National Bureau of Stanaaros

Library. Ml Mmin. BidsgEP 2 5 1969

r''

NSRDS-NBS 29

.

A111D1 ^67174

i tioton Cross Sections,

NBS

Attenuation Coefficients, and

NATL INST OF STANDARDS & TECH RTC. 1

_nergy Absorption Coefficients

From 10 keV to 100 GeV

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

X J ". j

T
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. Today,

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- Located at Boulder, Colorado 80302. Located at 5285 Port Royal Road. Springfield, Virginia 22151.
UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary,

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

t 4) P

Photon Cross Sections, Attenuation Coefficients,

and Energy Absorption Coefficients

From 10 keY to 100 GeV

J. H. Hubbell

Center for Radiation Research

National Bureau of Standards

Washington, D.C. 20234

NSRDS-NBS 29

Nat. Stand. Ref. Data. Ser., Nat. Bur. Stand. (U.S.), 29, 85 pages (August 1969)

CODEN: NSRDA

Issued August 1969

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. , 20402 — Price 75 cents
uu*t*u ut STANDARDS

JAN 1 2 1970

Not ACC,

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Library of Congress Catalog Card No. 73-600412
Foreword

The National Standard Reference Data System is a Government-wide effort to provide for the

technical community of the United States effective access to the quantitative data of physical

science, critically evaluated and compiled for convenience, and readily accessible through a

variety of distribution channels. The System was established in 1963 by action of the President’s

Office of Science and Technology and the Federal Council for Science and Technology.

The responsibility to administer the System was assigned to the National Bureau of Standards and an Office of Standard Reference Data was set up at the Bureau for this purpose. Since

1963, this Office has developed systematic plans for meeting high-priority needs for reliable ref- erence data. It has undertaken to coordinate and integrate existing data evaluation and compilation

activities (primarily those under sponsorship of Federal agencies) into a comprehensive program,

supplementing and expanding technical coverage when necessary, establishing and maintaining

standards for the output of the participating groups, and providing mechanisms for the dissemination of the output as required.

The System now comprises a complex of data centers and other activities, carried on in

Government agencies, academic institutions, and nongovernmental laboratories. The independent

operational status of existing critical data projects is maintained and encouraged. Data centers

that are components of the NSRDS produce compilations of critically evaluated data, critical

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functions derived from standard reference data. In addition, the centers and projects establish

criteria for evaluation and compilation of data and make recommendations on needed modifications

or extensions of experimental techniques.

Data publications of the NSRDS take a variety of physical forms, including books, pamphlets,

loose-leaf sheets and computer tapes. While most of the compilations have been issued by the

Government Printing Office, several have appeared in scientific journals. Under some circumstances, private publishing houses are regarded as appropriate primary dissemination mechanisms.

The technical scope of the NSRDS is indicated by the principal categories of data compilation projects now active or being planned: nuclear properties, atomic and molecular properties,

solid state properties, thermodynamic and transport properties, chemical kinetics, colloid and

surface properties, and mechanical properties.

An important aspect of the NSRDS is the advice and planning assistance which the National

Research Council of the National Academy of Sciences-National Academy of Engineering provides. These services are organized under an overall Review Committee which considers the

program as a whole and makes recommendations on policy, long-term planning, and international

collaboration. Advisory Panels, each concerned with a single technical area, meet regularly to examine major portions of the program, assign relative priorities, and identify specific key problems in need of further attention. For selected specific topics, the Advisory Panels sponsor subpanels which make detailed studies of users’ needs, the present state of knowledge, and existing

data resources as a basis for recommending one or more data compilation activities. This assembly

of advisory services contributes greatly to the guidance of NSRDS activities.

The NSRDS — NBS series of publications is intended primarily to include evaluated reference

data and critical reviews of long-term interest to the scientific and technical community.

A. V. Astin, Director.
Contents

Page

1. Attenuation and energy absorption coefficients 1 1.1. Introduction 1 1.2. Physical constants; units; notation 2

1.2.1. Physical constants and conversion factors 2

1.2.2. Notation and units 3

1.3. Definition and significance of narrow-beam attenuation coefficient 5

1.4. Tabulation of attenuation coefficients 9

1.5. Definition and significance of energy-absorption coefficients and related quantities 9

1.5.1. Modes of energy transfer 9

1.5.2. Conditions under which the coefficients are useful 14

1.5.3. Evaluation of the coefficients from the cross sections 15

1.6. Tabulation of energy absorption coefficients 16

2. Photon cross sections 21

2.1. Scope 21

2.2. Classification of interactions 21

2.3. Atomic photoeffect (photoelectric absorption) 24

2.4. Scattering 27

2.4.1. Compton scattering. Klein-Nishina formula 27

2.4.2. Electron binding corrections to Compton scattering. Rayleigh scattering 28

2.4.3. Radiative corrections. Double Compton effect 32

2.5. Electron-positron pair production 33

2.5.1. General discussion 33

2.5.2. Pair production in the field of the nucleus 33

2.5.3. Pair production in the field of an electron 37

2.6. Photonuclear absorption 39

3. Tabulation of cross sections for elements and compounds 40

4. References 78

IV
Photon Cross Sections, Attenuation Coefficients, and Energy Absorption

Coefficients From 10 keV to 100 GeV*

J. H. Hubbell

This report updates and extends previous NBS tabulations. Section 1 contains the information

of most immediate practical use: (a) a tabulation of the attenuation coefficient for 23 elements (iH

to 92 U) between 10 keV and 100 GeV and (b) a tabulation of the energy absorption coefficient for air, water, and 18 elements between 10 keV and 10 MeV, and for air, water, and 7 elements up to 100 MeV.

Section 2 contains detailed information on the predominant processes (photoelectric absorption,

Compton scattering and pair production) and a brief discussion of other processes which combine

to give the attenuation coefficient. Theoretical and experimental data are reviewed, and auxiliary tables and approximation formulas are given. Section 3 contains tabulations of cross sections for the predominant processes between 10 keV and 100 GeV for 23 elements and for 13 compounds and

mixtures. Key words: Attenuation coefficient; Compton scattering; cross section; energy absorption coefficient; gamma rays; pair production; photoelectric absorption; photons; x-rays.

1. Attenuation and Energy Absorption Coefficients

1.1. Introduction

The first modern systematic compilation of

photon 1 interaction cross sections and attenuation

coefficients, covering the energy range 10 keV to 100 MeV, was done by White 2 [1952] and appeared

in NBS Report 1003 (unpublished).3 Her tables were subsequently published in the Handbook of

Radiology [1955] and in the 1955 edition of Beta

and Gamma-Ray Spectroscopy [1955]. Storm, Gilbert, and Israel [1958] further extended these

tables by interpolation to include all elements from

Z= 1 to 100.

With some revisions the tables from NBS Report

1003 were published in NBS Circular 583 [1957],

and were revised in the 10—100 keV region by

McGinnies [1959] in NBS Circular 583 (Supplement). Davisson [1965] further updated these tables

using more recent theoretical estimates of atomic

photoeffect and electron-field pair production.4 The present compilation, an earlier version of

which has been presented elsewhere (Hubbell and

"Supported primarily by the NBS Office of Standard Reference Data. Support was

also received from the Defense Atomic Support Agency.

1 The terms “x-ray,” “gamma-ray,” and “photon” are used interchangeably throughout this work.

2 Referred to in her later work [1957], as White-Grodstein.

3 Earlier compilations which are partly theoretical, and which cover less extensive

or lower energy ranges, include those of Jdnsson [1927-8], Victoreen [1943-9], Woo

and Sun [1947], Davisson and Evans [1952], and G. Allen [1950-1967]. The well- known data of S. J. M. Allen [1930-1967] appearing in the Handbook of Chemistry

and Physics are experimental and have not been revised since 1933.

4 Davisson’s [1965] tables are accompanied by an extensive review article. Other

reviews include those by Latyshev [1947], Bethe and Ashkin [1953], Fano [1953], Evans [1955, 19631, Hayward [1958], Fano, Spencer, and Berger [1959], Fano,

Zerby, and Berger [1962], and Koch, MacGillavry, and Milledge [1962]. For further references to original data and to other compilations there are available extensive

bibliographies by Glocker [1950] and Stainer [1963] in the low energy region and by Toms [1965] in the high energy region.

Berger [1968]), is based on a new analysis of all available information. We were of course guided

strongly by methods and results contained in previous compilations, particularly those of White

[1952], but have also gone back to the original

experimental and theoretical literature.

We retain the format of White for the main tables

(sec. 3) but we have extended the energy range up

to 100 GeV and have taken into account new data

including the following:

(a) Photoeffect calculations by Hultberg et al. [1968], Rakavy and Ron [1965-7] and Pratt

and Schmickley [1967].

(b) Calculations of double Compton scattering and

radiative corrections to Compton scattering by

Mork [1968].

(c) Nuclear-field pair-production radiative corrections calculated by Mork and Olson [1965] and

screening effects evaluated by Sorenssen

[1965-6],

(d) Electron-field pair-production calculations by

Mork [1967] which combine Votruba’s [1948]

theory with that of Borsellino [1947] and Ghizzetti [1947], and include the radiative correction.

(e) Calculations of coherent and incoherent scat- tering by Storm and Israel [1967].

(f) Additional experimental data including, among

others, the total cross section measurements

by Barkan [1956], Wiedenbeck [1962], Barlett

and Donahue [1963, 1965], Heinrich [1966],

Hughes and Woodhouse [1966], Carter et al. [1967], McCrary, Plassman et al. [1967],

Perkin and Douglas [1967], and Knerr and

Vonach [1967],

1
In addition, we tabulate various related coefficients that can be used to compute the transfer

of energy to the medium, namely: (a) the mass

energy-absorption coefficient, (b) the mass energytransfer coefficient, and (c) the mass absorption

coefficient.5 These coefficients were obtained by

updating and extending the work of R. Berger

[1961] and Allison [1961].

In the present work we have taken 10 keV as a lower limit on the energy range considered. Tabulations which extend to lower energies include

those by Brown [1966] (Z— 1 to 100; 1 keV—10

MeV), McMaster et al. [1967] (87 elements Z=l to 94; 1 keV—1 MeV), and by Storm and Israel [1967]

(Z—l to 100; 1 keV—100 MeV). For light elements

at lower energies, Henke et al. [1967] have used

their own experimental data and those of others to provide a compilation of attenuation coefficients versus energy for the 17 elements He through Ar

over the energy range 0.030 to 6.0 keV. Additional

low-energy attenuation coefficient tabulations for use by electron microprobe analysts (the coefficients are given at characteristic x-ray emission wavelengths) include, among others, those by Birks

[1963], Heinrich [1966], Frazer [1967], and

Theisen and Vollath [1967].

1.2. Physical Constants; Units; Notation

1.2.1. Physical Constants and Conversion Factors 6 Z atomic number,

M atomic weight in gig- atom,

m electron rest-mass= 9.1091T0-28

g, me2 electron rest-mass energy= 5.11006-105 eV,

c velocity of light = 2. 997925-1010 cm s-1

.

3 For definitions of these coefficients see Secs. 1.2. and 1.5. A great variety of names

and symbols have been used for these coefficients, and readers interested in the nomenclature used by various authors should consult R. Berger [1961].

6 Note: Numerical values given here are those recommended in 1964 by the Committee on Fundamental Constants of the National Academy of Sciences — National Research Council [1964]. They are based on the atomic weight scale in which M= 12.0000 for C

12

e elementary charge^ 1.60210T0-19 Coulomb = 4.80298T0-10 cm3/2 g

1/2 s

-1 (e.s.u.), re classical electron radius = e

2 /(mc2

) = 2.81777T0-13 cm,

re

2 =7. 9398 TO-26 cm2

, crT cross section for classical Thomson scat- tering from an electron = 87ire

2 /3 = 6.6516

•10-25 cm2

, Na Avogadro constant = 6.02252 TO23 = atoms/

mole,

ol fine structure constant = 7.29720-10-3 = 1/137.0388 « 1/137,

E photon energy in eV units (e.g.: keV,

MeV or GeV),

k photon energy in units of the electron rest- mass energy (i.e., me

2

units) = £ [MeV]/

0.511006,

q momentum transfer to an atom or electron

in units of me , A. photon wavelength in Compton units

0 =l/k = 0.51 1006/F [MeV],

A (A) photon wavelength in angstroms

(1 angstrom = 10-8 cm)=l. 23981 -10~2

/ £[MeV] 7 b barn= 10-24 cm2

.

In addition to the angstrom, which is based on the centimeter, two photon wavelength units. A* and xu. are in use which are based on characteristic x-ray emission

wavelengths. The recently-introduced A*-unit (Bearden [1967]) is presently identical with the angstrom within an uncertainty of 5 ppm. i.e.:

lA* = lA±5 ppm. The tungsten Ka, emission line has been recommended by Bearden as the x-ray wavelength primary standard with the value M WKa,) =0.2090100 A*

and hence

\(teKa,) = 0.2090100.4 ±5 ppm. The x-unit (xu). used in much of the older literature and occasionally in the present

literature, was intended to be 1

0

—

3

A but has taken on a variety of values because of

errors and inconsistencies in the various wavelength standards used. If the molybde- num Ka,. emission line is taken as a reference with the value (Bearden [1967]): A(Mo Ka,) * 707.831 xu

then

1 xu= 1.002056 -10 -3 A*

\(xu) = 12.37/£(MeV).
1.2.2. Notation and Units

Symbol Name or definition Units Where used

M “narrow beam” linear attenuation coefficient cm-1 Table 1.-5; Eqs (1.—1) to (-4)

P

absorber density g cm -3 Tables 1.—, 2

m/p mass attenuation coefficient = (Ttot [b/atom] • ( Na/M) 10 -24 [(cm2 g

-1 )/(b/atom)]

cm2 g

-1 Tables 1.-4; 3.-1 to 36; Eqs (1.-5) to (-7)

mfp mean free path=l//i.. cm Eq (l.-4a) = i /(m/p) g cm'2 Fig 1.-2

tin Half-value layer= 0.69315/m, cm Eq (1. —4b) = 0.69315/ (/i/p) g cm -2 Fig 1.-2

tiiio 1/10 — value layer= 2.3026/m, cm Eq (1. —4c) = 2.3026/ (m/p) g cm -2 Fig 1.-2 AV “volume of interest” in a medium,

for photon energy transfer estimates cm3 Eq (1.-9)

Men/P mass energy-absorption coefficient, allowing for escape from the volume of interest of all secondary

photons, including bremsstrahlung, as given in definition (17) in NBS Handbook 85 (ICRU Rep. 10b)

[1964]

cm2 g

-1 Fig 1.-3; Tables 1.-7, 8, 9; Eq (1.-10)

Ma/p mass energy-transfer coefficient allowing only

for the escape of Compton-scattered, fluorescence and annihilation photons, as given in definition

(16) in NBS Handbook 85 (ICRU Rep. 10b) [1964]

cm2 g" 1 Tables 1.—7, 8

M«/p mass absorption coefficient allowing for escape of Compton scattered photons only, as defined in eq (8f—48) of Evans [1963]

cm2 g

_1 Tables 1.-7, 8, 9

fr average fraction of photon energy transferred

to the medium as a result of photoelectric

absorption

dimensionless Eq (1.-10)

fc average fraction of photon energy transferred

to the medium as a result of a Compton collision dimensionless Eqs (1 -10), (2.-13)

Table 2.-8

/« average fraction of photon energy transferred

to the medium as a result of a pair production event dimensionless Eq (1.-10)

Re electron range (here used in the

“conti nuous-slowing-down-approximation”)

g cm"2 Table 1.-6

O-tot total photon interaction cross section per atom

(defined in this paper to include only photoelectric

absorption, Compton collision, and pair production)

b/atom Eqs (1.-5), (2.-24); Fig 2.-1

Tpe total photoelectric absorption cross section per atom = Ta + T/, + • • • b/atom Sec. 2.3.: Tables 2.^1, 5, 3.-1 to 3.-23; Fig 2.-1

Mr/p Tpe [b/atom] • (Na /M) 10 -24[ (cm2 g

_1 )/( b/atom ] cm2 g

-1 Eq (1.-10)

Ta, Ti, . . . photoelectric absorption cross section per atom

for /Cshell electrons, L-shell electrons, etc. b/atom Table 2.-6; Eq (2.-1)

ratio of total photoelectric to /Cshell

photoelectric cross section (above the /f-edge) _ Ta + T/. + T\t + • •

• 5 ta 8 — 1’ where 8 is the A^-edge “jump ratio”

.

