrometer employing 100 KG/sec field

modulation was used to record the ESR

spectra of gamma irradiated samples at room temperature. The TL recorder used

has been described in detail elsewhere^.

Results and Discussions

TL Glow Curves of Gamma Irradiated CaS04 (RE) Phosphors

All the CaS04 samples (doped and

undoped) exhibited varying TL outputs

but their TL glow curves were characteri

sed by the appearance of glow peaks at more or less the same temperatures; the

relative intensities of the various glow

peaks were also varying from sample to

sample-^. Actually about twelve glow

peaks could be resolved in each glow curve by 'partial bleaching technique'

and fig. 1 gives TL glow curve obtained

from gamma irradiated CaS04(Dy) phosphor

with all the glow peaks labelled from I to XII.

It is known that TL glow curves are characteristic of the various traps exis

234
ting in a phosphor which are thermally

deactivated as the temperature is progressively increased. From the similarity

of the glow peak temperatures obtained

for the sixteen samples it is amply

demonstrated that the dopants have not

altered the basic nature of the traps

already existing in the base matrix^ they

result only in different Imninescence

efficiencies. In fact the activation

energies of these traps have been found

to be directly proportional to the peak

temperatures independent of the dopant

added. That the impurities already

present in the starting material of CaS04

had no influence on the characteristic

TL glow peak temperatures obtained in all

the doped specimens was confirmed by

studying the TL glow curve pattern of

pure CaaO^ samples of different origins

all of which gave the same glow peak

temperatures-'-

Fig. 1. TL glow curve of gamma irradiated

CaS04(Dy)

E3R Spectra of Gamma Irradiated CaS04(RE)

Phosphors

None of the samples gave any ESR

signal prior to gamma Irradiation. The

ESR patterns show some remarkable

similarities except for the cases of

La, Lu, Od and Eu dopants in CaS04. The cause for this exception has not been

analysed in the present work. In

general, a six peak spectral pattern is seen having the same set of g-values

(2.001, 2.0022, 2.003, 2.004, 2.0057 and

2.0113) and even the four exceptional

cases exhibit peaks which could have

enveloped the above generally observed

six peak spectral patterns.

As the ESR of irradiated solids is

due to the unpaired trapped charge

carriers in the material, the similarity

of the ESR patterns obtained above can be

construed to demonstrate that the

different traps are the basic nature of

the host material and the dopants

influenee only the relative populations

in the various traps. Whether the trapping species shown in the ESR spectra are

the same which are involved in the TL

glow curves was verified by ESR-TL

correlation studies the result of which

are shown in the next section.

ESR-TL Correlations

Gamma Dose vs. ESR-TL Signals Build-up

The ESR signal intensity obtained

for various gamma irradiations has been

monitored and plotted in fig. 2 for the case CaS04 (Tm). The ESR signal intensity

increases with dose till about lO^R

beyond which saturation sets in. This

pattern is very much analogous to the TL

intensity vs dose relationship shown in

the same figure. A condition has thus

been satisfied for a possible conclusion

that the trapping species involved both

in ESR and TL are the same.

voL I I I I I n 1

I I I I I I uL 1 L I i I I ! 1

^ 10' I0» 10^ GAMMA DOSE («) '

. Fig. 2. Gamma dose build-up curves for

ESR and TL in GaS04 (Tm).

Room Temperature Decay Characteristics

of ESR-TL Signals

Further evidence for the nature of

the trapping species being the same both

in the TL and ESR, has been provided by

the parallel nature of the decay patterns

of these signals for storage of the gamma

irradiated sample at room temperature.

Fig. 3 presents tne results obtained for

the case of CaS04 (Tm).

Thermal Annealing Characteristics of

ESR-TL Signals

The bleaching of the ESR signals of

235
Fig. 3. Decay of TL and ESR of gamma

irradiated CaSO^CTm) for storage

at RT.

gamma irradiated CaSO^ phosphors corres- ponding to various stages of bleaching

of the TL signal was studied after

annealing the samples at different temperatures successively. The temperatures

chosen were 400°K, 500°K, 675°E and 800°E

and samples were heated for half an hour

each at these temperatures. These

treatments successively erased the TL

signals in four stages of three peaks

each: I-III, IV-VI, VIl-IX and IX- XII

respectively. The ESR patterns were

almost identical for all the samples and

fig. 4 presents the thermal annealing

behaviour of the ESR signal for the case

'of gamma irradiated GaS04(Tm).

Fig. 4- Typical thermal annealing characteristics of ESR signals of

gamma irradiated CaSO^ powders.

The presence of isolated paramagnetic radicals like SO a, SO3 etc. in

gamma irradiated sulphate salts like

K2SO4, Na2S04, BaS04 etc almost independent of their environment in the crystal

lattice, has been verified by many

workers. Hariharan et al obtained

isotropic lines with g-values of 2.0045

and 2.01 respectively for SO5 and

anisotropic lines for SO4 and SO2 in

irradiated Na2S04 crystals at room temperature; Gromov et alA obtained axially

symmetric lines for SO3, O2 and 0 in

K2SO4; Morton et al-' observed that SO4

could be observed even upto 300°K in

irradiated K2SO4 and SO3 is the more stable radical at higher temperatures;

Spitsyn et al° detected SO4 in irradiated

SrS04 350°C; Gupta et al'

identified the complicated powder

spectrum obtained at LNT for irradiated

BaS04 ^1"*=^ radicals like SO4, SO-j, SO2,

SO2 and 0^.

The range of g-values deducible for

the various signals in the six-peak

envelope obtained for the CaS04 powder

in the present study compare well with

the range of g-values reported for many

of the radicals mentioned above. It is,

therefore, reasonable to expect that ESR

signals obtained in the present study of

gamma irradiated GaS04 are mostly due to

host lattice radicals like SO4, SO3, 0^

etc and that the stability of these

radicals has been affected by the individual RE dopants to different extents as indicated by the differences in the

intensities of these signals.

The individual indentification of the

various radicals in the complicated sixpeak ESR spectra obtained, is rather

difficult as these have been obtained for

powder samples and at a single frequency.

However a careful examination of the

spectrum and its annealing behaviour

(fig. 4) does reveal that the various

radicals are bleached effectively at

different temperatures (the ESR spectrum

does not bleach uniformly over its entire

field range). The less complicated,

nearly isotropic line (g 2.0040) seen in

the penultimate stage of the annealing

process, perhaps belongs to SO5 radical

which has been observed at comparably

high temperatures with more or less the

same g-value in sodium ajad potassium

sulfates. The line F is evidently

composed of superimposed signals and the

signal represented by the part which is

completely bleached by annealing at

400°K is probably due to 0^ having a near

isotropic g-value of about 2.012. In the

context of TL, these various radicals,

expecially SO4, 30^ and 0^ represent

radicals with trapped holes characterised

by different activation energies.

Conclusion

Prom the foregoing results and dis236
cussions, it can be concluded that hole

traps provided by the host lattice ions

having configiirations of SO^, SO^, 0^

etc. give rise to the observed TL glow

curve pattern in CabO^ and addition of

rare-earth ions seem to affect the

stability of these various traps to

different extents. Combined with our findings on the TL emission spectra it

could be said that the TL process in

CaaO^ (RE) is perhaps similar to that in

CaF2(RS) involving RS^t^^^^^^^^^^-RE^^

reactions with simultaneous trapping and

release of holes at the sxilphate sites

during irradiation and heating respectivelyAcknowledgements

I am grateful to M.V. Krishnamurthy

and W.D. Sastry or Radiochemistry Division for their help in recording the

ESR spectra. Thanks are also due to

V.M. Bapat for the help he rendered

during the course of this work.

References

1. Nambi, K.S.V, Ph.D. Thesis, Gujarat

Univ., Ahmedabad (I974j.

2. Atkins, P.W. and Symons, M.G., 'The

Structure of Inorganic Radicals

Elsvier Pub. (1967 )

3. Hariharan, N. and Sobhanadri, Mol.

Phys. 17, 507 (1969).

4. G-romov, V.V. and Morton, J.R., Can.

J. Ghem. M. 527 (1966).

5. Morton, J.R., Bishop, D.M. and

Randic, M. , J. Ghem. Phys. 1885

(1966).

6. Spitsyn, V.I., G-romov, V.V. and

Karaeva, G.G., Dokl. Akad. Nauk, 5. S.S.R., 1^, 178 (1964).

7. Gupta, N.M., Luthra, J.M. and

Shankar, J., Rad. Eff. 21, 151 (1974).

Discussion

S . I'lakra

I feel that heating the sample and

detecting the emitted light is not the

only possibility for TL evaluation.

Efforts like yours besides theoretical

importance are of practical importance

too

K.V.S. Nambi

Thank you for your kind comments.

237
NBUTEON DOSE EVALUATION USING CALCULATED NEUTRON SPECTRA

S. Makra

Central Research Institute for Physics

1525 Budapest II4. P.O.B. 49 Hungary

Measurements carried out at shielded neutron sources such as nuclear reactors and neutron generators showed the importance of

intermediate energy neutrons not recorded by most of the commonly

used monitors. Based on these measurements correction factors were

established for scintillation survey instruments, track plates,

activation detectors and other routinely used devices. Although

this simple technique has proved to be very useful, the need for a more sophisticated evaluation method was evident. With this in

mind we started with the calculation of neutron spectra transmitted

through and reflected from shielding slabs. Calculations were performed by using the MUSPALB albedo code developed in our Institute as well as with the 05R code written in Oak Ridge, USA.

Over the last four years spectra for different reactor and neutron

generator sources with H2O, polythene, concrete, beryllium,

aluminium, graphite, iron, boron loaded polythene and iron-concrete

mixture shields were calculated for thicknesses ranging from 5 cm

to 200 cm. Calculated spectra were used for personnel-, survey-,

and nuclear accident dosimetry evaluation. International comparison

measurements have shown the value of this evaluation method. For

illustration several examples are given.

(Computer code, dose, dosimetry, monitor, neutron, shielding, spectrum)

Introduction

Early measurements of the stray

neutron field carried out at shielded

neutron sources showed, that the energy

spectrum of the neutrons in such circumstances is quite wide. The leakage spectrum of shielded nuclear reactors,

radioactive neutron sources, or even 15

MeV neutron generators span from the source energy down to the eV range or even to thermal energies. Dosimeters

used for personnel monitoring, on the

other hand, in spite of the considerable

progress achieved in the past decades,

do not cover this wide energy range

in Fig. 1. In my lecture I intend to

albedo dosimeter

boron -loaded detectors

! track plate

scint. counter

gas- filled cou nter

moderated counters

I I I I I I I [ I U . thermal 10^ 1 10 10* 10^ lo" 10* 10* 10^ Energy ( eV

)

Pig. 1. Diagram showing the energy range

of some commonly used neutron

monitors.

show how evaluation techniques can be

established to take into account the

fraction of the neutron dose not recorded by a given dosimeter. This

requires the knowledge of the spectrum

in question. In the first part I shall

deal with investigations performed with

moderator devices, these bulky instruments are not used as personnel dosimeters (it's somewhat difficult to wear

a 20 lb sphere on top of your working

clothes!) but the information yielded by

them is readily applicable to dosimetry

evaluation. In the second part I shall

discuss problems concerning leakage

spectrum calculations and their applications in dosimetry evaluation.

Dose Fraction Measurements

Theoretical considerations as well

as monitoring results showed the importance of the intermediate energy neutrons not monitored by the commonly used

neutron dosimeters.

Nachtigall's measurements^ showed

that the contribution of the neutrons

in the energy range 0.5 eV - 0.1 MeV to

the total dose is quite high; sometimes

exceeding 90 /. in the vicinity of

experimental and power reactors in

Fig. 2. Another important conclusion

was that the intermediate dose fraction

varies by more than an order of

magnitude depending on several parameters, which were not established

238
during the course of these investigations .

iJ 1 i

I

0-10 tl-» 21-30 31-« *viO SV-M 61-70 71-»0 «1-«> 91-«I0 "A

Fig, Dose percentage due to 0.5 eV - 0.1 MeV neutrons averaged from

data for 135 measuring sites

(Nachtigall, 1965).

In Budapest in 1967, we commenced

with the investigation of the stray

radiation field of our experimental

reactors using a measurement technique p similar to that developed by Nachtigall:

The neutron dose rate for the whole

energy spectrum in question was monitored by rem-counters, the dose resulting from the slow and fast neutrons < being monitored by scintillation

counters. Owing to the similarity in

the responses of the slow neutron

survey and personnel monitors (boronloaded scintillators and cadmium

covered films) on the one hand, and

those responses of the fast neutron

survey and personnel monitors (proton

recoil scintillation counters and track

plates) the results were applicable for

personnel dose evaluation. Figures 3 and 4 illustrate typical monitoring

results^. Based on several measurements similar to the one shown here

calibration factors were established.

For instance the multiplication

factor of 9 - 32 was established as that applied to track plates in order

to obtain the total neutron dose for

the hall of our iVV/R-S type reactor.

The introduction of this correction

considerably improved the accirracy of our dose evaluation and at the same time emphasized the importance of the

search for dosimeters with a wider

energy range.

Fig.

%

100 r

50

mrem /h 10

0.1

aoi

point o

o — o

o

( total neutron dose O 0 0

> o

o

X

X gannnna

X " ^ X^ X

X

fast neutrons °

Slow 1 A

i neutrons

1 1 1 1 1 1 1 1 T 1 1 1 1 50 100 150 cm

3. Dose equivalent vs. height over the top shield of the WWR-S rea- ctor for neutrons in the 10"^ _ 10' eV, E<0.5 eV and E>1 MeV

energy range (denoted as "total

neutron dose", "slow neutrons",

and "fast neutrons", respectively) as well as for gamma

radiation.

0 L 6

S I t -f s i f top shield concrete iron Slit

annular

shield

s I f T

shield at biological irradiation

facility

f t

hall

Fig. 4. Percentage dose of slow, intermediate and fast neutrons, as well as gamma rays at different

sites of the shield of the

WWR-S reactor.

Average Energy Determinations

Average energy determinations of

the radiation field yield information

which is also applicable for dosimetry

evaluation. For this pixrpose several

techniques were developed. One, developed in the Lawrence Radiation

Laboratory*^ is based on the determination of the spatial distribution of the

thermalized neutrons inside a moderator.

For source energies from a few tens of

keV up to 15 MeV the shape of the distribution is a measure of the source

energy. The multisphere technique^

makes use of the variation in the

counting rate ratio of different diameter Bonner-sphere counters when irradiated with different energy neutrons.

In oiir laboratory both techniques were investigated with the aim of developing

a theory for average energy determina239
tions and for checking calculations and

measiirements . It was shown that both

techniques, owing to imavoidable instrument distortions, measure a quantity

differing from the mean energy" » 7,

Mean energy and another widely used

quantity the effective energy, are defined as follows:

Je.m (E) dE mean energy h

effective energy ^^^^=Jf^^L^^^l^

where 9 (E) represents flux density and

the d(E) weight function is the flux-todose conversion function. Both E and

^eff ii3-ve a practical significance. However measjirement techniques determine a quantity B which is defined as average energy E = J

k(E).y (E) dE

k(E).cp (E)dE

where k(E) is a weight factor, characteristic for the^instrument , the quantitymeasured but

lly used.

S or "^Qff is the one actuaA monitoring result is given in

Fig. 5 as an example showing the

relationship between these quantities.

These results not only show a good

agreement between theory and measurement but emphasize the importance of

using well-defined terms, as a discrepancy of a factor of two may occur if

instrument response is not correctly

taken into account.

E^f,E (MeV)

2.0

1.0

0.5

B bS

spheres

30 40 50 60 wt% Fe

Calculated and measured effective energies, and average

energies behind a 100 cm thick

iron-loaded concrete wall. Measured and calculated effective

energies (open circles and hatched stripes, respectively) are presented for both the Block

and Shon, and the paired spheres

technique. The horizontal range

of the hatched stripes corres- ponds to the estimated iincertainty in the fraction of the iron

aggregate (35-50 wt '/).

Although average energi

fractions obtained by measur

to be very useful in dosimet

the need for a more sophisti

tion method was evident. Wi

mind we started with the cal

neutron spectra transmitted

reflected from different shi

es and dose

ements proved

er evaluation,

cat ed evaluath this in

culation of

through and

elding slabs.

Spectrum Calculations

For the calculation of the spectrum

modifying effect of different shields we used two computer codes ; one, the

MUSPALAB code developed by Vertes^ makes use of the so called albedo formalism,

the other, the 05R5S, is a Monte Carlo

code. The original version of this code,

the 05R, was written in Oak Ridge9, and

was adapted to our institute's IGL 1905

computer, and several modifications were performed in order to reduce the running

timelOjll, Both codes caxi handle neutron

sources with different energy and angular

distributions. The shielding layers are taken as planar, calculations can be made

for one-component slabs, for mixtures and

for laminated shields. Both transmitted

and reflected neutron spectra are calculated. The energy range of the output

spectra spans from the maximum source

energy down to thermal energies.

Using the computer codes MUSPALB and

05R5S spectrum calciilations were performed

for several different reactor and monoenergetic sources and for several shielding layers. Fission, light-water moderated reactor, fast reactor escape and

monoenergetic neutrons were taken as

source, the shielding layer composition

was water, polyethylene, lucite, concrete,

aluminium, beryllium, iron, and several

mixtures of iron, concrete and boron. The

shield thickness ranged from 10 to 60 cm

in the 05R5S calculations, and from 5 upto

120 to 200 cm when using the MUSPALB code.