, as defined by Kirchner [1930]

T/. + Tu + • • •

dimensionless Table 2.-6 Eq (2.-2)

3
1.2.2. Notation and Units — Continued

Symbol Name or definition Units Where used

or Compton (“incoherent”) collision cross section b/electron or b/atom

Sec. 2.4.; Table 2.-8; Eq (1.-8); Fig. 2.-1

Help ere [b/atom] (N^/M) • 10“24 [(cm2 g" 1 )/(b/atom)] cm2 g

-1 Eq (1.-10)

<XAV arc as given by the Klein-Nishina formula b/electron Table 2.-8; Eqs (2.-8), (-9), (-11)

°c <Tc as given by Hasting’s empirical fit to <x£A b/electron Eq (2.-12)

crBD u c

cre for bound electrons b/electron

or b/atom

Sec. 2.4.2; Eq (2.-18); Fig. 2.-3

(jK u ccrc for a /Cshell electron b/electron Fig 2.-2

S(q,Z) incoherent scattering function dimensionless Eq (2.-18)

O-H Rayleigh (“coherent”) scattering cross section per atom

b/atom Sec. 2.4.2; eq (2.-22); Fig. 2.-4

F(q. Z) atomic form factor dimensionless Eq (2.-22)

6C criterion angle for assessing importance of Rayleigh

scattering

degrees or radians

Eq (2.-23); Fig. 2.-4

cr(“scattering,

with coherent”)

total bound-electron scattering cross section = of/"

1 + cr« b/atom Sec. 2.4.2; Tables 2.-9, 3.— 1 to -23

<1bS:o Mork correction to ac = cr (double Compton)+cr

(radiative correction)

b/electron Tables 2.-8; Eq (2.-25)

cr(“scattering,

without

coherent”)

free-electron scattering cross section, including

radiative corrections = cr

A,v + Acr^l b/electron or b/atom

Tables 2.-8. 3.-1 to -23

K total pair production cross section = k„+ Ke b/atom Sec. 2.5; Eq (2.-42)

hJp /<[b/atom] • (Na/M) • 10 -24 [(cm 2 g

_1 )/(b/atom)] cm2 g

_I Eq (1 -10)

K„ cross section for pair production in the field of an atomic nucleus

b/atom Sec. 2.5.2: Tables 2.-10. 3.-1 to -23; Eqs (2.-26), (-30), (-31)

Ke cross section for pair production in the field of the atomic electrons (“triplet” production)

b/atom Sec. 2.5.3; Tables 2.-15, 3.-1 to -23; Eqs (2.-27), (-38), (-39)

V ( Ke/Kn) dimensionless Secs. 2.5.1. 2.5.3; Table 2.-15; Eqs (2.-41) to (-43)

K®H (Born) • Kn as formulated by Bethe and Heitler in the Born

approximation

b/atom Table 2.-11; Eqs (2.-30), (-31), (-33), (-34), (-36)

-AkTMm Davies-Bethe-Maximon Coulomb correction to

/<J[ w (Born)

b/atom Table 2.-12; Eqs (2.-28), (-30), (-31)

SHFS Hartree-Fock-Slater screening corrections

to K„ b/atom Table 2.-13; Eq (2.-31)

O'ph. total photonuclear cross section = cr(y, n) +m(y, p)+ • • • b/atom or mb/atom

Sec. 2.-6; Eq (2.-44)

£« energy at which the maximum. o"0 , of the cr,^. resonance peak occurs MeV Table 2.-16; Eq (2.-44)

r width at half-max. of the peak MeV Table 2.-16; Eq (2.-44)

4
1.3. Definition and Significance of NarrowBeam Attenuation Coefficient

The most important quantity characterizing the

penetration and diffusion of gamma radiation in

extended media is the attenuation coefficient, p.. This quantity depends on the photon energy E and

on the atomic number Z of the medium, and may

be defined as the probability per unit pathlength

that a photon will interact with the medium.

Consider, as a typical situation, a slab of material

of thickness t located between a narrowly col- limated source of monoenergetic gamma ray photons

and a narrowly collimated detector, as indicated in

figure 1.—1. In a layer dx within the slab there will occur a reduction of the intensity, /, of the gamma

ray beam, due to:

(1) outright absorption, or

(2) scattering out of the beam.

The resulting fractional reduction of the beam

intensity, — dllI , is proportional to the “narrow

beam” attenuation coefficient, fx, and to the layer

thickness, dx, i.e., — dill — /x dx. (1-1)

Integrating this equation and assuming that the

beam intensity incident on the slab has the value

Io, one obtains for the intensity transmitted through

the slab the value

I(t) =/o exp j— J

/x(x)dx^- (1.-2)

For a homogeneous medium this reduces to

I{t) = h e

-'xt

. (1.-3)

For situations more complicated than the narrow- beam experiment, the attenuation is still basically

exponential but is modified by two additional factors. The first of these, sometimes called a “geometry factor,” depends essentially on the source geometry and involves, for example, the insertion

of the inverse square law in eq (1.-3) for a point

isotropic source. The other factor, often called the

“buildup factor,” takes into account secondary

photons produced in the absorber (mainly as the

result of one or more Compton scatters) which

reach the detector. The determination of such

FIGURE l.-l. Arrangement for experimental determination of

narrow-beam attenuation coefficients.

buildup factors constitutes a large part of gamma

ray transport theory.

In the narrow-beam equation (1.—3), the absorber

thickness t in which the beam intensity is reduced

by a factor e (i.e., I/Io— 1/e = 0.36788), is called

the mean-free-path. One mean-free-path (mfp) also

represents the average distance traveled by a photon

between successive interactions. Analogous quantities are the half-value layer and one-tenth-value

layer, tm and tmo, in which the intensity is re- duced by \ and respectively.7 ® These quantities can be evaluated graphically from an experimental narrow beam attenuation curve, as indicated in

figure 1.—2 for 137 Cs (£' = 0.662 MeV) gamma rays

in concrete and lead. They are related to the at- tenuation coefficient according to

1 mfp= 1/p., (l.-4a)

ii /2 = (—In i)/p= 0.69315/p, (l.-4b)

and

fi/io = (— In ro)l/x= 2.3026/p. (l.-4c)

From the above discussion it is apparent that

the attenuation coefficient fx has dimensions of an

inverse length. Hence, if t is in cm, in, ft, etc., the

corresponding values of p must be in units oi

cm-1

, in-1

, ft-1

, etc., and as such are called “linear

attenuation coefficients”. However, although

linear attenuation coefficients are convenient for

engineering application, they are proportional to the absorber density, p, which usually does not

have a unique value but depends to some extent on the physical state of the material. Therefore, it is common practice, for purposes of tabulation, to remove this density dependence and to use the

“mass attenuation coefficient” p/p which, if p is in cm-1 and p is in g/cm3

, will be in the customary

units of cm_2

/g.

FIGURE 1.—2. Semilog plot of narrow-beam attenuation of

137Cs (0.662 MeV) gamma rays in lead and concrete.

Graphical determinations ol the mean-free-path and of the 1/2- and 1/10-value layers are indicated.

7,1 It should he noted that the ICRU (see, for example. NBS Handbook 85 (1964] defines a hall-value layer (HVL) in terms of exposure rate (intensity weighted by tile ability of the radiation to produce ion pairs in air) rather than intensity. The difference between these definitions can lead to different half-value layer thicknesses if the source

is not monoenergetic.

335-734 0-69—2 5
The mass attenuation coefficient p/p is proportional to the total photon interaction cross section

per atom, <xtot ? i-e., t° the sum of the cross sections

for all the elementary scattering and absorption

process. This relation is

cm2 cm2 p . g . u tot atom

atoms

A g-atom

M g

g-atom

O’tot b

atom

NaIM-10-24

, (1.-5)

where Na is Avogadro’s number (6.02252 TO23 atoms/g-atom) and M is the atomic weight of the

absorber material. Table 1.— 1 lists values of

{Na/M)' 10~24 for a number of elements, in addition

to typical values for p, and similar information is given in table 1.-2 for some mixtures. The cross

section per atom, o-t0o should be used in prefer- ence to pip as a basis for interpolation vs. Z be- cause of the dependence of pip on the atomic

weight, M. Not only does M vary irregularly from

element to element, but values of M can differ

from those given in table 1.—1 depending on the

isotopic composition of a given sample. The effects

of isotopic variation on crtot (excluding photonuclear interactions) are negligible in comparison

with effects on p/p.

Table l.-l. Values of the atomic weight M, the factor (NJM)

X 10 ~24 for converting attenuation data from b/atom to cm2g~1

, and typical densities p for converting from cm2g~ l to cm_1

.

Element

M*

atomic wt. X ©

1 rfk * *

z Symbol

cm2 /

b g/g — atom g / atom g/cm3

1 H 1.00797 0.5975 0.00008988 g, (H2) 2 He 4.0026 .1505 .0001785 g

3 Li 6.939 .08679 .534 4 Be 9.0122 .06683 1.85

5 B 10.811 .05571 2.535

6 C 12.01115 .05014 2.25 (graphite)****

7 N 14.0067 .04300 .001250 g, (N,) 8 O 15.9994 .03764 .001429 g, (02 ) 9 F 18.9984 .03170 .001696 g. (F2 ) 10 Ne 20.183 .02984 .0008999 g

11 Na 22.9898 .02620 .971 12 Mg 24.312 .02477 1.74

13 A1 26.9815 .02232 2.70

14 Si 28.086 .02144 2.42

15 P 30.9738 .01944 CO 1 LO ^0

16 S 32.064 .01878 1.96-2.07

17 Cl 35.453 .01699 .003214 g, (Cla ) 18 Ar 39.948 .01508 .001784 g

19 K 39.102 .01540 .87 20 Ca 40.08 .01503 1.55

Table l.-l. Values of the atomic weight M, the factor (NA/M)

X 10~24 for converting attenuation data from b/atom to cm2g~1

, and typical densities p for converting from cm2g~ 1 to cm-1 .—

Continued

Element atomic wt. Na—— x io~24 ** M

P***

Z Symbol g/g- atom cm2 /

b g / atom g/cm3

21 Sc 44.956 .01340 3.02 22 Ti 47.90 .01257 4.5 23 V 50.942 .01182 5.87 24 Cr 51.996 .01158 7.14 25 Mn 54.9380 .01096 7.3

26 Fe 55.847 .01078 7.86 27 Co 58.9332 .01022 8.71 28 Ni 58.71 .01026 8.8 29 Cu 63.54 .009478 8.93 30 Zn 65.37 .009213 6.92

31 Ga 69.72 .008638 5.93 32 Ge 72.59 .008297 5.46 33 As 74.9216 .008038 5.73 34 Se 78.96 .007627 4.82 35 Br 79.909 .007537 3.12 1

36 Kr 83.80 .007187 .003743 g 37 Rb 85.47 .007046 1.53 38 Sr 87.62 .006873 2.6 39 Y 88.905 .006774 3.8 40 Zr 91.22 .006602 6.44

41 Nb 92.906 .006482 8.4 42 Mo 95.94 .006277 9.01 43 Tc (99) (.006083) [11.50] 44 Ru 101.07 .005959 12.1 45 Rh 102.905 .005853 12.44

46 Pd 106.4 .005660 12.25 47 Ag 107.870 .005583 10.49 48 Cd 112.40 .005358 8.65 49 In 114.82 .005245 7.43 50 Sn 118.69 .005074 5.75-7.29

51 Sb 121.75 .004947 6.62 52 Te 127.60 .004720 6.25 53 I 126.9044 .004746 4.94 54 Xe 131.30 .004587 .005896 g 55 Cs 132.905 .004531 1.873

56 Ba 137.34 .004385 3.5 57 La 138.91 .004336 6.15 58 Ce 140.12 .004298 6.90 59 Pr 140.907 .004274 6.48 60 Nd 144.24 .004175 7.00

61 Pm (145) (.004153) [7 22] ******

62 Sm 150.35 .004006 7.7 — 7.8 63 Eu 151.96 .003963 [5.259]

64 Gd 157.25 .003830 [7.948] 65 Tb 158.924 .003790 [8.272]

66 Dy 162.50 0.003706 [8.536] 67 Ho 164.930 .003652 [8.803]

68 Er 167.26 .003601 [g 05J J ***** 69 Tm 168.934 .003565 [9.332]

70 Yb 173.04 .003480 [6.977]

71 Lu 174.97 .003442 [9.872] 72 Hf 178.49 .003374 13.3 73 Ta 180.948 .003328 17.1 74 W 183.85 .003276 19.3 75 Re 186.2 .003234 20.53

6
Table l.-l. Values of the atomic weight M, the factor (N A/M) X 10 ~ 2i for converting attenuation data from b/atom to cm2g~ l

, and typical densities p for converting from cm2g~ l to cm~'.—

Continued

Element

M,*

atomic wt. —Na x 10-24 ** M

Z Sym- cm 2 /

b

bol gig- atom g / atom g/cm 3

76 Os 190.2 .003166 22.8 77 Ir 192.2 .003133 22.42-22.8

78 Pt 195.09 .003087 21.4 79 Au 196.967 .003058 19.3 80 Hg 200.59 .003002 13.55 1

81 T1 204.37 .002947 11.86 82 Pb 207.19 .002907 11.34 83 Bi 208.980 .002882 9.78 84 Po (210) (.002868) [9.32] 85 At (210) (.002868)

86 Rn (222) (.002713) .00996 g

87 Fr (223) (.002701)

88 Ra (226) (.002665) 5(?) 89 Ac (227) (.002653) [10.07] 90 Th 232.038 .002595 11.00

91 Pa (231) (.002607) [15.37] 92 U 238.03 .002530 18.7 93 Np (237) (.002541) [19.36] 94 Pu (242) (.002489) [19.84] 95 Am (243) (.002478) [11.7]

96 Cm (247) (.002438) [~ 7] 97 Bk (249) (.002419) 98 Cf (251) (.002399) 99 Es (254) (.002371)

100 Fm (253) (.002380)

Table 1.-2. Conversion factors and densities, similar to those

in table l.-l , for a few compounds and mixtures.

Substance Conversion

factor P

cm2 / b g / molecule glcm3 H2 0

SiO-2 Nal

Air (20 °C, 76 cm Hg)

Concrete

0.03344

.01002 .004019

1.00 1, 0.917 (ice) 2.32 3.667 0.001205 g

2. 2-2.

0.8 N H2SO4 soln Bone

1 .049 1 1. 7-2.0

Muscle ~1

Polystyrene, (CsHsln

Polyethylene, (CH2 ) n Polymethyl methacrylate

(Lucite), (C5 H802 )h Bakelite (typical),

1.05-1.07 0 92

1.19

1.20-1.70 Pyrex glass (Corning No. 7740) 2.23

for energies above 100 MeV where screening of

the nuclear charge by the atomic electrons becomes

important. Experimental evidence for such irregularities is still inconclusive for photon energies

between 10 keV and 100 MeV.

If the absorber is a chemical compound or a mixture, its mass attenuation coefficient pip can be

approximately evaluated from the coefficients pilpi

for the constituent elements according to the

weighted average

‘Atomic weights are those recommended in 1961 by the International Union of Pure

and Applied Chemistry, based on M = 12.0000 for C 12 (Weast and Selby [1966-1967]). These values are based on average isotopic abundances and ignore natural and artificial variations. In practice, for example, M can vary from 6.01513 for pure 3 Li6 to 7.01601 for pure 3 Li 7

, with a corresponding variation in the conversion factor from

0.1001 to 0.08584. **Na = Avogadro’s number = 6.02252 X 1023 atoms/g-atom, C

12 scale (National Academy of Sciences — National Research Council Committee on Fundamental

Constants [1964]). “‘Densities are for common solids, except as denoted liquid (!) or gas (g), at 20 C, from the compilation by Trent, Stone, and Lindsay [1963] and in square brackets [

] from the Handbook of Chemistry and Physics (Hammond [1966-1967]). Gas densities are at S.T.P.: 0 °C, 76 cm Hg. ““Graphite theoretical density, based on x-ray diffraction data. Commercial-grade

pile graphite, according to Loch [1960], has a density range of 1.5-1. 9 g/cm3

. ‘““Density values for erbium vary in the literature from 4.77 as listed by Trent,

Stone, and Lindsay [1963] to the values 9.05 and 9.16 given in the Handbook of Chemistry and Physics (Hammond [1966-1967]). ****“The density of Pm147 as measured by Wheelwright [1969] is 7.22 g/cm -3

. Rau and Fano [1968] have examined the pos- t sible effect of irregularities in atomic shell struc- ture on interpolation of atomic cross sections with

respect to Z. Their results suggest that irregularities in the cross sections are most likely at the noble

gases: He, Ne, Ar, Kr, Xe, and Rn, and at the noble

metals (filling of the d-subshells): Cu, Pd and Au.

At low energies (

10 keV) where the outer atomic

electrons can play a significant role Manson and

Cooper [1968] predict such irregularities in the

photoeffect (see sec. 2.3) and Storm and Israel

[1967] predict similar effects for Compton scatter- ing (see fig. 2.-3, sec. 2.4.2.). Also Sorenssen

[1965, 1966] predicts irregularities in the nuclearfield pair production cross section (see sec. 2.5.2)

pip ~ 2 Wipilpi , (1.-6)

i

where Wi is the proportion by weight of the ith

constituent. For example, for water (H2 O:

Mh = 1.00797; M«= 15.9994),

P

P

(H2 0)

2 • 1.00797 pi

18.0153 p

(H)

15- 9994

tt (0) , 18.0153 p = 0.1119 — (H) + 0.8881 — (O). (1.-7)

P P

Values of u>i for some additional compounds and

mixtures are given in table 1.—3. The limitations of the “mixture rule” in eq (1.-6) are that it ignores changes in the atomic wave-function resulting from changes in the molecular, chemical or crystalline environment of an atom. Above

10 keV errors from this approximation are expected

to be less than a few percent (except in the fine- structure regions just above absorption edges which

are most sensitive to such changes), but at very low

energies (10-100 eV) errors of as much as a factor

of two can occur. A survey of present knowledge of

limitations of the mixture rule is given by Deslattes [1969].

7
Table

1.-3.

F

ractions-by-weight

,

Wj,

of

elements

in

some

mixtures

and

compounds.

These

values

were

used

for

deriving

tables

3.-24

to

3.-36

from

tables

3.-1

to

3.-23

according

to

eq

(1.-6).

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s- CD

CTJ 0-1 "5b

« O

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<u „ A c

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a. JTu

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o i_5 Sacu

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8
1.4. Tabulation of Attenuation Coefficients

Table 1.-4 contains mass attenuation coefficients,

fjilp [cm2 /g], obtained by inserting in eq (1.-5)

values of Na/M • 10-24 [(cm2 g

-1 )/(b/atom)j from

table l.-l and values of crtot combined from individual cross sections quantitatively discussed in section 2. Specifically, we have used for crtot the sum

O’tot ~ Tpe “f CTc H” K (l._8)

of the photoelectric absorption (rpe), Compton col- lision (crc) and pair production (k) cross sections per

atom. For reasons discussed in section 2.4.2. the

Rayleigh scattering cross section, o^, is omitted

from the sum in eq (1.-8) in table 1.-4. Hence, our

resulting values of p/p correspond to the columns

“total, without coherent (scattering)” of WhiteGrodstein [1957] and Davisson [1965].

Values of the attenuation coefficient including

coherent scattering and the effect of electron binding on incoherent scattering are given in the tables

in section 3. The relative importance of these effects

is indicated in table 2.-15. The photonuclear effect

has been omitted from the tables in section 3 but

could be included using information in section 2.6. Values of pip extrapolated to the absorption edges can be found in the tables in section 3. For convenience, we have reproduced in table

1.—5 the Hungerford [1960] compilation of linear

attenuation coefficients, p [cm-1 ], at 1, 3, and 6

MeV for a number of common materials associated

with shielding. With the exception of air, these

values have not been revised, but agreement with

table 1.-4 is within 1 to 2 percent.