Some typical results are shown in

the following figures: Fig. 6 shows

fission neutrons after passing through

20 cm and 100 cm thick boron-loaded concrete; in Fig. 7 spectra of fission neu- trons are plotted after passing through

100 cm thick iron-concrete shields of

different mixing ratio-'-^,- for neutron

generator survey evaluation, the spectra

displayed in Fig. 8 were applied-'-^.

Spectrum Comparison and Evaluation

In 1972 after calculating several

hundreds of leakage spectra we commenced

the compilation and evaliiation of spectra

calculated by us or taken from the literature . The final purpose of this work

is to prepare a compendium of neutron

leakage spectra to facilitate dosimetry,

primarily nuclear accident dosimetry

240
a(ire) CONCRETi- . B

TransrrifUed Ftsscfi Scectra

&Dron coritefTl (\vt'/>'

\0 lOOlyV ) Energy

Fig. 6, Flux density vs. energy plots of

fission neutrons after passing

through 20 cm and 100 cm thick

concrete with different boron

contents (in wt X).

Fig. 7. Effect of the concrete-iron

mixing ratio on the shape of the

spectrujn and on the flux reduction of fission neutrons after

passing through a slab 100 cm thick. Parameter: Fe content in

i 1 ;

I I

10'' 1 -a Ki' \cf \& yc? io' Energy (eV

)

Fig. 8. Spectra of monoenergetic neutrons

transmitted through 60 cm concrete. The flux density of thermal

neutrons depends only slightly

on source energy.

evaluation, by making available spectra

to laboratories involved in dosimetry,

but lacking manpower and/or computers to

develop their own computation techniques.

In order to facilitate spectrum com- parison and evaluation several handling

codes were written. SPEC TRANS- 2^4, for

instance, calculates the spectra for 48

predetermined energy intervals, computes

kerma and dose-equivalent spectra as well

as dose fra-ctions and a,verage energies.

The calculated spectra are written on a magnetic tape and plotted in a variety of

different formats. Another computer code

used for spectrum hajidling is the

TRESPASS-'--'

,

Some representative results are presented in Figs. 9 and 10: Fig. 9 shows

spectra of fast neutron sources transmitted through 50 cm thick iron as measured

in the Soviet Union and calculated by us?

Fig. 10 shows fission neutrons passed

through 40 cm water slabs calculated by

the 05R5S and the MUSPAIB code^°; Fig. 11

gives results for 5 MeV monoenergetic

neutrons and a 10 cm berated Polythene

slabl7,18.

For the calculation, handling and

application for evaluation of neutron

spectra a computer code family has been

developed, vfhich is shown schematically

in Fig. 12.

241
Fig. 9. Spectra transmitted thxough 30 cm iron or steel slabs. The calculation for a fission spectrum and

pure iron (solid line) is compared with two spectra measured at

the IBR fast reactor} the "Fe-Mn" curve (dotted line) is for a

f erro-manganese steel, while the

"Fe alloy' curve (dashed line) is

for a steel containing Mn, Cr, Ni

and Co.

HI

P-K

r-,-r-r-^-,—

N, /N L

M, /N,

2 '^.4

1. I? MoV

16.9-'. 26 .7

30.0

1.02 ^'lfV 16.3%

30. 7'/.

Itf'

EHtHCTItVI

inpMS. 10.0 CH unicR fission, cosine distr.

Fig. 10. Pission neutrons after passing

through 10 cm water calculated

by the 05R5S and the MUSFALB

codes. For comparison the follo-

.' wing quantities are given: fraction of transmitted neutrons,

. mean energy, percentages of alow

and E>2.5 MeV neutrons in the

transmitted spectrum.

rNPulS SPECTRUM

CAtCULATlNO COOES

I LIBRARY j 05BSS IBtSPASS

SprcTBi*i

Data STonAOE

formot SPtCTRLM \ \ »o»c*'"u"» LIBRAffy I I prfnloull

5PECtBANS-5

FITTING CODE

0(ne data

Pig. 12. Scheme showing the computer code

family used for spectrum calculation and dosimetry evaluation.

Spectrum Applications for Dosimeter

Evaluation

Survey Results of Shielded Reactors

In the early sixties only fast and

slow neutron detectors (cadmium covered

film, slow and fast neutron scintillation counters, track plates) had been

used in our institute for reactor sur- veys and personnel monitoring. In 1966,

Bonner sphere techniques were introduced.

In order to improve the precision of the

neutron dose evaluations, calculations were performed for determining the rea- dings of the devices mentioned above.

Calculated results-'-^ for two rem counters are given in the following three figures

(Figs. 13-15)-'- 9, and their response functions are shown in Fig. 16. Results

show that, as a rule, Bonner sphere

survey results can be considered as quite

242
f50

Fig. 13^ Relative response of two rem

counters for fission neutrons

which have passed through con- crete + iron layers of different

thickness es

41(0 C!9 c

o

Q.

lO

Oj

«<

I.

25 cm ^ sphere

so fOO Fig. 14. Relative response of two rem

counters for fission neutrons

which have passed through water

layers of different thicknesses.

Fig. 15. Relative response of two rem

counters for fission neutrons

which have passed through iron

layers of different thicknesses,

0.6 0.4

0.2

\\\\

\ \

-3r^ \

\ 1 \

X)^ 10' 1 10 10^ 10* 10^ 10^ 10^ Neutron energy (eV)

Fig. 16. Relative deviations of the DNA-1 rem counter (dashed curve)

and a 10-in. Bonner sphere

(solid curve) from the ICRP

response curve.

acc\irate (there is little point in applying a correction smaller than 10%),

however for a 100 cm thick iron-shielded

reactor a 30/. over-reading occurs which

we consider to be significant.

The evaluation of a proton recoil

scintillation survey instrument measurement requires much sophistication, as the

set of graphs shown in Fig. 17 proves it.

Here, the instrument reading is plotted

against shield thickness for a lightwater reactor. Parameters are shielded

composition and detector discrimination

level. The two upper graphs show that

for iron-loaded concrete, independent of

the mixing ratio as well as the discrimination level, the relative reading is

0.4 - 0.5> i.e. an average correction

factor ^2 can be applied. This is not

true for iron shields where the detector

reading happens to be one or even two

orders of magnitude lower than the actual

dose strongly depending both on shield

thickness and discriminator setting.

Dose percentages of intermediate

energy neutrons (1 eV < E <1 MeV i.e.

energy range not monitored by t he, old1.0

the

OS

« 10 c

oa

1 -

I 1 concrete fX fe, £t -

1

concrete *30Xft. £^

- iOMtV

~ f.2MeV

1

1 1 1 1

1 1 1

^ t^MiN .

1 1 1 1 1 1 0 20 1,0 to iO fOO 120 t*0 d(cm) Fig. 17. Relative response of fast neutron

detector for various shield materials and discrimination levels.

243
fashioned slow and fast neutron survey

instilments) are illustrated in Fig. 18

determined by measurement and calculation. It should be noted that the

fairly good agreement between theory and

experiment may be misleading, for in

many cases complicated shield geometry,

scatter, or other factors impossible to

include into the calculation model may cause large discrepancies.

>too

50

a>

ino

xs 40

Fig. 18,

: Fe leV < E c -1 MeV

concrete t30%Fe

J

V1—1—1—

—1—1—1—1 ...1 I 1 20 W 60 80 -100 d (cm)

Dose fractions of intermediate

energy neutrons behind the

shields of light-water reactor

sources. Circles: measured

values J lines: calculated data.

Evaluation for a Scattered Neutron Field

—I—

I—I—I—I—I—I—I—I—I—

I—I—I—

I—1—I—I—1—I—[-

REFLECTED REACTOR SPECTRA

•••••• Mj,(o««J«f^

4; 20 cm Fe

ii:25cm Al

' I I 1 I I i__i L .J_i i I I I I I

10 10 10

ENEflCY(Evl

Fig. 19. Spectrum from a light-water re- actor after being reflected from

slabs of different materials.

The following results show an exam- ple of the application of backscattered

spectra in dosimetry evaluation for com- plex geometries. The ZR-6 critical

assembly is a light-water moderated,

enriched uraniiim fuel system, located in

a well some distance below floor level.

Neutron radiation in the reactor hall is

due mainly to scattering from walls and

other structures. The walls are of

concrete, while aluminium and iron are

the other structural materials. The

contribution to the dose of the radiation

scattered from different materials

varies from point to 'point in the hall.

Thus the dose at a given point can be

expressed as the linear combination of

the doses due to the scatter by concrete,

Al, and Fe:

D = kgDc + kpg^Fe + ^Al^Al

By using these spectra correction

factors for the nuclear emulsions and

fast neutron scintillation monitors, as well as for sulphur activation detectors

routinely used for neutron monitoring were obtained (Table 1). These results - which were proved by measurements for some selected cases - show that average

correction factors can be used with rea- sonable accuracy:

K(E > 1 MeV) = 2.1 + 0.5

for nuclear emulsion and scintillation

proton recoil detectors and

K(B> 2.5 MeV) = 8o5 + 3

for sulphur activation detectors.

Nuclear Accident Dosimeter Calibrations

where D^, Dpg and D^^ denote the respective

doses resulting from the scattering by

concrete, iron and aluminium, and kj^-s are

the relevant weight factors. Owing to the

complexity of geometry the k factors

cannot be determined. Instead, we determined the maximum possible variation

in spectral shape, in Fig. 19 (Makra,

1973).

The two preceding examples were for

complex situations where simplifications were unavoidable. Far more accurate

evaluation was applied in the problems

discussed here.

Highly sophisticated evaluation techniques can be used when the source spectrum and the irradiation geometry are

244
Table 1

Correction factors for detectors

having 1 MeV and 2.5 MeV energy thresholds, irradiated with the radiation of the

ZR-6 critical assembly, scattered from

the walls and from other structures. The

spread of the values is caused by the

spectrum changes of the assembly due to

differences in water reflector thickness.

Reflecting

Correction

(fission - factor

reactor)

material E > 1 MeV E> 2.5 MeV

concrete 1.7 - 2.2 5.6 - 7

iron 1.9 - 2.6 8.3 -11.5

aluminium 1.6 - 2.1 5.9 - 8.0

well known. This was the case when we performed calibration r\ins at the Oak

Ridge National Laboratory with the Dosar

facility^O or in Vinca near Belgrade, „^

Yugoslavia, with a heavy water assembly'^.

As an example the dose evaluation procedure for NAD dosimeters positioned on human phantoms will be discussed here.

For the Dosar irradiations the following

calculation steps were used: 1) the leakage spectmm of the facility was determined by the ORNL staff using the DOT

code ,• 2) we determined the modifying

effect of the shields, by using the

MUSPALB code. 3) The backscattering

effect of the phantom was taken into

account modelling the phantom with a water slab and determining the backscattered spectriim with the MUSPALB code

using the spectrum obtained in the previous step as input. 4) The summed

direct + reflected spectra were used as

a model spectrum for fitting to flux

values of the NJ^D activation detectors.

As an illustration, spectra for a 13 cm thick iron shield are shown in Fig. 20.

The same procedure was applied for

the evaluation of our measiirements performed at the Vinca heavy-water reactor.

In this case the reactor escape spectrum

was calculated at Chalk River using the

05R code^5, otherwise the procedure was identical with that discussed previously.

z

a.»

bJ

OiA

«>,S MeV ( \ f-((E)(IE-1 '

1 o.weV ;/ y

a3

// \

direct ,/ \i '/ \l direct reflected // \\

1 \\ 02

1 \\ ;/ 1

// 1 '/ \

f \ '1 \

1 1 1 1 1

-

0.1

10'* 10"' K)* X)^ K)"* 10"' Kf 1o' NEUTRON ENERGY (MeV)

Fig. 20. Steel filtered spectrum of the

Oak Ridge Health Physics Research Reactor (solid line) and the same as modified by the reflection of a water-filled human

phantom (dashed line).

Conclusion

Spectra of neutrons passed through

or reflected from different slabs may be

calculated and applied for dosimeter

evaluation. As the use of such spectra

considerably improves evaluation techniques the application of spectrum calculations is being continued. One of the

purposes of our work is to prepare a compendium of neutron spectra which makes

available these spectra in a readily

applicable form to scientists involved

in neutron dosimetry evaluation.

Acknowledgements

Thank are due to my co-workers,

J. Palfalvi, L. Koblinger and P. Zarand

for their contribution, as well as to

Dr. P. Vertes for the development of the

14USPALB computer code and to Dr. H. Ing

(Chalk River Nuclear Laboratories, Canada)

for the valuable discussions.

245
References Y.T. Song

1. Wachtigall, D. , Atompraxis 11 (1965)

203.

2. Nachtigall, D., Proc. Conf. Neutron

Monitoring for Radiological Protection 329 IAEA Vienna 1967-

3. Makra, S., Toth, M., KFEI Kozl. 16

(1968) 381.

4. Block, S., Shon, F.J,, Health

Physics 8 (1962) p. 533.

5. Nachtigall, D. , Rohloff, P., Jul-213

-ST report (1964)

6. Makra, S., KPKI-70-6-HP report (1970)

and lectiire No. 107, Second IRPA

congress, May 3-7 1970, Brighton,

England

7. Attix, F.H. (editor). Topics in

Radiation Dosimetry. Academic Press,

New York, London, 1972 p. 433.

8. Vertes, P., Nukleonik 12 (1969) 67.

9. Irving, D.C., Freestone. R.M., Kam,

F.B.K., ORNL-3622 (1965).

10. Lux, I., Koblinger, L. , KFKI-73-2

report (1973)-

11. Koblinger, L. , KFKI-74-47 report

(1974)

12. Makra, S., Vertes, P., Kernenergie

16 (1973) p. 378.

13. Makra, S., Palfalvi, J., Vertes, P.,

Health Phys. 26 (1974) 29-

14. Palfalvi, J., KFKI-73-57 report

(1973) . 15. Palfalvi, J., KFKI-74-48 report

(1974) . 16. Palfalvi, J., Koblinger, L. , KFKI74-63 report (1974)

17 . Makra , S .

, Palfalvi , J ., Zarand , P .

,

Proc. Conf. Neutron Monitoring for

Radiation Protection Purposes, 47,

IAEA Vienna, 1973.

18. Allen, F.J., Futterer, A., Wright,

W., Budka, A., BRL 1130 report

(1961).

19. l^lakra, S., Bekes, B., Proc. Conf.

Advances in Physical and Biological

Radiation Detectors p. 425 f IAEA,

Vienna, 1971.

20. Makra, S., Zarand, P., KFKI-71-82

report (1971).

21. Palfalvi, J.. Makra, S., KFKI-74-68

report (1974).

22. Poston, J.W., Knight, J. P.,

Whitesides, G.E., Health Phys. 26

(1974) 217.

23. Ingf H., Private communication 1973-

1) Mixed use of average and mean

energy need clarification.

2) Calculating fast neutron spectra

throxigh iron, what cross-section did you

use?

3) Direct + scattered and Direct

neutron spectra were compared. However,

direct and direct + scattered had exactly same spectrum, though scattered were

about 20X need clarification.

4) You made comment on optimum

mixing ratio in connection of your spectrum calculation. How coiild it be used?

S. Makra

1) The terms I used are defined in some of my earlier papers (e.g. 1st IRPA

Congress Lecture, Brighton, 1970) and in

condensed form in Attix 's recent Radiation Dosimetry book. Mean energy is a mean value without any weight factor;

effective energy is weighted by kerma

or dose-equivalent, effective energy is

weighted by detector response.

2) The earlier calculations Abagian

data were used, for recent calculations

the 05R library was obtained from RSIC

3) The direct and direct + reflected

spectra displayed were flux per unit lethargy

(linear scale) _vs. energy (log scale)

plots. The very similar shape in this case actually means that the low energy

neutron contribution for the upper curve

is considerably higher than for the

lower one.

4) We did not develop any code for

optimum mixing ratio determination.

However, comparison of results for

several mixing ratios can be used for a general orientation.

246
UTILIZATION OF PLASTIC SCINTILLATOR IN

THE MEASUREMENT OF UNCHARGED RADIATIONS

P.K. Sarkar and K.N. Kirthi

Health Physics Division

Bhabha Atomic Research Centre

Bonibay-400085

Uncharged radiations like neutrons and gamma rays produce scintillations in plastic scintillator through secondary charged particles.

The energy distributions of these recoil particles are related to the

energy distribution of the incident radiation. An attempt has been

made in the present work to get back the original incident spectrum

from the recoil distribution. The computer code UNFOLD designed for

the purpose makes a minimiim-variance, maximum likelihood estimate of

the incident spectrum by iterative least square technique. Neutron

spectra from different Be(a,n) source and 252 Qf spontaneous fission

have been measured. The results agree well with those published.

Plastic scintillator proves to be more useful when the incident gamma

spectrum is continuous in nature because the Compton continuum produced

in the scintillator has a well defined integral relationship with the

incident gamma spectrum. Continuous gamma spectrum in Apsara reactor

beam hole has been estimated using the technique developed.