Estimated uncertainties:

Due to gaps in available experimental data, and

the various approximations and ranges of applicability of different theories, the accuracy of the

pip entries in table 1.-4 is not the same for all values of E and Z. In the region dominated by the

Compton effect, we estimate the uncertainty to be about 1 percent. Estimates of uncertainties for

low-, medium- and high-Z materials are as follows:

(1)

Low-Z materials:

For elements hydrogen through oxygen this 1 percent uncertainty estimate extends from 100

MeV down to about 30 keV. Below 30 keV uncertainties of as much as 5 to 10 percent may be

present because of (a) poor knowledge of the photoeffect for low Z’s, (b) corrections to experiments for

high-Z impurities and (c) departures of the Compton

cross section from Klein-Nishina theory. Above

100 MeV the contribution of the triplet cross section

(see sec. 2.5.3) is increasingly important and strongly

affected by screening. The theory of the triplet cross section has, except for hydrogen (Wheeler and

Lamb [1939]) and for results for He by Knasel[1968],

so far only been worked out with the Thomas-Fermi

model of the atom. Uncertainties in pip from this source may be 5-10 percent.

(2) Medium-Z materials:

For elements sodium through copper uncertainties of 1 to 2 percent are present at low energies (10 keV to 1 MeV) because of uncertain partitioning of experimental totals into photoeffect

and scattering totals. At medium energies (1 to 100 MeV) uncertainties of 2 to 3 percent are present because of uncertainties in the pair production cross section, particularly in the 10 to 30

MeV photonuclear giant resonance region. Above

100 MeV the pair production in the field of both

nucleus and electrons is better-known theoretically than at lower Z. Uncertainties in pip in

this region are estimated to be 1 to 2 percent.

(3) High-Z materials:

For elements molybdenum through uranium the

uncertainties at low energies (10 keV to 1 MeV)

range from 1 to 2 percent far from an absorption edge to 5 to 10 percent in the vicinity of an

edge. In the range 1 to 100 MeV uncertainties

from pair production estimates are 2 to 3 percent and above 100 MeV 1 to 2 percent.

The high-energy data from 100 MeV to 100

GeV in this report are based completely on theory.

As shown in figure 1.— 3, they are in general agreement with available experimental data up to 13.5 GeV.

1.5. Definition and Significance of EnergyAbsorption Coefficients and Related

Quantities

1.5.1. Modes of Energy Transfer

The effects of gamma rays on irradiated media

are largely indirect, i.e., they occur via electrons

(or positrons) which are set in motion as a result

of gamma ray interactions with matter, and then

dissipate their energy as they are brought to

rest. The relation between electron (or positron)

energy deposition in a medium and the various

physical, chemical, and biological effects is complicated and, in most cases, not well understood.

However, it is commonly assumed that the amount

of energy absorbed per unit mass of the medium

(absorbed dose) is a significant parameter which

provides a basis for discussing radiation effects.

The transfer of energy from photons to electrons, and vice versa, takes place in a complex

chain of events with feedbacks as indicated in the

flow diagram in figure 1.-4. 8 Following this flow

diagram, a complete treatment of an energy deposition problem should take into account all indicated energy transfer routes leading to electron

collision losses and associated typical effects

such as are listed in the bottom triangle. 9

8 Although the diagram in fig. 1.-4 treats electrons and positrons alike, there are

actually small differences in the rates by which they lose energy (see Nelms [1956, 1958] and Berger and Seltzer [1964]).

!l Additional energy transfer routes, not shown in fig. 1.-4, occur in the case of of nuclear absorption. The neutrons, charged particles and gamma rays resulting from such an event will, in turn, either directly or indirectly transfer additional kinetic energy to electrons. These additional routes were disregarded by R. Berger [1961], Allison [1961] and in the present work.

9
Table 1.-4. Values of the mass attenuation coefficient p-lp [cm2 /g\, excluding Rayleigh (coherent) scattering, the effect of binding on Compton scattering, and the photonuclear effect, for a number of elements. That is, values here are (rpe + crc + k„ + Ke ) b/atom -(NffM) • 10_24 ‘[(cm2 g

-I )/(b/atom)] using values of Tpe, err, k„ and kc discussed in section 2 and tabulated in section 3. For coefficients extrapolated to absorption-edges, see sec. 3 tables.

PHOTON

ENERGY

HYDROGEN

Z= 1

BERYLLIUM

Z = 4 BORON

Z = 5 CARBON

Z = 6 NITROGENZ = 7 OXYGENZ= 8 SODIUM

Z= 11 MAGNESIUMZ= 12

Mev

1.00-02 3.85-01 5.36-01 1.09+00

cm2 lg

2.17+00 3.57+00 5.58 + 00 1.51 + 01 2.03+01

1.50-02 3.76-01 2.68-01 4.18-01 7.22-01 1.09+00 1.62+00 4.37+00 5.98+00

2.00-02 3.69-01 2.06-01 2.66-01 3.88-01 5.41-01 7.54-01 1.88+00 2.56+00

3.00-02 3.57-01 1.71-01 1.92-01 2.30-01 2.76-01 3.35-01 6.39-01 8.39-01

4.00-02 3.46-01 1.59-01 1.71-01 1.93-01 2.12-01 2.36-01 3.55-01 4.37-01

5.00-02 3.35-01 1.52-01 1.61-01 1.79-01 1.87-01 1.99-01 2.54-01 2.98-01

6.00-02 3.26-01 1.47-01 1.55-01 1.70-01 1.74-01 1.81-01 2.09-01 2.36-01

8.00-02 3.09-01 1.39-01 1.45-01 1.58-01 1.60-01 1.62-01 1.70-01 1.83-01

1.00-01 2.94-01 1.32-01 1.38-01 1.50-01 1.50-01 1.52-01 1.52-01 1.61-01

1.50-01 2.65-01 1.19-01 1.24-01 1.34-01 1.34-01 1.34-01 1.31-01 1.36-01

2.00-01 2.43-01 1.09-01 1.13-01 1.23-01 1.23-01 1.23-01 1.18-01 1.22-01

3.00-01 2.11-01 9.45-02 9.85-02 1.07-01 1.06-01 1.07-01 1.02-01 1.06-01

4.00-01 1.89-01 8.47-02 8.83-02 9.55-02 9.54-02 9.54-02 9.14-02 9.44 - 02 5.00-01 1.73-01 7.73-02 8.06-02 8.72-02 8.71-02 8.71-02 8.34 - 02 8.61-02