(Apsaraj energy distribution; gamma ray; iterative; neutron;

plastic; recoil; scintillator; UNFOLD)

Introduction

Mixed radiation fields exist in many

nuclear environments of applied and basic

interest. An example of particular

importance is the incore radiation field

of a reactor, consisting, mainly of

neutrons and gamma rays. In the measurement of a radiative component of such

mixed fields the usual procedure is to

employ a certain detection system which

responds only to that particular component and discriminates against others.

Though it is well known that total discrimination against background is

impossible, the actual choice of

detection system is often based primarily

upon this very requirement. Existence of

a non-zero sensitivity to background

implies an experimental interdependence

among the components of a mixed radiation

field. Due to this complementary

relationship, an improved definition of

any given component automatically

provides more precise knowledge of the

remaining ones.

The present effort is directed

towards the development of a general

method for measuring both the continuous

gamma and neutron component of a mixed

radiation field. The technique applied

is charged particle recoil, the recoil

medium being a plastic scintillator.

Protons and electrons are the recoil

particles produced when plastic scintillator is exposed to neutrons and gamma

rays respectively.

Plastic scintillator is one of the

proton recoil detectors that can efficiently be used as a neutron spectrometer.

It has a basic advantage over the liquid

scintillators for its high detection

efficiency and convenience of handling.

Unlike anthracene or stilbene the pulse

height produced in plastic scintillator

does not depend on the direction of

neutron incidence nor it is sensitive to

thermal or mechanical shock. Kim-'- has

pointed out that if the disadvantage of

gamma response can be removed then

plastic scintillator promises to be a very

simple neutron spectrometer with high

efficiency and moderate energy resolution.

Young2 has shown that the resolution of a scintillator detector increases with the

decrease in the thickness till proton

escape from the scintillator tries to

affect resolution. Now, if proton escape

is also accounted for in estimating the

neutron spectrum a thin plastic detector

can give a high degree of resolution.

Apparently, it seems meaningless to use plastic scintillator in gamma spectrum

analysis because of its comparatively

bad resolution and mainly because it

produces a smeared rectangular distribution rather than clear photopeaks for mono energetic gammas. But when it

becomes evident that it is the Compton

recoil spectrometers that only can be

used in the precise determination of the

continuous gammas ray spectra^, the

plastic scintillator has the advantage

due to the fact that scintillations are mainly by the Compton electrons produced

247
in it due to the incident gamma radiation. being gaussian in nature.

In the recoil detection technique the

problem basically lies with the unfolding

of the incident distribution. The energyspectrum of the recoil particles gets a complicated smear in the observed pulse

height distribution due to multiple

scattering, non-linear light output and

photomultiplier statistics. Still, if

the response of the detector to monoenergetic incident radiation is known,

the incident spectrum can be estimated

by inverting the equation that relates the

incident spectrum to the observed distribution. But if straight forward

matrix inversion or iterative techniques

are employed amplification of the

fluctuations in the experimental pulse

height distribution or large oscillations

are likely to occur. Calculation of the Response Function

In view of the practical difficulty

associated with obtaining series of

monoenergetic neutron or gamma sources,

the response of the scintillator to those

radiations were calculated theoretically.

It is not practicable to use an analytic

expression for the response function,

since in general, the extremely complicated analytic expressions which exist are approximations not easily related to

practical counter configurations.

Several attempts were made to calculate

the response function in different ways.

They have been discussed elsewhere^^. In

the present case Monte Carlo technique

has been employed to calculate the

response functions.

Computer codes MECROS-N and

MECROS-G^ were developed to get the

response of the scintillator to neutrons

and gamma rays respectively. The present

calculations follow the course of each

neutron or gamma photon inside the

scintillator, collision by collision, and

calculates the energy deposited by the

charged particles produced due to

elastic scatterings and reactions. The

light pulse produced by the incident

radiation is obtained by summing up the

contributions of all the charged particles after multiplying them with proper

statistical weights and using proper

formulations for light output vs. particle energy. Biased Monte Carlo

technique i.e. Russian roulette and

splitting is adopted. The statistical

weight of the incident radiation after

each collision is multiplied with the

non-escape probability and is allowed

to make further collisions inside the

scintillator. The finite resolving

power of the spectrometer system has been

considered by making a random fluctuation

Monte Carlo technique, though it gives

the desired accuracy, does not yield an analytical expression from which the

incident spectrum can be deduced

directly. It requires an unfolding ii based on matrix con.figuration of

response function.

Unfolding the Measured Distribution

When a measuring instrument is fed

with a distribution g(s), the output

obtained becomes y(t). Thus the

function of the instrument can be looked

upon as an operator 0 and the situation

can be expressed in mathematical terms

as

fO] g(S) = y{t)

This equation can be written in

matrix notations as K.G. = Y where K is

the response matrix of n x m elements,

Y is the proton recoil distribution, and

G is the spectrum to be evaluated. An

easy solution to tais equation is

G = E"-^ Y

But this solution is not ixnique and

also it can be shown^ that G will not be

known accurately due to the statistics

associated with the observed data, what

at the most can be obtained is the

maximum likelihood estimate of 'G', based

on 'a priori' informations with error and variance minimised as far as possible. Error minimisation is carried

out by the usual least square techniques.

Variance is minimised by using the

weighting matrix and iterative techniques, resulting in a minimum variance

maximmn lilellhood estimate of the

spectrum. In order to remove spurious

fluctuations smoothing has been applied

to the observed data, using time series

and Fourier analyses.

Experiment and Results

For measuring the neutron spectrum

different thicknesses of scintillator were coupled to photomultipliers and

pulses were fed to a multichannel

analyser after a stage of conventional

amplifiers, Channel calibration was done by a ^^Co gamma source. Neutron

spectrum from different Be(a,n) sources and from spontaneous fission of 252cf

was estimated. Details of the experimental set up and results have already

been published4» 6 . Figs. 1,2,3 give

the estimated spectra of Pu-Be, Ra-Be

and 25'icf respectively. For measuring

gamma spectrum a single thickness of the

scintillator has been used. The

248
selection of the thickness has been made

by optimising resolution of the detector

and electron escape from the scintillate:

Continuous ganma background at Apsara

beam hole number 3 was measured. The

experiment was repeated with a lead

shielding of 2.5 cms thickness. The

observed and unfolded spectra are plotted in Figs. 4 and 5-

Fig. 1. Pu-Be Neutron . Spectrum.

miA FKOM * il J HANt) MOiM NO TM

LN£HGr ( Mt„

/

(THE. THO amis ^R£ NOT NORM>(LIS£.P TO £(JyAi. -(,Rt/J, A - - — PR£5£WT tVORK.

P/(TA f ROM THOMPSON et

I

Fig. 2. Ra-Be Neutron Spectrum.

Fig. 3. Californiujn-252 Spontaneous

fission neutron spectrum.

c -

Fig. 4. Observed and Unfolded Gamma

Spectrum taken with Plastic Scin

tillator at Apsara Beam Hole No.

(The Number of counts for the

unfolded spectrum is plotted in an arbitrary scale. The areas under the curves are not

normalised)

249
Pig. 5. Observed and Unfolded Gamma

spectrum taken with Plastic

scintillator at Apsara Beam Hole

No. 3 after 2.5 cms Lead shielding.

(The number of counts for the

unfolded spectrum is plotted in an arbitrary scale. The area^ under

the curves are not normalised)

Discussion

It is evident from the results shown

that both the continuous gamma spectrum

and the neutron spectrum in presence of

gamma field can be estimated by plastic

scintillator with fairly good accuracy.

In order to separate out the two com- ponents of a mixed radiation field, first

the neutron spectrum has to be estimated,

then it has to be converted to the proton

recoil distribution in the scintillator

used to measure the gamma spectrum. The

pulse height spectrum due to proton

recoil distribution has to be subtracted

from the observed pulse height spectrum.

The pulae height distribution thus

obtained can be used to unfold the gamma component

Though plastic scintillator has poor

resolution in case of discrete gamma

peaks, the high degree of Compton domi- nance makes it very useful where the

spectrum is continuous. In the case of

neutron spectrum estimation, the most

important limitation lies in the

Judicious selection of number and energy

range of thin scintillator employed to

resolve the spectrum. However, this

limitation becomes insignificant when we take into cognizance the fact that

plastic scintillator can efficiently be

used to determine both the neutron and

gamma component of a mixed field. Work

is in progress in determining the two

components sep&rately, using the method

suggested in the present paper.

Acknowledgements

The authors are thankful to Dr. A.E.

Ganguly for his constant encouragement

and valuable guidance and also to Shri S. D. Soman for his keen interest in the

work. We thank Dr. M.R. Iyer and Shri

Hari Singh for their help.

References

1. KIM, CM., A theoretical comparision of

4ii fast neutron spectrometers, UCRL9604 (I960)

2. Young, W.R., Neutron spectra from

organic scintillators, UCRL-16149

(1965).