6.00-01 1.60-01 7.15-02 7.45-02 8.07-02 8.05-02 8.06-02 7.72-02 7.96-02

8.00-01 1.40-01 6.29-02 6.55-02 7.09-02 7.08-02 7.08-02 6.78-02 6.99-02

1.00 + 00 1.26-01 5.65-02 5.89-02 6.37-02 6.36-02 6.37-02 6.09-02 6.29-02

1 .50 + 00 1.03-01 4.60-02 4.79-02 5.19-02 5.18-02 5.18-02 4.97-02 5.12-02

2.00 + 00 8.75-02 3.94-02 4.11-02 4.45-02 4.45-02 4.46-02 4.28-02 4.42 - 02

3.00 + 00 6.91-02 3.14-02 3.28-02 3.57-02 3.58-02 3.60-02 3.49-02 3.61-02

4.00 + 00 5.81-02 2.66-02 2.80-02 3.05-02 3.07-02 3.10-02 3.04-02 3.16-02

5.00 + 00 5.05-02 2.35-02 2.48-02 2.71-02 2.74-02 2.78-02 2.76-02 2.87-02

6.00 + 00 4.50-02 2.12-02 2.25-02 2.47-02 2.51-02 2.55-02 2.56-02 2.68-02

8.00 + 00 3.75-02 1.82-02 1.95-02 2.16-02 2.21-02 2.26-02 2.32 - 02 2.44-02

1.00 + 01 3.25-02 1.63-02 1.75-02 1.96-02 2.02-02 2.09-02 2.18-02 2.31-02

1.50 + 01 2.54-02 1.36-02 1.49-02 1.70-02 1.78-02 1.86-02 2.02-02 2.16-02

2.00 + 01 2.15-02 1.22-02 1.37-02 1.58-02 1.67-02 1.77-02 1.96-02 2.12-02

3.00 + 01 1.74-02 1.10-02 1.25-02 1.47-02 1.58-02 1.70-02 1.96-02 2.13-02

4.00 + 01 1.54-02 1.04-02 1.21-02 1.44-02 1.56-02 1.69-02 1.99-02 2.17-02

5.00 + 01 1.41-02 1.02-02 1.19-02 1.42-02 1.56-02 1.70-02 2.02-02 2.22-02

6.00 + 01 1.33-02 1.00-02 1.18-02 1.43-02 1.57-02 1.72-02 2.06-02 2.27-02

8.00 + 01 1.24-02 9.91-03 1.18-02 1.44-02 1.60-02 1.75-02 2.13-02 2.35-02

1.00 + 02 1.19-02 9.92-03 1.19-02 1.46-02 1.63-02 1.79-02 2.18-02 2.41-02

1.50 + 02 1.13-02 1.00-02 1.22-02 1.50-02 1.68-02 1.86-02 2.28-02 2.53-02

2.00 + 02 1.12-02 1.02-02 1.24-02 1.53-02 1.72-02 1.91-02 2.35-02 2.60-02

3.00 + 02 1.11-02 1.04-02 1.28-02 1.59-02 1.78-02 1.98-02 2.44-02 2.70-02

4.00 + 02 1.12-02 1.06-02 1.30-02 1.62-02 1.82-02 2.02-02 2.49-02 2.76-02

5.00 + 02 1.13-02 1.08-02 1.32-02 1.64-02 1.85-02 2.05-02 2.52-02 2.80-02

6.00 + 02 1.13-02 1.09-02 1.34-02 1.66-02 1.87-02 2.07-02 2.55-02 2.83-02

8.00 + 02 1.15-02 1.11-02 1.36-02 1.69-02 1.90-02 2.10-02 2.59-02 2.87-02

1.00 + 03 1.16-02 1.12-02 1.37-02 1.71 -02 1.92-02 2.12-02 2.61-02 2.90-02

1.50 + 03 1.17-02 1.14-02 1.40-02 1.73-02 1.95-02 2.16-02 2.65-02 2.93-02

2.00 + 03 1.18-02 1.15-02 1.41-02 1.75-02 1.96-02 2.18-02 2.67-02 2.% -02

3.00 + 03 1.20-02 1.16-02 1.43-02 1.77-02 1.99-02 2.20-02 2.69-02 2.98-02

4.00 + 03 1.20-02 1.17-02 1 .44 - 02 1.78-02 2.00-02 2.21-02 2.70-02 3.00-02

5.00 + 03 1.21 -02 1.18-02 1.44-02 1.79-02 2.00-02 2.22-02 2.71-02 3.01-02

6.00-03 1.21-02 1.18-02 1.45-02 1.79-02 2.01-02 2.22-02 2.72- 02 3.02-02

8.00 + 03 1.22-02 1.19-02 1.45-02 1.80-02 2.02-02 2.23-02 2.72-02 3.02-02

1.00 + 04 1.22-02 1.19-02 1.46-02 1.80-02 2.02-02 2.23-02 2.73-02 3.03-02

1.50 + 04 1.22-02 1.19-02 1.46-02 1.81-02 2.03-02 2.24-02 2.74-02 3.03-02

2.00 + 04 1.23-02 1.20-02 1.47-02 1.81-02 2.03-02 2.24-02 2.74-02 3.04-02

3.00 + 04 1.23-02 1.20-02 1.47-02 1.82-02 2.03-02 2.25-02 2.74-02 3.04-02

4.00 + 04 1.23-02 1.20-02 1.47-02 1.82-02 2.03-02 2.25-02 2.75-02 3.05-02

5.00 + 04 1.23-02 1.20-02 1.47-02 1.82-02 2.04-02 2.25-02 2.75-02 3.05-02

6.00 + 04 1.23-02 1.20-02 1.47-02 1.82-02 2.01-02 2.25-02 2.75-02 3.05-02

8.00 + 04 1.23-02 1.20-02 1.47-02 1.82-02 2.04-02 2.25-02 2.75-02 3.05-02

1.00 + 05 1.23-02 1.20-02 1.47-02 1.82-02 2.04-02 2.25-02 2.75-02 3.05-02

10
Table 1.-4. (Continued)

PHOTON

ENERGY

ALUMINUM

Z= 13 SILICON

Z = 14

PHOSPHORUS

Z =15

SULFUR

Z= 16 ARGON

Z= 18 POTASSIUM

Z=19

CALCIUM

Z = 20 IRON

Z = 26

Mev cm-lg

1.00-02

1.50-02

2.00-02

3.00-02

2.58 + 01

7.66 + 00

3.24 + 00

1.03 + 00

3.36 + 01 9.97 + 00

4.19 + 00 1.31+00

4.02 + 01

1.20 + 01 5.10 + 00

1.55 + 00

5.03 + 01

1.52 + 01 6.42 + 00

1.94 + 00

6.38+01

1.95+01

8.27+00

2.48+00

8.01 + 01 2.46+01

1.05+01

3.14+00

9.56+01

2.96+01

1.26+01

3.82+00

1.72 + 02 5.57+01

2.51 + 01 7.88+00

4.00-

02

5.00-

02 6.00-02

8.00-02

5.14-01

3.34-01

2.55-01

1.89-01

6.35-01

3.96-01

2.92-01

2.07-01

7.31-01

4.44-01

3.18-01

2.15-01

8.91-01

5.27-01

3.67-01

2.38-01

1.11 + 00 6.30-01

4.20-01

2.52-01

1.39+00

7.77-01

5.12-01

2.96-01

1.67+00

9.25-01

5.95-01

3.34-01

3.46+00

1.84+ 00 1.13+00

5.50-01

1.00-01

1.50-01

2.00-01

3.00-01

1.62-01

1.34-01

1.20-01

1.03-01

1.73-01

1.40-01

1.25-01

1.07-01

1.75-01

1.38-01

1.22-01

1.04-01

1.89-01

1.45-01

1.27-01

1.08-01

1.89-01

1.36-01

1.17-01

9.79-02

2.16-01

1.50-01

1.28-01

1.06-01

2.37-01

1.59-01

1.33-01

1.09-01

3.42-01

1.84-01

1.39-01

1.07-01

4.00-

01

5.00-

01 6.00-01

8.00-01

9.22-02

8.41-02

7.77-02

6.83-02

9.54-02

8.70-02

8.05-

02

7.06-

02

9.28-02

8.46-02

7.82-02

6.86-02

9.58-02

8.72-02

8.06-02

7.08-02

8.68-02

7.90-02

7.29-02

6.40-02

9.38-02

8.52-02

7.87-02

6.90-02

9.66-02

8.78-02

8.09-

02

7.09-

02

9.21-02

8.29-02

7.62-02

6.65-02

1.00 + 00

1.50 + 00

2.00 + 00

3.00 + 00

6.14-02

5.00-02

4.32-02

3.54-02

6.35-02

5.18-02

4.48-02

3.68-02

6.17-02

5.03-02

4.36 - 02 3.59-02

6.36-02

5.19-02

4.49-02

3.71-02

5.75-02

4.69-02

4.07-02

3.38-02

6.20-02

5.06-02

4.39-02

3.66-02

6.37-02

5.20-02

4.52-02

3.78-02

5.96-02

4.87-02

4.25-02

3.62-02

4.00 + 00

5.00 + 00

6.00 + 00

8.00 + 00

3.11-02

2.84-02

2.66-02

2.44 - 02

3.24-02

2.97-02

2.79-02

2.57-02

3.17-02

2.92-02

2.75-02

2.55 - 02

3.29-02

3.04-02

2.87-02

2.68-02

3.02-02

2.80-02

2.67-02

2.51-02

3.28-02

3.06-02

2.91-02

2.76-02

3.40-02

3.17-02

3.03-02

2.89-02

3.31-02

3.14-02

3.05-02

2.98-02

1.00 + 01 1.50 + 01 2.00 + 01 3.00 + 01

2.31-02

2.19-02

2.16-02

2.19-02

2.46-02

2.34-02

2.33-02

2.38-02

2.45-02

2.36-02

2.35-02

2.42-02

2.58-02

2.51-

02

2.52-

02 2.61-02

2.44-02

2.41-02

2.44-02

2.55-02

2.70-02

2.68-02

2.73-02

2.86-02

2.83-02

2.83-02

2.89-02

3.05-02

2.98-02

3.07-02

3.21-02

3.45-02

4.00 + 01 5.00 + 01 6.00 + 01 8.00+01

2.24-02

2.30-02

2.35-02

2.44-02

2.45-02

2.52-02

2.57-02

2.67-02

2.50-02

2.57-02

2.64-02

2.74-02

2.70-02

2.78-02

2.86-02

2.98-02

2.66-02

2.75- 02 2.84-02

2.96-02

2.99-02

3.10-02

3.19-02

3.34-02

3.19-02

3.31-02

3.42-02

3.58-02

3.65-02

3.82-02

3.95-02

4.16-02

1.00 + 02

1.50 + 02

2.00 + 02

3.00 + 02

2.51-02

2.63-02

2.71-02

2.82-02

2.75-02

2.89-02

2.99-02

3.10-02

2.83-02

2.98-02

3.07-02

3.19-02

3.07-02

3.24-02

3.34-02

3.48-02

3.06-02

3.25-02

3.34-02

3.48-02

3.45-02

3.68-02

3.77-02

3.93-02

3.70-02

3.94-02

4.05-02

4.22-02

4.32 - 02 4.58-02

4.75-02

4.94-02

4.00 + 02

5.00 + 02

6.00 + 02

8.00 + 02

2.88-02

2.92-02

2.95-02

3.00-02

3.17-02

3.22-02

3.25-02

3.30-02

3.27-02

3.32-02

3.35-02

3.40-02

3.56-02

3.61-02

3.65-02

3.70-02

3.56-02

3.61-02

3.65-02

3.71-02

4.02-02

4.08-02

4.12-02

4.19-02

4.32-02

4.38-02

4.43-02

4.50-02

5.06-02

5.14-02

5.19-02

5.27-02

1.00 + 03

1.50 + 03

2.00 + 03

3.00 + 03

3.02-02

3.07-02

3.09-02

3.12-02

3.33-02

3.38-02

3.41-02

3.44-02

. 3.44-02

3.48-02

3.51-02

3.54-02

3.74-02

3.80-02

3.83-02

3.86-02

3.75-02

3.80-02

3.82-02

3.86-02

4.23-02

4.29-02

4.32-02

4.36-02

4.55-02

4.61-02

4.64-02

4.68-02

5.32 - 02 5.39-02

5.43 - 02 5.48-02

4.00 + 03

5.00 + 03

6.00 + 03

8.00 + 03

3.13-

02

3.14-

02

3.15-

02

3.16-

02

3.45-

02

3.46-

02

3.47-

02

3.48-

02

3.56-

02

3.57-

02

3.58-

02

3.59-

02

3.88-

02

3.89-

02

3.90-

02

3.91-

02

3.87-02

3.89-02

3.89-02

3.91-02

4.38-

02

4.39-

02

4.40-

02

4.41-

02

4.70-02

4.72-

02

4.73-

02

4.74-

02

5.50-

02

5.51-

02

5.52-

02 5.54-02

1.00 + 04

1.50 + 04

2.00 + 04

3.00 + 04

3.16-

02

3.17-

02

3.17-

02

3.18-

02

3.48-

02

3.49-

02

3.50-

02 3.50-02

3.59-

02

3.60-

02

3.61-

02 3.61-02

3.91-

02

3.92-

02

3.93-

02 3.93-02

3.91-

02

3.92-

02

3.93-

02 3.93-02

4.42-

02

4.43-

02 4.43-02

4.44 - 02

4.75-

02

4.76-

02

4.77-

02 4.77-02

5.55-

02

5.56-

02

5.56-

02

5.57-

02

4.00 + 04

5.00 + 04

6.00 + 04

8.00 + 04

3.18-02

3.18-02

3.18-02

3.18-02

3.51-02

3.51-02

3.51-02

3.51-02

3.61-

02

3.62-

02 3.62-02

3.62-02

3.94-02

3.94-02

3.94-02

3.94-02

3.93-02

3.93-

02

3.94-

02 3.94-02

4.45-02

4.45-02

4.45 - 02 4.45-02

4.77-

02

4.78-

02 4.78-02

4.78-02

5.57-

02

5.58-

02 5.58-02

5.58-02

1 .00 + 05 3.19-02 3.51-02 3.62-02 3.94-02 3.94-02 4.45-02 4.78-02 5.58-02

11
Table 1.-4. (Continued)

PHOTON

ENERGY

COPPER

Z = 29

MOLYBDENUM

Z = 42 TINZ = 50 IODINEZ = 53 TUNGSTENZ= 74 LEADZ = 82 URANIUM

Z = 92 ABSORPTION

EDGES

Mev cm2lg

1.00-02 2.23 + 02 8.40 + 01 1.39 + 02 1.58 + 02 1119.12 + 01 1.28 + 02 1.73 + 02

|l 1.50-02 7.33 + 01 2.68 + 01 4.53 + 01 5.34 + 01 1.39 + 02 | 1.12 + 02 6.03 + 01 Em EDGE

2.00-02 3.30 + 01 1.17 + 01 2.02 + 01 2.47 + 01 6.51 + 01 8.34 + 01 6.85 + 01 Ln

. L, EDGES

3.00-02 1.06 + 01 2.83 + 01 4.07 + 01 7.98 + 00 2.18 + 01 2.84 + 01 3.96 + 01

4.00-

02

5.00-

02

6.00-

02

4.71 + 00

2.50 + 00

1.52 + 00

1.30 + 01 6.97 + 00

4.25 + 00

1.89 + 01

1.04 + 01 6.32 + 00

2.23 + 01

1.23 + 01 7.55 + 00

9.97 + 00

5.40 + 00

3.28 + 00

1.31 + 01

7.22 + 00

4.43 + 00

1.87 + 01 1.04 + 01 6.45 + 00 8.00-02 7.18-01 ] 1.92 +10 2.90 + 00 3.52 + 00 7.66 + 00 2.07 + 00 3.04 + 00

1.00-01 4.27-01 1.05 + 00 1.60 + 00 1.91+00 4.29 + 00 5.23 + 00 1.71 + 00 K EDGE

1.50-01

2.00-01

3.00-01

2.08-01

1.48-01

1.08-01

3.99-01

2.28-01

1.31-01

5.77-01

3.07-01

1.55-01

6.74-01

3.49-01

1.68-01

1.50 + 00 7.38-01

3.02-01

1.89 + 00 9.45-01

3.83-01

2.47 + 00

1.23 + 00 4.85-01

4.00-

01

5.00-

01

6.00-

01 8.00 — 01

9.19-02

8.22-02

7.52-02

6.55-02

1.01-01

8.59-02

7.67-02

6.52-02

1.10-01

9.11-02

7.91-02

6.55-02

1.16-01

9.36-02

8.07-02

6.61-02

1.80-01

1.29-01

1.03-01

7.73-02

2.20-01

1.54-01

1.20-01

8.56-02

2.73-01

1.85-01

1.40-01

9.64-02

1.00 + 00

1.50 + 00

2.00 + 00

3.00 + 00

5.86-02

4.79-02

4.19-02

3.59-02

5.77-02

4.68-02

4.14-02

3.66-02

5.71-02

4.59-02

4.08- 02 3.67-02

5.75-02

4.60-02

4.09-02

3.69-02

6.39-02

4.88-02

4.34-02

4.01-02

6.90-02

5.10-02

4.50-02

4.16-02

7.54-02

5.39-02

4.70-02

4.35-02

4.00 + 00

5.00 + 00

6.00 + 00

8.00 + 00

3.32-02

3.18-02

3.10-02

3.06-02

3.48-02

3.43-02

3.43-02

3.50-02

3.54-02

3.53-02

3.57-02

3.69-02

3.59-02

3.59-02

3.63-02

3.78-02

3.98-02

4.06-02

4.16-02

4.39 - 02

4.14-02

4.24-02

4.34-02

4.59-02

4.34-02

4.44-02

4.54-02

4.79-02

1.00 + 01

1.50 + 01 2.00 + 01 3.00 + 01

3.08-02

3.23-02

3.39-02

3.68-02

3.62-02

3.93-02

4.23-02

4.70-02

3.85-02

4.25-02

4.61-02

5.17-02

3.95-02

4.38-02

4.76-02

5.36-02

4.63 - 02 5.24-02

5.77-02

6.59-02

4.84-02

5.48-02

6.06-02

6.96-02

5.06-02

5.73-02

6.36-02

7.33-02

4.00 +01

5.00 + 01 6.00 + 01 8.00 + 01

3.91-02

4.10-02

4.25-02

4.48-02

5.05-02

5.32-02

5.53-02

5.86-02

5.57-02

5.88-02

6.13-02

6.51-02

5.78-02

6.11-02

6.37-02

6.76-02

7.16-02

7.60-02

7.94-02

8.45-02

7.57-02

8.04-02

8.41-02

8.96-02

7.99-02

8.50-02

8.89-02

9.48-02

1.00 + 02

1.50 + 02

2.00 + 02

3.00 + 02

4.65-02

4.94-02

5.11-02

5.32-02

6.09-02

6.48-02

6.72-02

7.00-02

6.77-02

7.21-02

7.48-02

7.80-02

7.04-02

7.50-02

7.78-02

8.11-02

8.81-02

9.39-02

9.76-02

1.02-01

9.34-02

9.96-02

1.03-01

1.08-01

9.84-02

1.06-01

1.10-01

1.15-01

4.00 + 02

5.00 + 02

6.00 + 02

8.00 + 02

5.44-02

5.52-02

5.58-02

5.66-02

7.16-02

7.27-02

7.35-02

7.45-02

7.98-02

8.10-02

8.19-02

8.31-02

8.30-02

8.42-02

8.51-02

8.64-02

1.04-01

1.06-01

1.07-

01

1.08-

01

1.11-01

1.12-01

1.13-01

1.15-01

1.17-01

1.19-01

1.21-01

1.22-01

1.00 + 03

1.50 + 03

2.00 + 03

3.00 + 03

5.72-02

5.79-02

5.83-02

5.88-02

7.53-02

7.62-02

7.67-02

7.73-02

8.38-02

8.49-02

8.56-02

8.62-02

8.71-02

8.84-02

8.90-02

8.96-02

1.09-01

1.11-01

1.11-01

1.12-01

1.16-01

1.18-01

1.18-01

1.19-01

1.23-01

1.25-

01

1.26-

01 1.27-01

4.00 + 03

5.00 + 03

6.00 + 03

8.00 + 03

5.90-

02

5.91-

02

5.93-

02

5.94-

02

7.77-02

7.79-

02

7.80-

02

7.81-

02

8.65-02

8.67-

02

8.68-

02 8.70-02

9.00-02

9.02-02

9.04-

02

9.05-

02

1.13-01

1.13-01

1.13-01

1.13-01

1.20-01

1.20-01

1.20-01

1.20-01

1.27-

01

1.28-

01 1.28-01

1.28-01

1.00 + 04

1.50 + 04

2.00 + 04

3.00 + 04

5.95-

02

5.96-

02 5.96-02

5.98-02

7.83-02

7.85-02

7.85-

02

7.86-

02

8.71-02

8.73-

02

8.74-

02

8.75-

02

9.06-02

9.08-02

9.10-

02

9.11-

02

1.14-01

1.14-01

1.14-01

1.14-01

1.21 -01

1.21-01

1.21-01

1.21-01

1.28-01

1.29-01

1.29-01

1.29-01

4.00 + 04

5.00 + 04

6.00 + 04 8.00+ 04

5.98-02

5.98-02

5.98-02

5.98-02

7.86-02

7.86-

02

7.87-

02

7.88-

02

8.76-

02

8.77-

02 8.77-02

8.77-02

9.11-02

9.11-

02

9.12-

02 9.12-02

1.14-01

1.14-01

1.14-01

1.14-01

1.21-01

1.21-01

1.21-01

1.21 -01

1.29-01

1.29-01

1.29-01

1.29-01

1.00 + 05 5.98-02 7.88-02 8.77-02 9.12-02 1.14-01 1.21-01 1.29-01

12
Table 1.-5. Gamma-ray linear attenuation coefficients fi.[cm~ l ], for various materials of interest in shielding.

Except for slight revisions for air, a this is the compilation by Hungerford [1960] from data in the Hogerton-Grass Reactor Handbook [1955].

Material Density q Linear attenuation coefficient fj. [cm-1

] [g/cm3

] 1 MeV 3 MeV 6 MeV

Aira

) (20 °C, 76 cm Hg pressure) 0.001205 0.0000765 0.0000431 0.0000304

Aluminum 2.7 0.166 0.0953 0.0718

Ammonia (liquid) 0.771 0.0612 0.0322 0.0221

Beryllium 1.85 0.104 0.0579 0.0392

Beryllium carbide 1.9 0.112 0.0627 0.0429

Beryllium oxide (hot-pressed blocks) 2.3 0.140 0.0789 0.0552

Bismuth 9.80 0.700 0.409 0.440 Boral 2.53 0.153 0.0865 0.0678

Boron (amorphous) 2.45 0.144 0.0791 0.0679

Boron carbide (hot pressed)

Bricks

2.5 0.150 0.0825 0.0675

Fire clay 2.05 0.129 0.0738 0.0543

Kaolin 2.1 0.132 0.0750 0.0552

Silica 1.78 0.113 0.0646 0.0473

Carbon 2.256) 0.143 0.0801 0.0554

Clay

Cements

2.2 0.130 0.0801 0.0590

Colemanite borated 1.95 0.128 0.0725 0.0528

Plain ( 1 Portland cement : 3 sand mixture)

Concretes

2.07 0.133 0.0760 0.0559

Barytes0

) 3.5 0.213 0.127 0.110 Barytes-boron frits0

) 3.25 0.199 0.119 0.101 Barytes-limonite 0

) 3.25 0.200 0.119 0.0991 Barytes-lumnite-colemanite0

) 3.1 0.189 0.112 0.0939

Iron-Portland0

) 6.0 0.364 0.215 0.181 MO (ORNL mixture) 5.8 0.374 - 0.222 0.184 Portland11 ) (1 cement: 2 sand: 4 gravel mixture) f 2.2

l 2.4 0.141 0.154 0.0805

0.0878

0.0592

0.0646

Flesh0

) 1.0 0.0699 0.0393 0.0274

Fuel oil (medium weight) 0.89 0.0716 0.0350 0.0239

Gasoline

Glass

0.739 0.0537 0.0299 0.0203

Borosilicate 2.23 0.141 0.0805 0.0591 Lead (Hi-D) 6.4 0.439 0.257 0.257 Plate (avg) 2.4 0.152 0.0862 0.0629 Iron 7.86 0.470 0.282 0.240 Lead 11.34 0.797 0.468 0.505 Lithium hydride (pressed powder) 0.70 0.0444 0.0239 0.0172

Lucite (polymethyl methacrylate) 1.19 0.0816 0.0457 0.0317

Paraffin

Rocks

0.89 0.0646 0.0360 0.0246

Granite 2.45 0.155 0.0887 0.0654

Limestone 2.91 0.187 0.109 0.0824

Sandstone

Rubber

2.40 0.152 0.0871 0.0641

Butadiene copolymer 0.915 0.0662 0.0370 0.0254

Natural 0.92 0.0652 0.0364 0.0248

Neoprene 1.23 0.0813 0.0462 0.0333

Sand 2.2 0.140 0.0825 0.0587

Type 347 stainless steel 7.8 0.462 0.279 0.236

Steel (1% carbon) 7.83 0.460 0.276 0.234 Uranium 18.7 1.46 0.813 0.881 Uranium hydride 11.5 0.903 0.504 0.542 Water

Wood

1.0 0.0706 0.0396 0.0277

Ash 0.51 0.0345 0.0193 0.0134

Oak 0.77 0.0521 0.0293 0.0203

White pine 0.67 0.0452 0.0253 0.0175

“ From table 3.-27.

11 Graphite theoretical density. See table 1

. — 1 , footnote ***.

1 Concrete mixtures for shielding reported by Gallaher and Kitzes [1953].

d Elemental composition, wl %: hydrogen, 1.0; oxygen, 52.9; silicon, 33.7; aluminum, 3.4; iron, 1.4; calcium, 4.4; magnesium, 0.2; carbon, 0.1; sodium

1.6; potassium, 1.3.

* Composition, wt %: oxygen, 65.99; carbon, 18.27; hydrogen, 10.15; nitrogen, 3.05; calcium, 1.52; phosphorus, 1.02.

335-734 0-69—3 13
100

10

1.0

0.1

0.01

~T-r*-

B—B"

92 U > razPb

„Ta >

JL*±

Xe

iSn J

,Mo J

29Cu

t

22Ti 1

I3 AI >

6c> —I

4 Be>

.A.'>

l H

>

EXPERIMENTAL ^ O GATES, et ol [i960, 1962] • BROOKES, et al [1967] JONES [1959, I960] V DE WIRE, el al [l95l] KENNEY, et al [|954]

ANDERSON, et al [l956] A COOPER [1955] MALAMUD [1959] ® NICHIPORUK [1967] A WALKER, et ol [1966] B FIDECARO, et al [1962] 4 KNASEL 8 WALKER [|968]

THEORETICAL : THIS COMPILATION

10 10 10 PHOTON ENERGY, MeV

10

Figure 1.-3. Comparison of present total cross sections (rtot (= rpe + cr c + k„ + Ke ) (see tables in section 3) above 100 MeV with available experimental data.

1.5.2. Conditions Under Which the Coefficients are Useful

At high energies the range of secondary electrons tends to become comparable with the gammaray mean free path, as indicated by the ratios in

table 1.-6. Under such conditions the computation of gamma-ray energy deposition in a medium requires a cascade calculation involving

coupled electron and photon transport equations. 10 However, at energies below 10 MeV where the

travel of electrons is of less significance, it may

be sufficient to treat the problem in terms of the

gamma-ray flux and either the “mass energyabsorption coefficient” or one of the various approximations such as the “mass energy-transfer

coefficient” or “mass absorption coefficient” discussed in the following section 1.5.3.

10 For a calculation of this type see, for example, that of Brysk [1954J.

The amount of energy, e, absorbed per unit time

in a “volume of interest,” AV, at a point r in the

medium, can be expressed as the sum of two terms.

The first term describes the conversion of photon

energy to electron kinetic energy and involves the

mass energy-absorption coefficient. The second

term describes the migration of energy into and out

of the volume of interest in the form of kinetic

energy of electrons. Thus one can set up the energy

balance equation:

€=[ (drFp(r) r)-E-^(E)

J At- Jo p

+ [€,« — €0ut] (1.-9)

in which e, €;«, and eoui are in MeV s _1

, p(r) is the

density of the medium in g cm-3

at r, E is the photon energy in MeV, and fxen /p(E) is in cm2 g

_1

. The

quantity 4>(E, r), with dimensions MeV-1 cm-2

s

_1

, represents the flux per unit energy interval (integrated over all directions) of photons, including

secondaries, with energies between E and E+dE.

14
Photon

source

FIGURE 1.-4. Flow diagram of conversion of energy from one form to another in the course of photon energy absorption in a medium.

To be complete, the diagram should also contain a box labelled “excitation energy of nuclei, as well as

lines representing the emission of secondary neutrons, charged particles, and gamma rays. This box has been

omitted in order to prevent the diagram from becoming unduly complicated, and because the energy absorption coefficients presented here do not take into account photonuclear absorption.

Table 1.-6. Ratios of the electron range,* Re , to the photon mean-free-path, (lip), based on electron data of Berger and

Seltzer [7964] and photon data from tables 1.—4 and 3.-24, —26, -27, and ~28.

Photon

energy

[MeV]

iH 6 c 13"^ 26^e 50^ n 82 Pb Air h2 o

Concrete Nal

Re'P

0.01 0.000041 0.00058 0.0091 0.076 © o 00 0.11 L-edges

A'-edge

0.0014 0.0012 0.0074 | 0.085 Iodine

A-edge

0.1 0.0020 0.0024 0.0030 0.0073 0.043 0.17 0.0025 0.0023 0.0029 0.041

1.0 0.027 0.031 0.034 0.036 0.040 0.053 0.031 0.030 0.033 0.039

10.0 0.077 0.11 0.13 0.18 0.23 0.29 0.11 0.11 0.12 0.22

100.0 0.22 0.55 0.81 1.1 1.5 1.8 0.53 0.56 0.69 1.4

a

) Here we use the mean range as calculated in the continuous-slowing-down approximation.

Under conditions of electronic equilibrium,11 tin— tout, and the second term vanishes. When the

size of the volume of interest, AV, is large compared

with the ranges of the secondary electrons involved,

the term [e in — e0ud is small compared with the

integral term and may be disregarded.

11 Electronic equilibrium prevails if the gamma-ray flux distribution is effectively constant over a region having dimensions of the order of the range of the secondary

electrons. Discussions of this concept and its application are given in NBS Handbook

85 [1964J and in a number of dosimetry texts (see, for example, Whyte [1959] and

Johns [1961]).

1.5.3. Evaluation of the Coefficients From

the Cross Sections

The “mass energy-absorption coefficient,” /u, enl P

,

as specified in definition (17) in Appendix I of NBS

Handbook 85 [1964], takes into account all the

modes of energy transfer to electrons shown in

figure 1.-4. The other coefficients treated here,

namely the “mass energy-transfer coefficient"

P-kIp as specified in definition (16) in Appendix I of

15
NBS Handbook 85 [1964], and the “mass absorption

coefficient” pJp (sec. e.g., eq (8f-48) of Evans

[1963]), are approximate and neglect some of these

modes. The coefficients, pe/ilp, Pslp, and /x a/p, are

differently weighted sums of the probabilities per

unit pathlength (in g/cm2

) for photoelectric absorption (pT/p), Compton collision (pdp), and pair

production ( pK/p):

The weights fT , fc , and fK are conversion factors

which indicate, for the respective interactions, the

average fraction of the photon energy which is eventually converted into kinetic energy of electrons in the volume of interest. These weights,

therefore, must discount the amount of energy that

escapes from the volume of interest in the form of

secondary photons (which may include scattered

photons, annihilation radiation, bremsstrahlung,

and fluorescence radiation).

For penlp the weights account for the escape of

Compton-scattered, fluorescence, annihilation, and

bremsstrahlung photons. For pdp the weights

account for the escape of all of these except bremsstrahlung photons. For pa/p they account for the

escape of Compton-scattered photons only.

A certain part of the escaping photon radiation

may also interact with the medium in the volume

of interest and set electrons into motion there. This

possibility is automatically taken into account if one includes in the flux (f)(E , r) which multiplies

the coefficient not only unscattered (primary) photons, but also scattered photons, and all other

secondary photons, such as annihilation radiation. 12 On the other hand, the treatment must be consistent. That is, if in eq (1.-9) one uses values

of palp or PkIp i from which the escape of certain

secondary radiations is not discounted, then one

should use values of <t){E, r

)

computed without considering the contributions from these radiations.

R. Berger [1961] has evaluated the coefficients

/K , fc, and f

j

, including all energy transfer routes

shown in figure 1.-4, and from them the mass

energy-absorption coefficient penlp for air, water,

and 15 elements and pK/p for Al, Fe, and Pb over

the energy range 10 keV ^ E ^ 10 MeV. Tabulations

of penlp and palp have been made by Allison [1961]

12 Calculations of <f>(E , r) often include only Compton scattered photons in the secondary flux (see, for example, Goldstein and Wilkins [1954]). However, for 6- to 10-MeV primary photons in lead, the annihilation photon flux has been theoretically estimated to contribute from 4 to 7 percent to </>(£ , r) by Goldstein [1954] and by

Berger, Hubbell, and Reingold [1959], and contributions of this order of magnitude

have been observed experimentally by Hubbell, Hayward, and Titus [1957]. Also,

theoretical estimates of the fluorescence radiation component have been made by

Goldstein [1954], Veigele and Roper [1966], and Veigele and Balogh [1968].

for air, water, and seven elements over the range

10 keV ^ E ^ 100 MeV. His procedures are es- sentially the same as those of Berger, with the ex- ception that in discounting the escape of annihilation

radiation he did not consider the possibility of

annihilation of the positron while in flight. Thus, for

heavy elements (Z > 26) the Allison data are slightly

different from those of Berger at energies above the

pair production threshold, i.e., for E > 1.022 MeV.

This effect of annihilation in flight amounts to ~ 2 to 3 percent at 10 MeV, and presumably more

in the region E > 10 MeV, which was not included by

Berger.

Various other authors have presented values of

Palp which, as has been discussed, discount only

the energy-escape by the deflected photon in

Compton scattering. Data in this approximation

include the tabulations by White [1952] and Storm,

Gilbert, and Israel [1958], and the graphical data

of Evans [1955, 1963].

1.6. Tabulation of Energy Absorption

Coefficients

In tables 1.-7 and 1.-8 we present values of

Penlp , Palp , and PkIp , for air, water, and 18 elements

over the range 10 keV ^ E ^ 10 MeV. These data

are based on the interaction cross sections in section 2 and hence are consistent with the attenuation coefficients in table 1.—4 and in section 3. For palp , values of Compton scatter losses

(l —fc) pel

p

were subtracted from entries in table

1.-4. For pdp, the compilation of fluorescence

yields and average fluorescence photon energies

of R. Berger [1961] was used plus values for Sn

and U from Wapstra et al. [1959]. 13 For penlp the

weights fT , fc, and fK were taken directly or interpolated from Berger [1961], except values of f for

Sn and U, for which bremsstrahlung yield data

from Berger and Seltzer [1964] were used.

In addition, in table 1.— 9, we have excerpted the

values of penlp over the range 10 MeV ^ E =§ 100 MeV

from the tabulation by Allison [1961]. We also

include, for comparison, values of pa\p computed

from present cross sections for the same substances.

As discussed in section 1.5.3, the Allison data differ

from those of Berger in that positron annihilation

in flight was not taken into account. However, at energies above 10 MeV the approximation involved

in the use of energy-absorption or related coeffi- cients loses some of its validity because of the comparable distances traveled by electrons and photons

(see table 1.-6).

13 For a more recent and extensive summary of K-, L-, and 4/-shell fluorescence

yield data, see Fink et al. [1966].

16
Table 1.-7. Values of (a) the mass absorption coefficient p-Jp; ( b) the mass energy-transfer coefficient p-Jp; and

(c) the mass energy-absorption coefficient pe J_,pUnits are cm!/g (see footnote a).

Photon iH 6 c 7 N

energy

[MeV] vJq hkIq VenlQ vJq vk/q HenlQ vJq Vk/Q Ven/Q

0.01 0.00991 1.98 3.38 0.015 0.0110 0.538 0.908

0.02 0.0136 0.208 0.362

0.03 0.0186 0.0596 0.105

0.04 0.0231 0.0307 0.0494

0.05 0.0271 0.0234 0.0319

0.06 0.0305 0.0212 0.0256

0.08 0.0362 0.0205 0.0223

0.10 0.0406 0.021 6 0.0224

0.15 0.0481 0.0246 0.0248

0.2 0.0525 0.0266 0.0267

0.3 0.0569 0.0288 0.0287

0.4 0.0586 0.0296 0.0295

0.5 0.0590 0.0298 0.0297 0.0296

0.6 0.0587 0.0297 0.0295 0.0296 0.0295

C. 8 0.0574 0.0290 0.0288 0.0289 0.0289

1.0 0.0555 0.0280 0.0279 0.0280 0.0279

1.5 0.0507 0.025 7 0.0255 0.025 7 0.0255

2 0.0465 0.0464 0.0238 0.0235 0.0234 0.0238 0.0236 0.0234

3 0.0400 0.0399 0.0398 0.0210 0.0206 0.0204 0.0211 0.0207 0.0205

4 0.0355 0.0353 0.0352 0.0191 0.0187 0.0185 0.0194 0.0189 0.0186

5 0.0320 0.0319 0.0317 0.0178 0.0174 0.0171 0.0181 0.0177 0.0173

6 0.0294 0.0292 0.0290 0.016 9 0.0164 0.0161 0.0172 0.0167 0.0163

8 0.0255 0.0253 0.0252 0.015 6 0.0151 0.0147 0.0161 0.0156 0.0151

10 0.0229 0.0227 0.0225 0.0147 0.0143 0.0138 0.0154 0.0149 0.0143

a

) Values for hkIq and i*en lQ given only if different from i*a le.

Photon 8 o nNa i 2Mg

energy

[MeV] ValQ vk/q VenlQ vJq vk/q Ven!Q Va/Q vkIq Ven/Q

0.01 5.39 14.9 20.1 0.015 1.44 4.20 5.80 0.02 0.575 1.70 2.38

0.03 0.165 0.475 0.671

0.04 0.073 4 0.199 0.276

0.05 0.0438 0.106 0.144

0.06 0.0322 0.0669 0.0888

0.08 0.0249 0.0382 0.0475

0.10 0.0237 0.0297 0.0346

0.15 0.0251 0.0260 0.0279

0.2 0.0268 0.0265 0.0277

0.3 0.0288 0.0278 0.0288

0.4 0.029 6 0.0284 0.0294

0.5 0.0298 0.0285 0.0294

0.6 0.0296 0.0284 0.0293

0.8 0.0289 0.0277 0.0275 0.0286 0.0285

1.0 0.0280 0.0278 0.0268 0.0266 0.0277 0.0275

1.5 0.025 7 0.0254 0.0246 0.0245 0.0243 0.0254 0.0253 0.0251

2 0.0239 0.0236 0.0234 0.0230 0.0227 0.0225 0.0238 0.0234 0.0232

3 0.021 3 0.0208 0.0206 0.0208 0.0202 0.0199 0.0216 0.0210 0.0206

4 0.0196 0.0191 0.0188 0.0195 0.0188 0.0184 0.0204 0.0196 0.0191

5 0.0185 0.0179 0.0175 0.0186 0.0179 0.0174 0.0196 0.0187 0.0181

6 0.0177 0.0171 0.0166 0.0181 0.0173 0.0167 0.0190 0.0182 0.0175

8 0.0166 0.0160 0.0155 0.0174 0.0167 0.0159 0.0185 0.0177 0.0168

10 0.0160 0.0154 0.0148 0.0171 0.0164 0.0155 0.0183 0.0176 0.0165

335-734 0-69—4 17
Table 1.-7 (Continued)

Photon 13AI 14 Si 15P

energy

[MeV] HalQ HkIq f*en/Q vJq vk/q Pen/6 vJq Vk/q HenlQ

0.01 25.6 25.5 25.5 33.4 33.3 33.3 40.1 39.8 39.8 0.015 7.48 7.47 7.47 9.78 9.75 9.75 11.9 11.8 11.8 0.02 3.06 4.02 4.01 4.01 4.93 4.91 4.91 0.03 0.868 1.14 1.14 1.14 1.39 1.39 1.39

0.04 0.357 0.473 0.472 0.472 0.573 0.572 0.572

0.05 0.184 0.241 0.293

0.06 0.111 0.144 0.173

0.08 0.0562 0.0701 0.0820

0.10 0.0386 0.0459 0.0511

0.15 0.0286 0.0312 0.0323

0.2 0.0276 0.0293 0.0292

0.3 0.0283 0.0294 0.0288

0.4 0.0287 0.0298 0.0291

0.5 0.0288 0.0286 0.0298 0.0290

0.6 0.0286 0.0286 0.0296 0.0295 0.0288

0.8 0.0279 0.0277 0.0289 0.0288 0.0281 0.0278

1.0 0.0270 0.0269 0.0279 0.0277 0.0272 0.0270

1.5 0.0248 0.0247 0.0245 0.0257 0.0255 0.0253 0.0250 0.0248 0.0246

2 0.0233 0.0229 0.0226 0.0241 0.0237 0.0234 0.0235 0.0231 0.0228

3 0.021 3 0.0206 0.0202 0.0221 0.0214 0.0210 0.0217 0.0209 0.0204

4 0.0201 0.0193 0.0188 0.0211 0.0202 0.0196 0.0207 0.0198 0.0192

5 0.0194 0.0185 0.0179 0.0204 0.0194 0.0187 0.0201 0.0191 0.0184

6 0.0190 0.0181 0.0172 0.020 1 0.0191 0.0182 0.0198 0.0188 0.0179

8 0.0186 0.0177 0.0168 0.0197 0.0187 0.0177 0.0197 0.0187 0.0175

10 0.0185 0.0176 0.0165 0.0197 0.0188 0.0175 0.0197 0.0188 0.0174

Photon i 8 S 00 > 19^

energy

[MeV] vJq Hk/q VenlQ Va/Q Vk/q VenlQ hJq Pk/Q VenlQ

0.01 50.1 49.7 49.7 63.6 62.3 62.3 79.9 77.6 77.6 0.015 15.0 14.9 14.9 19.3 19.1 19.1 24.4 23.9 23.9 0.02 6.24 6.21 6.21 8.10 8.02 8.02 10.3 10.2 10.2 0.03 1.77 1.77 1.77 2.33 2.31 2.31 2.97 2.94 2.94

0.04 0.729 0.727 0.727 0.967 0.962 0.962 1.23 1.23 1.23 0.05 0.372 0.490 0.488 0.488 0.626 0.623 0.623

0.06 0.218 0.285 0.284 0.284 0.368 0.366 0.366

0.08 0.101 0.128 0.162 0.162 0.162

0.10 0.0610 0.0735 0.0915 0.0913 0.0913

0.15 0.0357 0.0377 0.0442

0.2 0.0311 0.0304 0.0343

0.3 o. 03 no 0.0278 0.0304

0.4 0.0301 0.0275 0.0298

0.5 0.0300 0.0273 0.0295 0.0293

0.6 0.0298 0.0270 0.0268 0.0292 0.0290

0.8 0.0290 0.0288 0.0262 0.0261 0.0283 0.0282

1.0 0.0280 0.0278 0.0253 0.0251 0.0273 0.0270

1.5 0.0258 0.0256 0.0253 0.0233 0.0232 0.0229 0.0252 0.0250 0.0247

2 0.0243 0.0238 0.0235 0.0220 0.0215 0.0212 0.0238 0.0233 0.0229

3 0.0225 0.0216 0.0211 0.0206 0.0198 0.0192 0.0224 0.0214 0.0208

4 0.0216 0.0205 0.0199 0.0199 0.0189 0.0182 0.0218 0.0206 0.0198

5 0.0211 0.0200 0.0192 0.0197 0.0185 0.0177 0.0215 0.0202 0.0193

6 0.0209 0.0197 0.0188 0.0196 0.0184 0.0174 0.0215 0.0202 0.0190

8 0.0208 0.0197 0.0184 0.0197 0.0186 0.0173 0.0218 0.0205 0.0190

10 0.0210 0.0200 0.0184 0.0201 0.0190 0.0174 0.0222 0.0210 0.0191

18
Table 1.-7 (Continued)

Photon 20^a 26 Fe 29 ^U energy

[ MeV] pJq pk/q PentQ PalQ Pk/q Pen/Q PalQ PkIq Menle

0.01 95.4 91.6 91.6 171 . 142. 142. 223. 160. 160. 0.015 29.4 28.6 28.6 55.5 49.3 49.3 73.2 59.4 59.4 0.02 12.4 12.2 12.2 24.9 22.8 22.8 32.8 28.2 28.2

0.03 3.65 3.60 3.60 7.72 7.28 7.28 10.5 9.50 9.50

0.04 1.51 1.50 1.50 3.31 3.17 3.17 4.56 4.24 4.24

0.05 0.770 0.764 0.764 1.69 1.64 1.64 2.35 2.22 2.22

0.06 0.447 0.444 0.444 0.989 0.961 0.961 1.39 1.32 1.32 0.08 0.197 0.196 0.196 0.422 0.414 0.414 0.593 0.573 0.573

0.10 0.109 0.223 0.219 0.219 0.311 0.302 0.302

0.15 0.0498 0.0821 0.0814 0.0814 0.108 0.106 0.106

0.2 0.0371 0.0498 0.0495 0.0495 0.0602 0.0597 0.0597

0.3 0.0318 0.0342 0.0335 0.0335 0.0371 0.0370 0.0370

0.4 0.0309 0.0308 0.0318

0.5 0.0304 0.0295 0.0298

0.6 0.0300 0.0299 0.0287 0.0286 0.0287 0.0286

0.8 0.0291 0.0289 0.0275 0.0273 0.0273 0.0272 0.0271

1.0 0.0281 0.0280 0.0278 0.0264 0.0262 0.0261 0.0261 0.0258

1.5 0.0259 0.0257 0.0254 0.0243 0.0241 0.0237 0.0240 0.0237 0.0233

2 0.0245 0.0240 0.0236 0.0233 0.0225 0.0220 0.0230 0.0222 0.0217

3 0.0231 0.0220 0.0214 0.0225 0.0212 0.0204 0.0225 0.0211 0.0202

4 0.0226 0.0213 0.0205 0.0225 0.0209 0.0199 0.0228 0.0211 0.0200

5 0.0224 0.0211 0.0200 0.0228 0.0211 0.0198 0.0233 0.0214 0.0200

6 0.0225 0.0211 0.0198 0.0232 0.0215 0.0199 0.0239 0.0220 0.0202

8 0.0229 0.0215 0.0198 0.0242 0.0226 0.0204 0.0251 0.0234 0.0209

10 0.0234 0.0222 0.0201 0.0252 0.0238 0.0209 0.0264 0.0248 0.0215

Photon

energy

[ MeV]

50 ^n 82 ^ 92 u

Pa/Q PkIq PenlQ pJq PkIq f^enlQ PalQ PkIq Penl6

0.01 139 . 136. 136. j 128 - 127 . 127. 173 . 171 . 170 . 0.015 45.2 43.7 43.6 112.0 91.7 91.7 "j 60.2 59.6 59 4 Z-m