3. Gold, R. and Olson, I.K., Analysis of

Compton continuum measurements, ANL7611

4. Sarkar, P.K.; Kirthi, Z.N. and Ganguly,

A.K., Response of plastic scintilla-.or

to neutrons, gamma-rays and charged

particles, BARC 756 (1974).

5. Burrus, W.R., Utilization of 'a priori' information in the statistical

interpretation of measured distributions, ORNL-3743 (1964).

6. Sarkar, P.K., Kirthi, K.N. and

Ganguly, A.K., A Technique of measxiring neutron spectrum. Proc . 2nd

Symposium on neutron dosimetry in

biology and medicine, Munich, Sept.

30 - Oct. 4 (1974)

Discussion

K.V.S. Nambi

Have you attempted to measure the

'skyshine' spectinim from the gamma

garden at BARC using a plastic scintillator and your unfolding technique?

P.K. Sarkar

Because of the experimental difficulties associated with such measurements

so far no attempt has been made. We have

a plan to do it in future.

H. Sanjeeviah

tor

1. Can one use a plastic scintillate measure bremsstrsiiLung spectra?

2. Bremsstrahlung radiation (EB or

IB) is generally of low intensity. So

will not the low efficiency of the

plastic scintillator hinder the measure- ment ? P.K. Sarkar

1. The continuous nature of

250
BremsBtrahlung spectra indicates that

plastic scintillator can be used to

measvire such spectra. But care should

be taken to have the response function

very precisely estimated. In fact

experimental estimation will be more

valuable than the theoretically calculated ones.

2. The efficiency factor can be

increased by increasing the thickness

(or volume) of the scintillator. In fact

provisions can be made to arrest all the

bi emsstrahlung radiations. But care

shovLLd be taken to optimise the thickness

because of light attenuation In the

scintillator.

Y. Furuta .

1. What is the lowest detectable

energy of neutrons ?

2. What data did you take from for

the relation between charged particle

energy and obtained pulse height of

charged particles ? P.K. Sarkar

1. The lowest energy which can be

discriminated against gamma backgrovind

is 1 MeV.

2. We have considered the formulation given by Lindstrom et al (Nucl.

Instr. and Methods ^8 (1972) 413)

primarily. But we also have performed

experiments at a ?an-de-Graaff

accelerator using our scintillator

to check the validity of the relationship for the present scintillatoi'

(supplied by Technical Physics Division,

BAEC )

251
NEUTRON SPECTROMETRY BY SANDWICH SURFACE BARRIER TECHNIQUE * O.P. Joneja

Bhabha Atomic Research. Centre

Tronibay, Bombay-400085

India

A neutron spectrometer using silicon surface

barrier detectors employing ^LiF as a radiating

material is developed. An incident neutron

interacts v;ith the radiating atom resulting in t\io

charged particles, which are detected by sandwich,

detector geometry and the corresponding sum pulses

from both, the detectors shall uniquely define the

incident neutron energy. This paper also presents

results obtained by Konte Carlo simulation of all

the correction factors for the detector head

employed. A new concept for resolution correction

is developed which brings dovm the lower energy

li:.iit of the detector system. The spectrometer is

employed for incore spectrum studies in case of a thermal reactor 'Kahter' and the results obtained

exhibit a good agreement with that of calculations

by GAl'I THERFiOS EXTERMINATOR Code.

(Detector; energy Ifeakage; ^Li5'; iionte

Carlo } neutron,- sandwich; spectrometry;

surface barrier) ,

Introduct ion

The study of neutron spectrum in

reactors offerSan effective tool to check

the validity of calculational methods, in

addition, the damage suffered by cons- truction material in high flux experimental and power reactors requires the

knowledge of fast neutron spectrum. The

neutron energy of interest in case of

fast and epithermal reactors is considered

to extend from 10 keV to 10 HeV and

uptil now the results from several experimental tecliniques are normalized to scan

such a vfide energy region. The present

method, however provides the spectrum

information for most of the energy region

of interest in a single shot. The

spectrometer head consists of two silicon

surface barrier detectors sandwiching a ^LiF layer. Although charged particles

produced due to °Li (n, a)T reaction

receive energy depending upon their angle

of ejection, the suiq of their kinetic

energy in principle remains constant and

is equal to energy of the incident

neutron plus Q value of the reaction.

Thus, for a continuous incident neutron

spectrum there will be one to one correspondence betv/een neutron energy and

sum,p\ilses but since the cross section

of *^Li(n, a )T reaction depends on neutron

energyj therefore spectrum unfolding from

pulse height information shall require an

efficiency correction.

Experimental Set-up

Tvjo identical silicon surface

barrier detectors each having an area

260 mm^ and a depletion depth of 500

microns, enclosing 150iigm/cm2 of ^LIF

layer in a sandv/ich geometry and housed

in a steel container forms a detecting

head. For the purpose of calibration,

each leg, comprising a detector and a

set of amplifying unit S3 is adjusted to

exhibit identical pulses for a given

energy loss in the respective detectors.

A fast coincidence along vfith a gate unit ensures detection of coincidence events

and elimination of single particle events.

The calibration; is accomplished by

tnermaliaing neutrons from an Am - a - Be

neutron source.

i'l02ite Carlo l-iethod

It can be easily visualized that a sandwich system operating in coincidence

mode shall suffer from the following

losses

1) V.'hen either one or both the particles escape from the finite

separation betv/een the detectors,

i.e., gap leakage.

2) There is no coincidence response

when both the particles hit the same detector, i.e., double res- ponse leakage.

*Tne work done at KFA-IRE, Juelich in V/est Germany

252
3) An event is also considered lost

when tiie pulse height resulting

from either detector falls below

the threshold setting, i.e., bias

leakage.

iTow, in case the failure of coincidence response due to above losses depends

upon neutron energy then spectriia unfolding without considering above effects

shall results in a distarted spectrum. In

order to evaluate all the leakages, a

i-Ionte-Carlo Code 'CQIiJCIDE' is developed

in Fortran IVl . The leakage simulation

is accomplished for an isotropic incident

neutron flux assuming that the lighter

charge particle is ejected isotropically

in the laboratory sj^stem. The output

lists all the leakages per observed

coincidence count for several neutron

energies and the results obtained for the

detector head employed are presented

in Pig. 1.

0 10 20 30 40 50 60 70 RO 90 100

Pig. 1. Leakage factprs obtained by Monte

Carlo for a °Li system (a-2.D0,

s=C.C12? cm) X-axis -n. energy

(I'leV), y-axis leakage factors/

registered count: for bias=1.5

HeV

Description of Thermal Assembly 'Kahter '

The sj)ectromet er is used for incore

spectrum studies in the case of a graphite

moderated assembly 'ilahter', at the

institute of reactor development at

Juelich in V/est G-ermany. The fuel

(U-Th)02 is fabricated in the form of

balls, each containing one gm of 235u

and 5 gms of ^'^^Ta. A uniform mixture

of coated particles and graphite com- pressed to a diameter of 5 cms forms the

core of a fuel ball, which is further

enclosea by a 5 rorn thick graphite

jacket. A cylindrical graphite structure

40 cms thick having an inner diameter

of 2.16 metres and height of 2.40 metres

with a slanting base and an additional

cylindrical passage leading to a

carrier belt forms core of the reactor.

The assembly is controlled with the

help of nine boron carbide rods. The

detector head in the present experiment

is located in an aluminium channel

situated a,t a distance of about 30 cms from the central absorber rod and about

140 cms from bottom of the core. -iesolution Correction and Comparison with

Calculations

The subject of resolution correction

in general nas been dealt by it. G-old2

and the standard expression for numerical

solution can be ^^rritten as Y = RX Y = output reactor

R = xiesponse matrix X = input

reactor

The input vector X can be determined by

matrix inversion, however this method

quite often is found to yield oscillatory

solutions and that is why one finds

nujaber of iterative schemes available in

literature but unfortunately none of

them can be recommended for a particular

measurement. It is interesting to state

that available iterative methods aim

at correcting the experimental data for

resolution vmereas in the present work

correction is attempted through cross section. In this method one has to

construct an advancing matrix from a detector response to thermal neutrons

and then transform the cross section

vector by matrix operation. The

advancing response matrix and the cross section transformation for thermal

response obtained at different power

levels is presented in Eigs. 2 and 3- The measured lethargy spectrum after all

the corrections is shown in fig. 4 along

with fission spectrum and calculated

reactor spectrum. It can be seen tnat

measured and calculated spectra agree

within +12/. over most of the energy

region of interest. The larger discrepancies belov; about 250 keV might

result from non reproducibility of the

response function and also lovfer

moderation in experimental results might

be due to the fact that during experiment detector head was not coinpletely

surrounded by fuel balls. IMso a relatively larger error in one of the

higher energy bands is expected to resijlt

from the fact that tne code employed for

calculations was good for thermal

reactor calculations and moreover tne

calculated spectra is averaged over a large volume containing the site of

experiment .