0.02 20.0 19.8 19.8 83.3 69.2 69.1 68.3 55.5 55.5 L U I

0.03 40.5 16.2 16.2 28.2 24.6 24.6 39.4 33.0 33.0

0.04 18.8 9.97 9.96 13.0 11.8 11.8 18.6 16.3 16.3 0.05 10. 2 6.25 6.24 7 10 6.57 6.54 10.3 9.30 9.25 0.06 6.20 4.20 4.19 4.31 4.11 4.08 6.34 5.82 5.78 0.08 2.78 2.19 2.18 1.96 1.87 1 . 86 2.94 2.76 2.73

0.10 1 . 49 1.26 1.25 5.12 2.28 2.28 1.61 1.54 1.52 K

0.15 0 485 0.446 0.442 1.80 1.16 1.15 2.39 1.12 1.19

0.2 0.226 0.211 0.209 0.8 69 0.637 0.629 1.15 0.712 0.704

0.3 0.0892 0.0853 0.0843 0.322 0.265 0.259 0.425 0.322 0.315

0.4 0.0550 0.0536 0.0530 0.168 0.147 0.143 0.222 0.184 0.178

0.5 0.0428 0.0423 0.0416 0.108 0.0984 0.0951 0.140 0.122 0.118

0.6 0.0361 0.0358 0.0353 0.079 3 0.0737 0.0710 0.100 0.0902 0.0864

0.8 0.0302 0.0301 0.0294 0.0525 0.0503 0.0481 0.0640 0.0599 0.0569

1.0 0.0271 0.0270 0.0264 0.0407 0.0396 0.0377 0.0479 0.0458 0.0432

1.5 0.0239 0.0233 0.0226 0.0303 0.0288 0.0271 0.0337 0.0317 0.0295

2 0.0234 0.0220 0.0210 0.0286 0.0259 0.0240 0.0310 0.0278 0.0255

3 0.0243 0.0219 0.0205 0.0300 0.0260 0.0234 0.0322 0.0276 0.0246

4 0.0259 0.0232 0.0212 0.0324 0.0281 0.0245 0.0346 0.0298 0.0256

5 0.0275 0.0247 0.0221 0.0350 0.0306 0.0259 0.0372 0.0324 0.0270

6 0.0290 0.0262 0.0230 0.0372 0.0331 0.0272 0.0394 0.0348 0.0281

8 0.0319 0.0292 0.0245 0.041 1 0.0378 0.0294 0 . 04'1 3 0.0392 0.0298

10 0.0344 0.0319 0.0258 0.0446 0.0419 0.0310 0.0468 0.0432 0.0312

19
Table 1.-7 (Continued)

Photon Air h2 o

energy

[MeV] pJq pk/q iuenl

Q

pJq pk!q Pen/e

0.01 4.63 4.61 4.61 4.79 0.015 1.27 1.27 1.27 1.28 0.02 0.512 0.511 0.511 0.512

0.03 0.148 0.149

0.04 0.0669 0.0678

0.05 0.0406 0.0419

0.06 0.0305 0.0320

0.08 0.0243 0.0262

0.10 0.0234 0.0256

0.15 0.0250 0.0277

0.2 0.0268 0.0297

0.3 0.0288 0.0319

0.4 0.0295 0.0328

0.5 0.0297 0.0296 0.0330

0.6 0.0296 0.0295 0.0329

0.8 0.0289 0.0289 0.0321

1.0 0.0280 0.0278 0.0311 0.0309

1.5 0.0257 0.0254 0.028 5 0.0282

2 0.0238 0.0236 0.0234 0.0264 0.0262 0.0260

3 0.021 2 0.0207 0.0205 0.0234 0.0229 0.0227

4 0.0194 0.0189 0.0186 0.0214 0.0209 0.0206

5 0.0182 0.0178 0.0174 0.0200 0.0195 0.0191

6 0.0174 0.0168 0.0164 0.0190 0.0185 0.0180

8 0.0162 0.0157 0.0152 0.0176 0.0170 0.0166

10 0.0156 0.0151 0.0145 0.0168 0.0162 0.0157

Table 1.-8. Values of pjp, p. K/p, and penlp extrapolated to the absorption edges from the low-energy and high-energy

sides, respectively. Units are cm'2 lg.

Absorption edge 5()S n 82 Pb 92 U

[keV] palP PkIp P-eulp [keV] Palp PkIp Penlp [keV] Palp Pslp PenlP

I 13.041 63.9 63.5 63.3 17.165 42.6 42.2 42.1

^III 162. 129. 129. 103. 80.1 80.1

r 15.205

109. 89.6 89.6 20.94560.2 49.4 49.4 ^II 142. 113 113. 85.5 66.9 66.9

/ 15.855

126. 102. 102. 21.771

77.4 61.2 61.1 M 154. 123. 123. 89.4 69.6 69.6

29.195

6.74 6.70 6.69 88.0051.51 1.45 1.44 115.62

1.09 1.05 1.04 43.5 16.7 16.7 7.12 2.47 2.47 4.62 1.66 1.66

20
Table 1.-9. Values of the mass absorption coefficient pufp and mass energy-absorption coefficient a pe Jp for photon energies 10 to 100 MeV.

Units are cm2/g.

Photon iH 7 n 8 o 13^-1 18^r energy

[MeV] Va/Q VenlQ ValQ VenlQ t*Je VenlQ vJq V-entQ vJq VenlQ

10 0.0229 0.0222 0.0154 0.0143 0.0160 0.0148 0.0185 0.0164 0.0201 0.0176

15 0.0188 0.0179 0,0145 0.0131 0.0153 0.0136 0.0187 0.0163 0.0211 0.0183

20 0.0166 0.0156 0.0142 0.0128 0.0152 0.0135 0.0192 0.0162 0.0222 0.0187

30 0.0141 0.0130 0.0142 0.0123 0.0153 0.0131 0.0203 0.0164 0.0240 0.0192

40 0.0129 0.0116 0.0144 0.0121 0.0156 0.0130 0.0212 0.0166 0.0254 0.0192

50 0.0121 0.0107 0.0146 0.0119 0.0160 0.0129 0.0220 0.0164 0.0266 0.0192

60 0.0117 0.0102 0.0149 0.0118 0.0163 0.0129 0.0227 0.0161 0.0276 0.0190

80 0.0111 0.0095 0.0153 0.0118 0.0169 0.0127 0.0238 0.0159 0.0290 0.0188

100 0.0109 0.0092 0.0158 0.0119 0.0174 0.0127 0.0246 0.0156 0.030 1 0.0184

Photon 26^e 82^

Air Water

eneigy

[MeV] vJe VenlQ vJq Ven/Q vJq Ventd v-Jq Ventd

10 0.0252 0.0212 0.0446 0.0324 0.0156 0.0145 0.0168 0.0155

15 0.0277 0.0223 0.0522 0.0352 0.0148 0.0132 0.0157 0.0141 20 0.0298 0.0230 0.05 87 0.0367 0.0145 0.0131 0.0153 0.0136

30 0.0330 0.0236 0.0682 0.0375 0.0146 0.0126 0.0152 0.0131

40 0.0354 0.0235 0.0747 0.0372 0.0148 0.0124 0.0153 0.0128

50 0.0372 0.0234 0.0796 0.0366 0.0151 0.0122 0.0156 0.0126

60 0.0387 0.0230 0.0834 0.0357 0.0154 0.0122 0.0158 0.0125

80 0.0410 0.0233 0.089 0 0.0334 0.0159 0.0121 0.0163 0.0125

100 0.0427 0.0217 0.0930 0.0301 0.0163 0.0121 0.0167 0.0124

‘‘Values of /x,.„/p in this table are taken directly from Allison [1961]. Hence the input cross-section data are those of White-Grodstein [1957], and positron annihilation in flight is not taken into account.

2. Photon Cross Sections

2.1. Scope

This section contains descriptions and tabulations

of the individual atomic cross sections for scattering,

absorption, and pair production that enter into the

computation of the attenuation, energy absorption,

and other related coefficients. The information

in this report is confined primarily to total cross

sections, although some angular distribution

information for Compton and Rayleigh scattering

is included. 14

2.2. Classification of Interactions

Interactions of photons with matter, by which

individual photons are removed or deflected from

a primary beam of x- or y-radiation, may be classified according to:

(1) The kind of target, e.g., electrons, atoms, or

nuclei, with which the photon interacts, and

(2) The type of event, e.g., scattering, absorption,

pair production, etc., which takes place.

U F°r further angular distribution data and formulas, reference for Compton scatter- ing can be made to Compton and Allison [1935], Davisson and Evans [1952], Nelms

[1953], Burton [1953|, Evans [1958], Curien [1962], Stinner et al.

[ 1 965 ] , and Veigele

[1965]; for the atomic photoeffect to Hultberg et al. [1968| and Pratt et al. [1964j; and

for electron-positron pair production to Heitler [ 1 954 ]

Possible interactions are summarized in table

2.-1 (adapted from Fano, Spencer, and Berger

[1959]). The relative magnitudes of cross sections for

these interactions as functions of energy are shown

in figure 2.-1, in which the vertical distance between

curves represents the percent contribution of an

indicated cross section to the total “electronic’' cross section (i.e. , excluding photo-nuclear effects).

It is apparent from figure 2.-1 that for attenuations of photons in this energy range the most

important interactions are:

(1) The photoelectric effect, rpe , (2) Compton scattering, <xc, and

(3) Electron-positron pair production, (k„ + Ke )- Rayleigh scattering, ctr, is usually of minor importance for the broad beam conditions typically

found in shielding but must be known for interpretation of experimental attenuation coefficient

data. Two-photon Compton scattering, together with

the radiative correction, amounts to less than

1 percent of ore below 100 MeV and is included in

the total Compton cross section err in figure 2.-1.

The photonuclear effect, is mostly restricted

to the region of the giant resonance around 10 to 30 MeV where, at the resonance peak, it may

amount to as much as 10 percent of the total

“electronic” cross section.

21
Table 2.— 1. Classification of elementary photon interactions.

Solid-line boxes indicate the major effects contributing to photon attenuation in matter. Dotted-line boxes indicate additional effects which contribute more than

1 percent over particular energy ranges.

Scattering

Multi-photon

effects

(d)

Elastic

(coherent)

(b)

Inelastic (incoherent)

(c)

i Rayleigh i

i scattering, i

: aR ~Z2

| (low energy limit •

Compton

scattering,

<3q ^ Z

Two-photon i

i Compton

i scattering,

; ~z

Elastic nuclear

scattering,

(y, y)~Z2

Inelastic nuclear

scattering,

(y. y')

Delbrtick

scattering,

~Z4

Modified

(y. v)

Type of interaction

Interaction with

:

Absorption

(a)

(1) Atomic electrons

(2) Nucleons

(3) Electric field surrounding

charged particles

(4) Mesons

Photoelectric effect

| ~Z4 (low energy)

rPe

1 ~Z5 (high energy)

Photonuclear reactions

(y, n), (y, p), photofission, etc.

^ph, 71 ^ ^ [E> lOMeV)

(1) Electron-positron

pair production in

field of nucleus,

(E ^ 1.02 MeV)

(2) Electron-positron

pair production in electron field, xe ~Z

(E ^ 2,04 MeV)

(3) Nucleon-antinucleon

pair production

{E > 3 GeV)

Photomeson production,

(E > 150 MeV)

Figure 2.-1. Relative contributions of the various photon interactions as functions of energy for carbon,

iron, and lead.

In these plots the vertical distance between curves represents the percent

contribution of the indicated process to the sum T„e + <Th + <r, + k„ + Ke (see tables in section 3).

22
The remaining small effects (resonance scattering

and Thomson scattering by the nucleus, Compton

scattering by nucleons, meson production, reso- nance scattering associated with meson production,

Delbriick scattering and nucleon-antinucleon

production) will not be treated here. For a general

discussion of these effects, including order of magnitude estimates, see Bethe and Ashkin [1953].

Recent photomeson data have been summarized by

Crouch et al. [1964], Allaby et al. [1966], Panofsky

[1968], and Joos [1968]. We have reproduced in

table 2.-2 the photomeson cross section compilation

by E. Lohrmann in the review by Joos [1968].

Table 2.-2. Meson photoproduction cross sections in p.b(10~30cm2

) , as summarized by

E. Lohrmann in the article by Joos [ 1968 ].

Reaction

yP^

Photon energy References

1 GeV \ GeV 3 GeV 4.5 GeV

p77° 24 4.7 1.5 0.6 70, 71, 72, 74

nTT° 50 5 2.2 1.0 70, 72, 73, 75, 76 pP

° Pw

20 17 17 45, 47, 52, 55

46, 51, 55

55

7 4 3 Pi

Pt, ~ 0.2 - 0.3 - 0.2 6 < 1 < 1 < 0.2 51, 55, 78, 79, 80

PX°(959)

Pf°

~0.7 - 0.2 - 0.9 -0.2 - 0.3 51, 55

52, 55

50, 55, 77, 81, 82

55, 77

52, 55, 77

53, 73, 83, 84

A++ (1238)t7-

A°77 + 48

2 8 4 2 A++d

_ - 4 - 2 - 1 AK+ 2 - 1 -0.5 -0.25

2°K+ - 0.6 - 0.2 - 0.1 53, 73 X+K° < 0.2 < 0.2 < 0.2 53 Y*°(1385)K+ 0.5 -0.2 53 Y*+

( 1385)K° 0.4 -0.1 53

[45] Brown-Harvard-MIT-Weizman Institute Bubble Chamber group (CEA-Bubble

Chamber Group) Phys. Rev. 146 (1966), 994.

[46] CEA-Bubble Chamber Group, Phys. Rev. 115 (1967), 1468, Contribution No. 278 to

this Conference. (See Joos [1968].)

[47] CEA-Bubble Chamber Group, Phys. Rev. 155 (1967), 1477.

[50] DESY-Bubble Chamber Collaboration, Phys. Letters 23 (1966), 707.

[51] DESY-Bubble Chamber Collaboration, Nuovo Cimento 46 (1966), 795.

[52] DESY-Bubble Chamber Collaboration, Nuovo Cimento 48 (1967), 262.

[53] DESY-Bubble Chamber Collaboration, Nuovo Cimento 49 (1967), 504.

[54] DESY-Bubble Chamber Collaboration, Nucl. Phys. B1 (1967), 668.

[55] DESY-Bubble Chamber Collaboration, Contribution No. 8 to this Conference. (See Joos [1968].)

[70] Data Compilation below 1.5 GeV: J. T. Beale, S. D. Ecklund, and R. L. Walker,

Report CTSL-42 CALT 68-108.

[71] Braunschweig, M., Husmann, D., Liibelsmeyer, K., and Schmitz, D., Phys. Letters 22 (1966), 705: Braunschweig, W., Contribution No. 140 to this Conference. (See Joos [1968].)

[72] Alvarez, R., Bar-Yam, Z., Kern, W., Lukey, D., Osborne, L. S., and Tazzari, S., Phys. Rev. Letters 12 (1964), 707.

[73] Elings, V. B., Cohen, K. J., Garelick, D. A., Homma, S., Lewis, R. A., Luckey, P. D., and Osborne, L. S., Phys. Rev. Letters 16 (1966), 474.

[74] Bolon, G. C., Garelick, D., Homma, S., Lewis, R., Lobar, W., Luckey, D., Osborne,

L. S., Switters, R., and Uglum, J., Phys. Rev. Letters 18 (1967), 926. »• [75] Buschhorn, G., Carroll, J., Eandi, R. D., Heide, P., Hiibner, R., Kern, W., Kdtz, U., Schmiiser. P., and Skronn, H. J., Phys. Rev. Letters 17 (1966), 1027; Phys. Rev.

Letters 18 (1967), 571.

[76] Boyarski, A., Bulos, F., Busza, W., Diebold, R., Ecklunk, S., Fischer, G., Rees, J., and Richter, B., Results presented at the Stanford Conference on Electron and

Photon Interactions at High Energies (1967), by B. Richter.

[77] CEA-Bubble Chamber Group, Contribution to the Stanford Conference on Electron and Photon Interactions at High Energies (1967).

[78 1 Bacci, C., Penso, G., and Salvini, G., Nuovo Cimento 44A (1966), 983.

[79] Prepost, R., Lundquist, D., and Quinn, D., Phys. Rev. Letters 18 (1967), 82.

[80] Heusch, C. A., Prescott, C. Y., Bloom, E. D., and Rochester, L. S., Phys. Rev.

Letters 17 (1966), 573, and Contribution No. 284 to this Conference. (See Joos

[1968].)

[81] Allaby, J. V., Lynch, H. L., and Ritson, D. M., Phys. Rev. 142 (1965). 887.

[82] Hauser, M. G., CALT-68-123.

[83] Anderson, R. L., Gabathuler, E., Jones. D., MacDaniel. B. C., and Sadoff. A.. Phys. Rev. Letters 9 (1962), 131.

[84] Peck, C. W., Phys. Rev. 135B (1964). 830.

23
The cross section for photoproduction of nucleonantinucleon pairs, as discussed by Vdovin [1957],

Bushev and Vdovin [1958], Segre [1958], Bertram

et al. [1966], and Earles et al. [1967], is three orders

of magnitude smaller than that for photomeson

production. The threshold for nucleon-antinucleon

pair production varies from 3.75 GeV (4 nucleon

masses) in the field of a proton at rest down to 3.0

GeV (3.2 nucleon masses) for protons moving in a complex nucleus.

2.3. Atomic Photoeffect (Photoelectric

Absorption)

In the atomic photoeffect, a photon disappears

and an electron is ejected from an atom. The electron carries away all the energy of the absorbed

photon, minus the energy binding the electron to the atom. The K-shell electrons, which are the

most tightly bound, are the most important for

this effect in the energy region considered in this

report. However, if the photon energy drops

below the binding energy of a given shell (see

table 2.-3), an electron from that shell cannot

be ejected. Hence, a plot of rpe versus photon energy

exhibits the characteristic “absorption edges” 15 which are shown for lead in figure 2.-1.

Although there have been a few direct measure- ments of Tpe or tk in the region between 0.1 and

3 MeV (see, for example, Latyshev [1947], Seeman

[1956], Hultberg and Stockendal [1959], Titus

[1959, 1965], Bleeker, Goudsmit, and DeVries [1962],

Dowe [1965], and Parthasaradhi et al. [1966]),

the best information in the high energy region is at present mostly theoretical.