253
?lg. 3. Plot detects the actual cross section data and the resolution,

corrscted cross section data

30, _ ^ . . ,

j'';,Lg. 4. Comparison of neasnred : calculated and fission <f'CJ)/U in

Kah+er core.

Acknowledgement s

1-Jy sincere thanks are due to Dr, R. hacker for providing all the facilities

and valuable suggestions. I shall also

like to thank Dr. P. Cloth for the

discussions. I would like to thank

Dr. P.K. Iyengar for suggesting the

problem and useful discussions. hlso , I v;ould like to thank Dr. i-I.P. Navalkar

for his interest and suggestions.

- '- • References

1. Joneja, O.P., Past bpectrum litudies

with 3iie burface Barrier Sandwich

Detector KPA, Internal report IRE - 25-73.

2. Gold, R. , Jin iterative unfolding

method for response j.iatrices, iil'JL - 6984 (Dec. 1964)

254
ROLE OP HIGH RESOLUTION Ge(Li) DETECTOR IN TRACE

ELEMENT STUDY IN WATER ACTIVATED WITH THERMAL NEUTRONS

J.M. Chatterjee (Das)*, E. Peeters and M.A. Castiauz

Institut Royal des Sciences Naturelles de Belgique

Rue Vautier 31» 1040 Bruxelles, Belgium

While chemical analysis is limited in its application of

element detection, gamma-ray spectrometry plays a big role in

the nondestmictive element detection in the neutron activated

samples with large volume high resolution Ge(Li) detector.

The water samples from the volcanic region of the island

SANTORINI (Greece) have been activated with thermal neutrons,

and the gamma-rays emitted by the long-lived radioisotopes

have been detected with high resolution Ge(Li) detector. The

analyzed results show the high concentrations of alkaline and

magnetic elements if compared with that of these elements in

the normal sea water samples. The presence of some rare earth

elements has been observed as well.

(Activation; analysis; element; gamma rays; Ge(Li)

detector; neutron; nondestructive; resolution;

spectrometry; water)

Introduction

The activation analysis has its

important role in the various fields of

radio analytical chemistry. The procedure

is applied successfully to the trace

element study in the samples of biology,

metallurgy, mineralogy, medicine, water,

air (pollution study) and also for industrial process control in different

laboratories. The direct counting with

the high resolution large volume Ge(Li)

detector has made possible the rapid and

precise determination of elements of

mult i elemental samples.

The procedure has been used to study

the trace elements of the water collected

from the region of living volcano

Santorini (Nisos-Thira, Greece).

Site Choice and Sample Collection

The region was chosen for several

reasons, particularly

a) Mere sight has been enough to

realize the existence of some elements;

the pronounced rusty red colour of iron

oxide visible on the rocks of the volcano

and the green sea water extending few km

from the source show the presence of

high. concentrations of iron.

b) The information on this region

Is very scanty; only some geological

study has been report e dl.

c) The place is very near to the

residential area and considered one of

the tourists' places in Greece.

d) The local people are living on fishing in the Aegean Sea and the sea of

Crete which surround the island.

Seven places including the bays were

chosen to cover the whole rim as well as the body of the volcano (fig. 1). The

hot water sources under the huge rocks

(steno source 1 and 2), the bays flowing

to the sea (Erinia, St. Georgia, St.

Nicolas), the natural lake of the

volcano, the hot vapour coming out had

been considered the main reservoirs of

different elements. The water from these

places and the vapour condensed were collected for sampling by sucking with

plastic syringe; 2 ml of sample was poured into the sterilized quartz vials

precautions were taken not to contaminate

them during collection. The vials are then sealed in the flame.

SANTORINI (NISOSTHIRA')

Eig.l. Shows the sites for sample collection.

Present address - E.S.C. Division, Saha Institute of Nuclear Physics, Galcutta-9

255
Experimental Procedure

With thermal neutrons of estimated

flux 3 X 10-'-2n/s/cm2, the samples were irradiated in the reactor of C.E.N.

( Saclay-France) for five days along with

standards prepared from Zn, Co, Br and

Hg compounds. The standards are used

as comparator and also for checking the

neutron flux in the reactor canal. An

empty quartz vial was irradiated to check

the impurity added to the sample from the

wall of the container.

The activated samples were then

cooled down for four weeks, the reason is,

during the irradiation extremely large

amounts of 24iTa, 38ci,4-22: and o^Br are produced and these short-lived nuclides

present an initial radiation problem and

their gamma-ray spectra mask the spectra

of other trace activation products.

1 ml of the activated sample was inserted into the disc of plexiglass

(internal diameter 19-9 mm and thickness

3.7 mm). Tvjo coxial right-angled Ge(Li)

detectors - ORTEC and PHILIPS - of active

voltunes 31-4. and 64 cc respectively were

used In combination with 16 Z multichanjiel

pulse height analyser ( Intertechnique

BA 163) • The analyser has the provision

for simultaneous accumulation of four

separ3.te spectra with proper analogue-todigital converter ( Intertechnique CT 102).

The detectors were incorporated with

preamplifier and the signals were amplified by CRTBC spectroscopy amplifiers;

their resolution had been 2.2 keV for

ORTEC and 1.8 keV for Philips on 1,332

keV ga,mma-ray from 60Co.

30-35 photopeaks of energy rsmges

100-2,000 keV from each sample were detected with the time interval of

14-15 vreeks. The coujiting time was adjusted according to the coimting

statistics desired. The major isotopes

sea^rched had been of half-lives from few

days to several years.

Result s and Discussions

The elements fo\ind are Ce, Hg> Cr,

Sr, Cs, Rb, Zn, Co, Pe, Sc, Eu, Se and

Br. Br is not observed in the measurements taken 18 weeks after irradiation.

Yerv interesting observations are made

in this region. Variable concentrations

of most of the elements are observed.

Ce and Gr are not found in all the

samples, Hg content is very high (500/)

in comparison with that in the normal

sea water2, (14-20 mg/'l of Sr is foxind

in the water samples but is totally

absent in both the samples of condensed

vapour) o Extremely large concentr3.tions

of Cs and Fe are found, the large

quantity of iron is visible from the rusty

red colour of the rocks. All other

observed elements have their concentrations more than those present in the

normal sea water. The absence of Sr, Cs

and Rb in the sample taken by condensing

the hot vapoixr from the outlet of orater

inay be due to (1) some geochemical change

in the molten part of the volcano and (2)

the filtration by the various earth layers

inside the volcano. Two more elements

Eu and Se have been detected in the

sample of vapour condensed. The large

concentration of Se in this sample is

noticeable

The presence of sulphur is apparent

from the yellow layer in the orater and

from the smell of H2S in the water sample

from hot sovocce. But this element could

not be detected because of its very short

half-life (5-07 m) . However, a gradual

and careful activation analysis of sea water and marine organisms will provide

much information about the geochemical

change and pollution of this region.

Acknowl edgement s

The authors wish to express their

heartiest thanks to Prof. A. Capart,

Director of the I.R.S.N.B., Bruxelles for

his active help during the measurement

and participation in sample collection.

One of the author J.M.C. is grateful to

IAEA, Vienna for sponsoring the

fellowship for the post-doctorate

research during this period.

References

1. Wikovich, D. and Heezen, B.C.,

Submarine Geology and G-eophysics; edited

W.E. Whittard and R. Bradshaw,

Proceedings of the 17th Symposium of the

Colston Research Society held in the

University of Bristol, 1965.

2. Bowen, H.J.M. and Gibbons, D., Radioactivation Analysis; Clarendon Press,

Oxford (1963)

256
SUI-n-IIKG UP OP THE DELIBBRATIOUS OF THE

INTERInTATIOHAL SYl^IPOSIUl'u ON RADIATION PHYSICS

By A.K. GangulyDirector, Chemical Group

Bhabha Atomic Research Centre

Trombay, Bombay-400085

INDIA

At the near conclusion of this

Symposium, a very successful one at that,

thanks are due to the untiring efforts

of Professor A.l-i. Ghose and to his

wonderful band of enthusiastic workers.

Historically, a national symposium

on metrology of radio-nuclides was held

in 1966 in Trombay which finally emerged

from its deliberations as essentially a

symposiiiin on Instrumentation in Radiation

Physics. This vj-as then appropriately

renamed as National Symposiiim on Radiation Physics organised in 1970. Now, at

the end of 1974, we are witness to this

International Symposium on Radiation

Physics. Papers, presented, and deliberations in the Symposium have also been

marked by progressive enlargement of

scope and enhancement of standards. My

intention in this summing up effort is

not to restate vrhat has been stated; in

fact I find the summary of this Symposium

has already appeared as a publication of

this symposium as abstracts of papers.