Most of the theoretical information has been on

the A-shell component tk (see, for example, Bethe

and Salpeter [1957], Erber [1959], Gavrila [1959],

Pratt [1960a], Nagel [1960], Hultberg et al. [1961],

15 As a note of raution. it should be mentioned that the high-energy side of an absorption edge exhibits a fine struc ture (see, for example. Faessler [1955], Sandstriim [1957], or Azaroff [1963]) such that for light elements, where the X-edge is well below 10 keV,

T,,e can oscillate by as much as a factor of five near the edge. However, for the region above 10 keV considered here, the oscillation is less than 10 percent and will be

disregarded, for practical purposes, in favor of a smooth extrapolation from the monotonic region back to the theoretical edge.

Table 2.-3. Energies of absorption edges above 10 keV.

Values are taken from Bearden [1964-1967] except numbers in parentheses, which are from Fine and Hendee [1955].

Element A-edge

[keV]

Element

K-edge

[keV]

L j

- edge

[keV]

f-II ' <-'dge [keV]

/-II]

' °dge

[keV]

31 Ga 10.368 66 DY 53.793

32 Ge 11.104 67 Ho 55.619

33 As 11.865 68 Er 57.487

34^e 12.654 69Tm 59.38 10.121

35 Br 13.470 70 Yb 61.30 10.490

36 Er 14.324 71 Lu 63.31 10.874 10.345

37 Rb 15.202 72 Hf 65.31 11.274 10.736

38^r 16.107 7 3Ta 67.403 11.682 11.132

39 Y 17.038 74 W 69.508 12.100 11.538 10.200

40 Zr 17.999 75 Pe 71.658 12.530 11.954 10.531 «Nb 18.987 7 gOs 73.856 12.972 12.381 10.868

42Mo 20.004 77 Ir 76.101 13.423 12.820 11.212

43Te 21.047 78 Pt 78.381 13.883 13.272 11.562 44^ 22.119 7jAll 80.720 14.354 13.736 11.921 23.219 soHg 83.109 14.842 14.212 12.286

46pd 24.348 8iTl 85.533 15.343 14.699 12.660

47 Ag

25.517 82 Pb 88.005 15.855 15.205 13.041

4 8 Cd 26.716 83 Pf 90.534 16.376 15.719 13.426

49 In 27.942 84 P° (93.112) (16.935) (16.244) (13.817) 50^n 29.195 85 At (95.740) (17.490) (16.784) (14.215)

siSb 30.486 86 Pn (98.418) (18.058) (17.337) (14.618)

52 Pe 31.811 87 Pr (101.147) ( 1 8. 638) (17.904) (15.028)

53l 33.166 ggRa (103.927) 19.236 18.486 15.444 54Xe 34.59 89 Ac (106.759) (19.842) (19.078) (15.865)

55 GS 35.987 90ph 109.646 20.464 19.683 16.299 5eBa 37.452 91 Pa (112.581) (21.102) (20.311) (16.731)

57 Pa 38.934 92 P 115.62 21.771 20.945 17.165

58 Ce 40.453 93^P (118.619) (21.417) (20.596) (17.614)

5 9 Pr 42.002 94 Pu (121.720) 23.109 22.253 18.054 eoNd 43.574 95 Am (124.876) (23.793) (22.944) (18.525)

ei Pm 45.198 96 Cm (128.088) (24.503) (23.640) (18.990)

62 Sm 46.849 97 Bk (131.357) (25.230) (24.352) (19.461)

63 Eu 48.519 98E^ (134.683) (25.971) (25.080) (19.938)

64 Gd 50.233 99 E^ (138.067) (26.729) (25.824) (20.422)

65Pb 52.002 ioo Fm (141.510) (27.503) (26.584) (20.912)

24
Pratt et al. [1964], Hall and Sullivan [1966], Gorshkov

[1967], Forssner [1968], and Hultberg et al. [1968]),

but some calculations including L- and higher-shell

contributions are now available (see, for example,

Pratt [1960b], Gavrila [1961], Ailing and Johnson

[1965], Matese and Johnson [1965], Schmickley and

Pratt [1967], Brysk and Zerby [1968], and the ex- tensive results by Rakavy and Ron [1967] which in- clude almost all the higher shells and cover the range

1 keV to 2 MeV). Uncertainties in ta due to screening

and other effects are probably about 2 percent over

the region from 0.2 to 100 MeV. However, the uncertainty of the total rpe (= ta + tl + tm + • • •) is probably more like 3 to 5 percent because of much

poorer knowledge of the outer shell contribution,

which amounts to as much as \ of Tk for the heavier

elements.

Extensive theoretical results for the photoeffect

in the soft x-ray region (0.1 to 2 keV) are now becoming available (Cooper [1962, 1964], Fano and

Cooper [1965], Manson and Cooper [1968], and

Fano and Cooper [1968]). The work of these authors

is based on the solution of the Schrodinger equation

in the dipole approximation, using self-consistentfield wave functions. Numerical results are given

for the photoelectric absorption in various outer

atomic subshells, with emphasis on the detailed

structure of the cross section near threshold. These

papers also provide a survey of recent experimental

results in the soft x-ray region obtained with synchrotron light and other soft x-ray sources.

In the energy range 10 keV to 0.2 MeV, although

the Rakavy-Ron calculations are in considerably

better agreement with experiments than are previous theoretical results, present estimates of rpe in

this region still rely heavily on high-precision total

attenuation coefficient measurements such as those

of Hahn [1934], Cuykendall [1936], Jones [1936],

Laubert [1941], Bearden [1958, 1966], Deslattes

[1958], Wiedenbeck [1962]; McCrary, Plassmann

et al. [1967], and others.

From these measurements “experimental”

values of rpe are obtained by subtracting theoretical

estimates of the scattering cross sections aB

cD+crR

from the observed values of <rtot. In the present tabulation in the region 10 keV ^

= E < 100 keV, we follow the subtraction procedure, using re-evaluated experimental crtot data and

scattering cross sections (ct^ + ctr) frem Storm and

Israel [1967], except for uranium for which Tpe is taken directly from Rakavy and Ron. Values of

Tpe for tin, tungsten and lead in this energy were

taken from a computer-assisted subtraction and

analysis in progress (McMaster, Del Grande et al.) and hence constitute a further updating of rpe , crtot and related quantities from values given by Hubbell

and Berger [1968].

At higher energies we present revised values for Tpe which take into account not only the numerical

calculations of rA by Pratt et al. [1964] used by

Davisson, but also the extensive rA calculations by

Hultberg et al. [1968]. Although we use the results

of Gavrila [1959] and Pratt [1960a] in the high energy

limit, we ignore, on the advice of Pratt, the extrapolated values of rA in table 2 in Pratt [1960a] for

Z/137 = 0.4 and 0.6 at energies E = 2, 3, 5 and 10

MeV.

As can be seen in table 2.-4, rpe varies over a wide range of magnitudes, decreasing with in- creasing energy except at the edges and increasing

with atomic number. To make interpolation more

reliable and convenient, it is important to scale

these values in some way. It was found that the

product Tpe ‘ (£[MeV])3 • Z

-4- 5 (above or between

absorption edges) varies by less than a factor of

three over the range Z = 1 to 92 and E= 10 to 500

keV, and the product rpe • £[MeV] • Z

-4 5 by less

than a factor of ten for Z— 1 to 92 and £' = 500 keV

to 100 MeV. Values of these products are presented

in table 2.-5.

For some purposes, particularly in machine computations, simple empirical formulas are desirable.

An empirical formula for the A-shell photoeffect

above 0.2 MeV is

n=\

ci n -P b„Z

1 -T c,iZ

E~Pn

b 1

•> atom ( 2.- 1 )

Table 2.-4. Total atomic photoeffect cross section ( b/atom), indicating the range of magnitudes

Photon Tpe energy [MeV]

«c 2sFe 82Pb

0.01 3.93 • 10' 1.59 • 104 O O

K-, L-edges

0.10 2.16 • 10-2 1.89 • 10' 1.76 • 103 1.0 2.89 • 10~5 3.38 • 10-2 6.39 • 10° 10 1.12 • lO-6 1.19 10-3 1.78 • 10-' 100 1.01 • 10-7 1.04 • 10-4 1.41 • lO-2

for which the parameters an , bn , cn and pn are given

in table 2.-6. This formula goes to the Pratt [1960a]

numerical values in the high energy limit and

reproduces the combined experimental and theoretical data fairly well. Deviations from these data over most of the range 0.2 MeV < E < oo and

13 <Z ^ 92 are less than 1 to 2 percent, and in no

case do they exceed 5 percent over this range.

For other empirical formulas see Biggs and Lighthill [1967].

Total Tpe values, such as those given in tables

2.-4 and -5, can be obtained approximately by

multiplying rK by the ratios t^/tr from table 2.-7.

Hultberg [1959] suggested that, for practical purposes, this ratio is energy-independent, and the

values in table 2.-7 are those derived by Davisson

[1965] from the compilation by Kirchner [1930]

of experimental A-edge data.

For elements iH through 53I the Davisson-Kirchner

ratios agree within 2 percent with the latest Aedge ratios in the compilation in progress by

335-734 0-69—5 25
Table 2.-5. Scaled values of the total photoelectric cross section r,*

Photon

energy [MeV]

iH a eC , 3ai 2 oCa •>eFe 2»Cu

Tpe [b/atom] • (£[MeV]) 3 • Z~4.5 . 109

0.01 9.13 12.4 11.1 8.87 6.82 6.17

0.02 6.71 10.1 10.6 9.25 7.93 7.27

0.03 5.59 8.50 10.1 9.13 8.29 7.83 0.05 4.45 7.60 9.29 8.79 8.37 8.11 0.10 3.32 6.80 8.21 8.23 8.11 8.09

0.20 2.62 5.77 7.40 7.91 8.00 7.98

0.30 2.44 5.49 7.24 7.92 8.09 8.15

0.5 2.56 5.88 7.80 8.70 9.07 9.22

Tpe[b/atom] £[MeV] • Z

1 cn O

CO

0.5 10.2 23.5 31.2 34.8 36.3 36.9

1.0 3.98 9.10 12.3 13.8 14.6 14.8 2 2.36 5.42 7.26 8.11 8.42 8.56

3 1.99 4.55 6.03 6.67 6.89 7.00

5 1.75 3.97 5.22 5.70 5.86 5.91 10 1.58 3.53 4.64 5.02 5.11 5.12 100 1.43 3.19 4.11 4.41 4.45 4.46

00 1.41 3.15 4.04 4.33 4.37 4.39

Photon Absorpenergy 4 >Mo soSn 74 W c

r

92 U tion [MeV] edges

Tpe [b/atom] • (£[MeV])3 Z 45 • 109

0.01 0.663 0.619 0.108 0.108 0.0995

0.02 0.730 0.714 0.615 0.560 0.314

Mil

0.03 6.00 4.88 0.693 0.640 0.612 Mi, 1 0.05 6.74 5.70 0.779 0.744 0.740

0.10 7.29 6.57 4.93 4.29 0.919 K

0.20 7.66 7.28 6.06 5.70 5.21 0.30 8.06 7.83 6.91 6.79 6.25

0.5 9.50 9.91 8.77 8.92 8.44

Tpe [b/atom] • £[MeV] • 2

'-4.5 . 109

0.5 38.0 39.6 35.1 35.7 33.8

1.0 15.5 15.6 15.0 15.6 15.1 2 8.77 8.73 8.25 8.64 8.26

3 7.10 7.11 6.49 6.70 6.51 5 5.92 5.86 5.19 5.30 5.11 10 5.04 4.93 4.28 4.35 4.19 100 4.30 4.16 3.56 3.44 3.49

00 4.22 4.11 3.50 3.39 3.44

a iH has only one A^-shell electron, hence values in this column contain an

additional factor of two to allow smooth interpolation to adjacent elements.

26
1 able 2.-6. Parameters for empirical fit [eq {2.-1)] to the K-shell photoelectric

cross section rK .

n «» K c n Pn

1 1 . 6268 - 10- 9 - 2 . 683 - 10- 12 4 . 173 - 10“ 2

1 2 1 . 5274 - 10- 9 - 5 . 110 - 10- 13 1 . 027 - 10“ 2 2

3 1 . 1330 - 10" 9 - 2 . 177 - 10- 12 1 <N 0 O

cm’ 3.5

4 - 9.12 • 10 -11 0 0 4

Table 2.-7. The experimental ratio (Tpe/TK ) K. edge as derived from Kirchner [1930] by Davisson [1965].

Element { Tpe/ TK)A" -edge Element ( Tpel rK)K-edge

iH 1.00 20^ a 1.11

4 Be 1.03 2fiFe 1.12

6c 1.04 29 Cu 1.13 7N 1.05 42 Mo 1.16

8 o 1.06 50 Sn 1.18 nNa 1.075 53 1 1.19

12Mg 1.08 74W 1.20

13AI 1.09 79^ 1.22

14 Si 1.09 8 2 Pt> 1.22

18 Ar 1.10 92 u 1.235 1|P - 1.10

McMaster, Del Grande, et al. For the heavier ele- ments 74W, 82 Pb, and 92 U some energy-dependence

in the ratio TpelTK is included, based on the RakavyRon results, from the K-edge to about 1 MeV where

the ratio joins smoothly with the values from table

2.-7.

Although not truly a smooth function of Z because

of irregularities in the higher electron shell structure, the ratios in table 2.-7 can be represented

with an accuracy of ± 2 to 3 percent by the empirical

fit

TpelTK - 1 + 0.01481 ln2Z - 0.000788 In3 Z. (2.-2)

ton (double Compton effect) and radiative cor- rections associated with emission and reabsorption

of virtual photons. These corrections are discussed

later in this section.

The relation between photon deflection and

energy loss for Compton scattering, assuming the

electron to be initially free and stationary, is determined from conservation of momentum and

energy between the photon and the recoiling electron (Compton [1923], Debye [1923]). This relation can be expressed as

E' 1 E ~ 1+ {E/mc2

) ( 1 — cos 6) ’ (2 “

3)

where E and E' are the energies of the photon

before and after the scattering, me2 is the electron

rest energy and 6 is the photon deflection angle.

In transport calculations it is often convenient

to use, instead of the energy variable, the wavelength of the photon in Compton units,

X = mc2IE = 0.51 10/£ [MeV]. (2.-4)

The increase in wavelength associated with a Compton scattering event in these units is

2.4. Scattering X' — X = 1 — cos 6 , (2.-5)

2.4.1. Compton Scattering. Klein-Nishina Formula

In Compton scattering, a photon collides with an

electron, loses some of its energy and is deflected

from its original direction of travel. The basic theory

of this effect, assuming the electron to be initially

free and at rest, is that of Klein and Nishina [1929].

This theory has been well confirmed experimentally

(see, for example, Meitner and Hupfeld [1930],

Hofstadter and McIntyre [1949], Cross and Ramsey

[1950], French [1965], Sahota et al. [1966], and

Gittelman et al. [1968]). Predictions of this theory

have been summarized and extensive tabulations

have been given by Nelms [1953], Burton [1953],

and Evans [1958, 1968],

Over most of the region in which Compton scat- tering is a major part of the total cross section, the

Klein-Nishina theory is directly applicable. Departures from it occur at low energies because of electron binding effects, and at high energies because

of the possibility of emission of an additional phowhere X and X' are the Compton wavelengths of the

photon before and after the deflection. The maximum shift in wavelength, occurring for a deflection

6= 180°, is two Compton units.

For unpolarized photons the Klein-Nishina

angular distribution function per steradian of solid

angle D is

d<Jc N

(9)1dCl = irf [ 1 + A(1 — cos 6) ]~2 X

X 1 + cos2 6

k

2

( 1 — cos 6)

2

1 + A(1 — cos d) _ cm2/electron

steradian

(2.-6)

in which k is the reciprocal of the incident photon

Compton wavelength

k= l/X = £’/mc2 = £’[MeV]/0.5110. (2.-7)

27
Integration of eq. (2.-6) over all angles gives the

total Klein-Nishina cross section

KN — « ,f

1 + ^ f 2(1 + A) In (1 + 2A)1

(T c 2 11 / e

1 ^2 1 + 2A A

In (1 + 2k) 1 +3A ] cm2 2k (1 + 2A) 2

J electron

This formula is not particularly suitable for

evaluation of a^ N at low energies because of near- cancellation between the logarithmic and purely

algebraic terms. For example, using 8-place arithmetic, errors of 1 to 2 percent will occur at 10 to 15 keV. Values of cr$N in table 2.-8 were computed

in double-precision arithmetic and we bebeve them

correct to the 5 signibcant bgures given.

For A 1, eq. (2.-8) can be expanded as ^=^^JTTw{1 + 2k+

-s k^ --2 k3+ h

,

8 4 7.6 _L_ __ 7-7 _

105 105

cm2 electron

(2.-9)

Using only terms through A

2

, the value of crfN

from eq. (2.-9) at 10 keV is within 0.001 percent of

that from eq. (2.-8). In the low-energy limit (A—+0)

this expression becomes the classical Thomson

cross section. 16

77-r| = 0.6652 • HU24 cm2 electron ( 2.- 10)

For k > 1, a useful approximation is (Heitler [1954]):

n-KN °C 77 ri 1 + 2 In (2 k)

2k

cn+

electron ( 2 .- 11 )

which is equivalent to eq (2.-8) as k-^>°°, and

gives a result differing by +0.6 percent at 100

MeV and by + 0.09 percent at 1000 MeV.

In addition, Hastings [1955] has fitted eq (2.-8)

by the empirical formula

cTcN ~ <j'c ~ 7rr|

/ C^ + C2 ^

2 + C3 ^ \

\1 + cfi£ + d-2^2 + d^)

cm2 electron

(2 .- 12 ) where £=1/(1 + 6A). The parameters have the

values

6=0.222037

Cl = 1.651035 d\ -— 12.501332

c2 = 9.340220 d2 = - 14.200407

c, = - 8.325004 d3 = 1.699075

For photon energies 0 ^ E ^ 1 MeV values of of

are within 0.1 percent of <t£n

, and for E ^ 100 MeV

16 However, extrapolation to this limit [cr£'v

]*..o = o+ is valid only for a free electron;

for bound electrons [ot]a.-o = 0.

are within 1.3 percent. However, at 1 GeV values of of are less than of‘v by 17 percent, and at 100 GeV

less by 44 percent.