Barring only a fevf all of them were presented during these 4t days. V/hat

this publication does not contain, is

free for discussion during these

scientific sessions.

In view of the above, I should like

only to re-state some of the high-lights

of the papers and discussions that

appear to me as significant. So, I hope, you will excuse me since this

talk will have some of my personal bias

built into it. I coxild not avoid this

inspite of myself.

The papers were excellently classified under broad headings of the

scientific sessions as 'Basic Interaction

Cross-Sections', 'Radiation Transport

Theory and Applications', 'Radiation

Scattering in Bulk Media', 'Radiation

Shielding' and 'Radiation Dosimetry and

Instrumentation '

There had been at the back of the

minds of most of the Indian participants,

the fact of the near completion of the

big radiation production machine, the

Variable Energy Cyclotron in this city.

Right in the beginning of the symposium,

the proceedings so\mded to me as an exercise in thinking aloud as to what of

the many good things we can do in

Radiation Physics and in Nuclear technology besides carrying out the basic

nuclear physics experiments with this

machine. Dr. Hubbell from the United

States presented to us the status of

photon cross-section data from 100 eV to

100 GeV range. Our interest at the

present moment is still towards lower

energies of this range, say from 100 HeV

to 100 eV. Workers are comfortable in

keV to a few MeV range. Radiation

Physics in this country has to take

better cognizance of the energies below

few keV and above a few HeV. The

tradition of radiation physics, which

in this country started with Sir J. G. Bose and Prof. M. N. Saha, as emphasized at this Conference, in this

ooimtry and elsewhere has to expand the

domain of energies Indicated above.

Dr. P. K. Iyengar in his talk on radiation physics and nuclear technology

eloquently emphasized the needs of R and

D efforts that can readily be imdertaken

in this country using the nuclear

reactors and the cyclotrons for the

development of material sciences. Using

radiation production machine as a tool

for Radiation Physics experiments,

research work has to come of age now in

this country in the light of the programme in technology and nuclear researches. V/ork in this line has been going

on for some time with the coming of the

fast reactor technology and the high

energy accelerators. This line of

activity is bound to take a new enlarged

dimension

Professor A.M. Ghose emphasized new techniq_ues for measureiiient of

angular scattering and his ideas about

the development of double scattered

neutron polarimeter are indications of some important developments. The Bose

Institute shows great promise in the

future developments in these directions.

Dr. P. Perey's talk on Gamma photon

production programme at ORNL appeared

particularly relevant in our context as well. It was stimulating to find re- appearance of a great interest in the

basic gamma spectrometry using sodium

iodide and development of the powerful

tecimique of spectrum unfolding. We,

in this country, have still a sustained

interest in sodium iodide crystal

spectrometry for very pragmatic reasons

257
and simultaneously we have also been

sustaining an interest in high energy

neutron (60 MeV neutron) spectrometry

using plastic scintillators. This work

is going to receive a fresh impetus since

mono-energetic neutrons of energy higher

than those available at Trombay, would be

available in Variable Energy Cyclotron.

Dr. D.V. Gopinath's presentation of

a generalised formulation of radiation

transport problems that has the sphere

to deal, in the onset, with photons,

neutral and charged particles, woiild be

a commendable attitude to maintain. In

covering the energy range, we are talking about, it V70uld be necessary that

v/e need further development in techniques

for precision measurement of cross sections in the low and high energy

ranges that have been indicated earlier.

Because in the final analysis, this is an essential input experimental data for

computational physics. A number of other

papers related to computational physics

as presented, laid very great emphasis

on the Monte Carlo techniques. Still we

do not have precision data at the low

energy end of the degraded high energy

particles of photons. Dr. D.K. Trubey,

from a very good practical angle laid

emphasis on development of shielding

standards. This is an activity which we

are yet to hatidle systematically.

Professor T. Hyodo discussed the

problems of gamma back-scattering and

techniques of measurements. It appeared

that the problems of low energy end of

the back-scattered spectrometry are still

to be handled coherently, specially when

the incident energy is comparable with

the K electron binding energy of heavy

nuclides.

Professor P.P. Kane produced an

evidence, during the discussion, indicative of the influence of the K electron

binding energy on the scattering of low

energy photons. The difficulty of dealing

with the miiltiply charged heavy ions as pointed out by Dr. S. Kukherjee is a problem in its own right. Researches on the stopping of multiply charged accelerated heavy particles produced in tbe

accelerators can be undertaken for

experimentation. Here I would like to

mention that the possible future

programme of VEC includes acceleration

of multiply charged heavy ions.

Dr. D.K. Trubey 's talk giving com- prehensive description of the ORNL

Shielding Information Centre, naturally

attracted attention for obtaining

information on the very topics on shielding enumerated in the talk.

Dr. W.S. Snyder's talk on radiation

dosimetry of human organs used for

computational purposes - the concept of

a Phantom of a Phantom and again the

computational techniques were based on the iionte Carlo methods.

S.C. Sharma presented a model based

on the experimental track structure for

computation of internal dose delivered

to an organ from an external source. On first hearing the approach developed

by Sharma and Katz, it appeared that the

model could be handled for micro dosimetric computation of internally deposited radio nuclides.

Dr. D.P. Regulla, while discussing

the versatility of luminescent dosimeters, attracted attention to a phenomenon in his experiment of TSEE.

An irradiated phosphor gave indications

of the emissions of exoelectrons of

about 300 eV. V/e are yet to understand

what these mean.

Dr. Y. Furuta emphasized the

present state of all-out development in

the field of neutron dosimptry by T.L.

Phosphors like^Li and 7Li?. The

problems of dosi.aetrj'' of high energy

neutrons in the tens of I-IeV range are

still to be resolved for health and

safety op erat i ons

V.'e have listened to an extremely

interesting lecture by Shri C. Ambasankaran , where the VEC machine was described in many of its constructional

details. It is heartening to note that

the various parts of the cyclotron, such

as the main magnet, coil, resonator tank

etc. are being fabricated indigenously.

When the machine is in operation,

towards the end of 1975, it will fulfil

the long felt need in India to carry out

studies of high energy neutrons, gamma

rays and multiply charged heavy ions.

In his talk on solar energy, a topic

apparently not directly associated with

the radiation physics. Dr. V.G-. Bhide

laid emphasis on the possibilities of

solar energy becoming a great hope for

the future energy requirements.

Dr. S. I-Iakra in his talk on

"iJeutron Dose Evaluation using calculated

Neutron Spectra ", brought up very

significantly the question of shield

optimisation. Even at this stage of

development of Codes and Techniques for

radiation transport, practical shielding

problems are still being handled on empirical or adhoc basis in great

majority of situations. Dr. G-opinath

and Dr. Trubey brought to our attention,

the existence of a code for optimisation

258
for a given sequential shield. It is

felt that it is still v/orth looking for

prescription of shields both in regard

to thicknesses of the individual layer

of materials and their sequence for a given set of shield materials.

\'le have been listening to a whole

series of excellent papers from Indian

authors and the abstracts to which I made

a mention earlier gives an account of

the present state of activitxes in radiation physics research. 'Ve missed listening to new efforts in radiation

physics based on the recent developments

of theoretical principles.

Professor L.S. Kothari dealt v/ith

the theory of neutron thermalization and

Dr. Sharma dealt with the model of a track structure and Professor G-hose

indicated some indigenous methods for

using the principles of geometrical

optics: in the development of techniques

for radiation measurements. While

explaining the mechanism of Radiation

Damage, Dr. P.K. Iyengar mentioned

development of theoretical models for

development in radiation physics. Dr. R

Ramanna, in his inaugural speech felt

that this symposium will be able to give

some indication as to where we ;,jO from

here in radiation physics. I feel that

in some later symposia we should also

invite some of those theoreticians who are also interested in seeing hjome

applications of their theory.

259
NBS-1 14A (REV. 7-73)

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1. PUBLICATION OR REPORT NO. NBS SP-4612. Gov't Accession

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4. TITLE .'\ND SUBTITLE

RADIATION PHYSICS - Proceedings of the International

Symposium on Radiation Physics, held at Bose Institute,

Calcutta, India, Nov. 30-Dec. 4, 1974

5. Publication Date January 1977

6. Performing Organization Code

7. AUTHOR(S) Proceedings Editors: A. M. Ghose, D. V. Gopinath,

J. H. Hubbell. S. C. Rov.

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Organized by: Bose Institute, Calcutta, India

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symposium, recognizing radiation physics as the thread held in common by a variety of medical, engineering and scientific disciplines, was to bring

together specialists from these disciplines to report on, exchange, and

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brought together in this symposium include new measurements, theoretical

developments, compilations and applications of basic cross section and transport data for photon, electron, neutron and heavy ion beams interacting with

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Cross sections; dosimetry; electrons; neutrons; photons, radiation physics;

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