Also listed in table 2.-8 are values of the Compton

energy transfer fraction f$N

(for use in computing

p,Jp and pjp but not penlp) where

f

K

cN =a(TK

cN

l(T

K

cN. (2.-13)

The numerator acrgN is obtained by weighting the

right-hand side of eq (2.-6) by the fraction of the

photon energy transferred to the recoil electron.

This fraction is

k-k’ ^

A(1 — cos 6) k 1 + A(1 — cos 6)

(2.-14)

where A' is the energy of the deflected photon.

Combining eq (2.-6) with eq (2.-12) we have

1 A(1 — cos d)

dacr£N{d)ldn

[1 + k( 1 - cos 0)]

3

X 1 + cos2 6

A

2 (l — cos d)2

1 + A:(l — cos 6)

cm2 /electron

steradian

(0

Integration of the right-hand side of eq (2.-15) over

all angles yields:

<,0-^= 2777f

4A-2

2(1 + A-)2 1 + 3A- (l+A-)(2A-2 -2A—1)

A-2 (l + 2k) (1 + 2k)2 k

2(l + 2k)2

1 + A: 1,1

3(1 + 2A)3 V A-3 2k 2k3cm

electron

In (1 + 2A-)

(2.-16)

At low photon energies eq (2.-16) suffers from

loss of precision similar to that in eq. (2.-8). An

expansion of eq (2.— 16) useful for k 1 is

aO~(KN — _

1

777'f (1 + 2A')3

9 3 A + ?A2 + ? A-3

— — k

4 + — A-5 + — A

6 — — A

7 +

35

A +

35

A +

35

A 15

A +

cmelectron (2.-17)

2.4.2. Electron Binding Corrections to Compton Scattering. Rayleigh Scattering

In gamma ray transport theory and shielding

calculations, electron binding effects have usually

been either disregarded or treated very approximately by combining them with Rayleigh scattering.

The justification for this treatment is that for low-Z

28
Table 2.-8. Compton scattering cross section crc for a free electron.

These values were evaluated using eq. (2.-8) and modified by the Mork [1968] combined radiative and double-Compton corrections Acrw here listed.

The average fraction of photon energy transferred to the electron, /c, is also listed.

Photon crP Aof crc = crf‘v fF Photon o-r Aof crc = crF fF

energy + Aof energy + Acr£t MeV b/electron 6/ electron b/electron MeV b/electron b/electron b/electron 0.010 0.64039 (0.00000) (0.6404) 0.01876 40 0.017462 0.00012 0.01758 0.76004

.015 .62888 (.00001) (.6289) .02758 50 .014565 .00011 .01468 .76922

.02 .61791 (.00001) (.6179) .03605 60 .012541 .00010 .01264 .77624

.03 .59742 (.00002) (.5974) .05204 80 .0098806 .000090 .009970 .78650

.04 .57867 (.00002) (.5787) .06688 100 .0081976 .000082 .008280 .79385

.05 .56144 (.00003) (.5615) .08071 150 .0058182 .000075 .005893 .80600

.06 .54555 (.00003) (.5456) .09363 200 .0045506 .000070 .004620 .81379

.08 .51722 (.00004) (.5173) .11713 300 .0032086 .000067 .003276 .82378

.10 .49269 (.00005) (.4927) .13800 400 .0024992 .000066 .002565 .83024

.15

.2

.3

.44355

.40643 .35340

(.00007)

(.00008)

(.00010)

(.4436)

(.4065)

(.3535)

.18156

.21635

.26965

500

600

800

.0020568

.0017531 .0013609

.000067

.000065 .000059

.002124 .001818

.001420

.83493 .83858

.84402

.4

.5.6

.8

.31664

.28913

.26747

.23493

(.00013)

(.00014)

(.00016)

(.00018)

(.3168)

(.2893)

(.2676) (.2351)

.30962 .34136

.36751 .40866

1000 .0011174 .000051 .001168 .84799 1500

2000

3000

.00077951 .00060303 .00041929(.0000362)

(.0000283)

(.0000197)

(.0008158)

(.0006314)

(.0004390)

.85471 .85913

.86492

.21118 (.00020) (.2114) .44004 4000 .00032365 (.0000152) (.0003389) .86874

1.0 5000 .00026462 (.0000124) (.0002771) .87156

1.5 .17156 (.00023) (.1718) .49468 6000 .00022439 (.0000105) (.0002349) .87378

2.0 .14634 (.00024) (.1466) .53084 8000 .00017288 (.0000081) (.0001810) .87713

3.0 .11508 (.00024) (.1153) .57732

.60693

10 000 .00014115 (.0000066) (.0001478) .87960 4 .095963 .00024 .09620 15 000 .000097550 (.00000458) (.0001021) .88386

5 .082856 .00022 .08308 .62799 20 000 .000074997 (.00000352) (.00007852) .88670

6 .073221 .00020 .07342 .64400 30 000 .000051721 (.00000243) (.00005415) .89047

8 .059877 .00018 .06006 .66720 40 000 .000039708 (.00000187) (.00004157) .89300

10 .050983 .00017 .05115 .68356 50 000 .000032335 (.00000152' (.00003385) .89488

15 .037708 .00015 .03786 .71004 60 000 .000027333 (.00000128) (.00002862) .89637 20 .030246 .00014 .03039 .72656 80 000 .000020958 (.00000099) (.00002194) .89864 30 .021995 .00013 .02212 .74713 100 000 .000017051 (.00000080) (.00001785) .90033

elements the K-shell binding energies are low in

comparison with the photon energies considered,

while for high-Z materials with substantial K-shell

binding energies these electrons are a small fraction of the total. The scattering of 0.662-MeV photons by K-shell

electrons of various heavy atoms has been measured

by Motz and Missoni [1961], Sujkowski and Nagel

[1961], and Yarma and Eswaran [1962]. The ratio

of the observed differential cross section dac(6)/dCl

to the Klein-Nishina differential cross section

dcr£N

{6) / dfl [eq (2.-6)] for tin and gold is given in

figure 2.-2, based on data of Motz and Missoni.

It is seen that for small angles the effect of binding

is to decrease the cross section, whereas for large

angles an increase occurs. The decrease and in- crease tend to compensate each other, so that for

the cases shown in figure 2.-2 the integrated cross

sections Or and cr£w [eq (2.-8)] agree within ex- perimental error. Similar measurements by Dowe

[1965] on thallium K-shell electrons suggest such

compensation may extend down to 0.122 MeV.

The usual Klein-Nishina cross section, which assumes that the target electron is free and at rest,

has been generalized by Jauch and Rohrlieh [1955]

to the case where the electron is free but in motion.

Motz and Missoni used this generalized theory to interpret their data at large angles. Their results,

obtained by averaging over the appropriate electron velocity distributions, are shown as the solid curves in figure 2.-2.

Figure 2.-2. Ratio of observed Compton scatter- ing from K-shell electrons (Motz and Missoni

[1961]) to Klein-Nishina theory, eq. (2.-6). The solid curves are extrapolations (by Motz and Missoni) to 0 = 180° using theory of Jauch and Rohrlieh [1955] which considers

electron velocities.

29
The binding corrections have usually been treated

in the impulse approximation, taking into account

not only the K-shell, but all the atomic electrons.

This involves applying a multiplicative correction,

the so-called “incoherent scattering function,”

S(q , Z), to the differential Klein-Nishina formula

[eq. (2.-6)]

dcrc (d) /dCl — S(q, Z)dcrZN (d)/dn. (2.-18)

The momentum transfer q is related to the photon

energies and deflection angle 6 according to q=yk2 + k' 2 -2kk' cos 0. (2.-19)

or, using eq (2.-3),

q — 2k sin |

• Vl + (

A

2 + 2k) sin2 9/(1 + 2k sin2 0),

( 2 .-20)

where q is in me units and k and k' are the photon

energies (in me2 units) before and after the deflection. Since binding effects are important mainly

for small momentum transfers, the approximation

k — k' ~ 0 is usually made, so that

Q

q ~ 2k sin -• (2.-21)

The incoherent scattering function S{q , Z) represents the probability that an atom be raised to any

excited or ionized state as a result of a sudden impulsive action which imparts a recoil momentum

q to an atomic electron. For K-shell electrons only,

S(q , Z) would correspond to the ratios shown in

figure 2.-2.

Rayleigh scattering is a process by which photons

are scattered by bound atomic electrons and in

which the atom is neither ionized nor excited. The

scattering from different parts of the atomic charge

distribution is then “coherent,” i.e., there are interference effects.

This process occurs mostly at low energies and

for high Z materials, in the same region where

electron binding effects influence the Compton

scattering cross section. Indeed, if each atomic

electron contributed independently to the cross

section, the onset of Rayleigh scattering for low

momentum transfer would exactly compensate for

the reduction of Compton scattering due to binding.

However, the various atomic electrons contribute

coherently to Rayleigh scattering, greatly increasing the probability for the process.

We shall restrict the following discussion to Rayleigh scattering in the narrower sense, in which the

coherence extends only over the Z electrons of

individual atoms. This coherence can also extend

to electrons of different atoms to give more striking

interference effects, such as Bragg-law diffraction

by crystal lattices.

Experimental studies of Rayleigh scattering have

been made by Moon [1950], Storruste [1950], Wilson

[1951], Mann [1956], Schopper [1957], Storruste and

Tjom [1958], Anand, Singh, and Sood [1963, 1964],

and Nath and Ghose [1964]. In interpreting these

measured data, one must also take into account

other, much less probable, elastic or quasi-elastic

scattering processes, such as Thomson scattering

by the nucleus, nuclear resonance scattering, and

Delbriick scattering (see sec. 2.2.), in addition

to Rayleigh scattering. Theoretical information on

these processes, including constructive interfer- ence effects between the different processes, has

been summarized by Moon [1950] and by Jauch and

Rohrlich [1955].

Detailed Rayleigh scattering calculations have

been made by Levinger [1952] for K-shell electrons

of tin, and by Brown et al. [1954—1957] for K-shell

electrons of mercury. In practice, it is necessary to consider the charge distribution of all Z electrons

at once. This can be done approximately through

use of an “atomic form factor” F(q , Z) based on

the Thomas-Fermi, Hartree, or other model of the

atom. The square of this form factor, [F(q, Z)]2

, is the probability that the Z electrons of an atom

take up a recoil momentum, q, without absorbing

any energy. In this process q is well-represented

by (eq (2.— 21) since it is assumed that k — k' = 0. The above probability [F (q , Z)]2

, is combined

with the low-energy limiting form of the KleinNishina differential formula [eq (2.-6)] to give the

differential Rayleigh scattering cross section for

unpolarized photons:

r

2 dcrR{d)ldCl — (1 + cos 2 6)[F{q, Z)

]

2

( 2 .-22)

Calculations of S(q, Z ) and F(q, Z) depend

on knowledge of the atomic wave functions; they can be done analytically for hydrogen and, for

other atoms, in various approximations based on

the Thomas-Fermi, Hartree, or other models. The

procedures used in such calculations have been

discussed by White-Grodstein [1957] for S(q, Z)

and by Nelms and Oppenheimer [1955] for F(q, Z).

Evaluations of crB

( P have until recently used

S{q , Z) values based on the Thomhs-Fermi model. 17 However, Cromer and Mann [1967] have now provided Hartree-Fock S(q , Z) data for the 39 spherically symmetric atoms. Corresponding Hartreemodel tabulations of F{q, Z) have been given by

Hanson et al. [1964] and by Cromer and Waber

[1965].

17 In addition to the Grodstein [1957) (and Davisson [1965]) results, extensive evalu- ations of cr

BL> based on the Thomas-Fermi model have been given by Brown [1966b)

1 ^ Z ^ 100, 1 keV to MeV and by Veigele [1965): 1 ^ Z 106, 0.1 keV to 1 MeV.

cm2/atom

steradian

30
Storm and Israel [1967] have used S(q, Z) values

of Cromer and Mann (and additional data from

Cromer) and F(q, Z) values from Hanson et al. to calculate cr?P and ctr (integrating over equations (2.-18) and (2.-22), respectively) for all elements Z = 1 to 100 and energies ranging up from

1 keV. Figure 2.-3 shows ratios of these values of

crfP (excluding interpolated values) to values given

by the Klein-Nishina formula [eq (2.-8)] for photon

energies of 1, 10, and 100 keV.

Cumulative angular distributions of ctr, based

on values of F(q, Z) from Nelms and Oppenheim

[1955], are displayed in figure 2.-4 forC, Fe, and

Hg. At high energies it is seen that Rayleigh scat- tering is confined to small angles (at 1 MeV more

than half the photons are scattered by less than

5°). At low energies, particularly for high-Z materials, the angular distribution is much broader.

Here, however, the Rayleigh scattering cross

section is small in comparison with photoelectric

absorption. On the basis of these considerations,

Rayleigh scattering is frequently disregarded in

gamma ray transport theory and shielding calculations (Fano, Spencer, and Berger [1959], Goldstein and Wilkins [1954]).

Rayleigh scattering can, however, be of importance in interpreting “narrow beam” attenuation coefficient measurements, depending on the

angular resolution of the apparatus. A useful simple criterion for judging the angular spread of Rayleigh scattering is (Moon [1950], Evans [1958]):

6C = 2 arcsin

"0.0133Z1/3 £[MeV] _ (2.-23)

where 6C is the opening half-angle of a cone containing at least 75 percent of the Rayleigh-scattered

photons (see also fig. 2.-4).

The sum (afD + ctr), rather than a

BD and (Tr

individually, has been tabulated in previous compilations (White-Grodstein [1957] and Davisson [1965]A

because this sum is less sensitive to errors from

approximations in the theory. In this report, since

present theory still relies on the impulse approximation and neglects initial motion of the electrons, we

retain the White-Grodstein format in our tables in

section 3. That is, in tables 3.-1 to 3.-36 we list the sum (ct^P + ctr ) (or “scattering, with coherent”

in the notation of White-Grodstein and Davisson),

in which crBA and ctr are the values given by Storm

and Israel [1967]. Also, in table 2.-9 we give these

results in the form of a percentage correction to the total “without coherent” cross section, <xtot , given in table 1.-4, viz

(<t

bd + (Tr ) — q

-P

'

O’tot x 100%. (2.-24)

Figure 2.-3. Ratio of the bound-electron Compton collision cross section, cr'f’ calculated by Storm and Israel [7967] to that for free electrons, cr* v

, evaluatedfrom

the Klein-Nishina formula.

31
At energies above 100 keV the sum (<Xc° + ctr)

given by Storm and Israel (based entirely on the

Hartree model) is within 1 percent of that given by

Figure 2.-4. Opening half-angle, 0 , of cone containing 25

percent, 50 percent, 75 percent, and 95 percent, respectively,

of photons Rayleigh-scattered from C, Fe, and Hg.

The function 6C (Eq. 2.-23) is included for comparison.

White-Grodstein and Davisson (based mostly on the

Thomas-Fermi model). However, between 10 and

100 keV there are differences of as much as 10

percent in either direction.

2.4.3. Radiative Corrections. Double Compton Effect

The radiative correction (of the order 1/137) is associated with emission and reabsorption of vir- tual photons whereas in the double Compton effect an additional real photon, usually very low in energy,

is emitted.

Because of the predominance of pair production

at high energies, experimental data on these effects are difficult to obtain and the existing experiments

by Cavanagh [1952], Bracci et al. [1956], Theus

and Beach [1957], and Burdet [1963] have large

uncertainties. Hence, the information is primarily

theoretical and has only recently become suffi- ciently quantitative for inclusion in tabulations.

We have relied on the recent theoretical results of

Mork [1968] who made a calculation combining the

radiative correction o-(rad. corr.) with the cross

section cr(double Compt.) for the double Compton

effect.

The differential formulas (Brown and Feynman

[1952], Mandl and Skyrme [1952]) for the two

effects each contain an “infrared divergence.”

These divergencies are of opposite sign, and in the

combined calculation they cancel each other to give a physically meaningful result.

The Mork correction, which must be added to the Klein-Nishina cross section,

Actc = ofdouble Compt.) + cr(rad. corr.)

(2.-25)

is given in table 2.-8 separately and in the combination with o-p. It is seen that the contribution

of Aerf to or is ~ 0.25 percent at 4 MeV, rising to ~ 1 percent at 100 MeV and — 5 percent at 1000

MeV.

Table 2.-9. Percentage by which crtot or pip is increased if coherent scattering effects are included.

Based on data by Storm and Israel [1967 1 taking into account Rayleigh scattering and the effect of electron binding on Compton scattering

Photon

energy [MeV].H eC 13 ai 2oCa 2sFe 2 S)Cu 42 Mo soSn 74 W 82 Pb 92 U

Absorption

edges

0.01 -.2 5.2 1.9 0.9 0.7 0.6 2.6 1.8 4.8 3.8 3.1 0.02 -.1 10.7 5.3 2.7 1.9 1.7 8.0 5.8 3.0 2.7 3.7

T-iii-edge - Z.n _ i-edges 0.03 0 9.0 8.4 4.6 3.2 2.8 1.8 1.6 5.2 4.5 3.7 0.05 0 4.7 10.6 7.9 5.7 5.1 3.2 2.8 9.4 8.1 6.6 0.10 0 1.4 5.8 8.4 8.2 8.0 5.9 5.0 3.4 3.3 11.7

• A-edge

0.20 0 0.5 2.0 3.8 5.0 6.0 7.2 6.9 5.3 4.9 4.4 0.30 0 < 0.5 1.0 2.0 3.1 3.6 5.8 6.2 5.8 5.4 5.0 0.50 0 < 0.5 <0.5 0.9 1.3 1.7 2.8 3.8 5.0 4.8 4.7

1.0 0 < 0.5 <0.5 < 0.5 < 0.5 0.5 1.1 1.2 2.2 2.6 2.8

2.0 0 < 0.5 <0.5 < 0.5 < 0.5 < 0.5 < 0.5 < 0.5 0.8 1.1 0.9

3.0 0 < 0.5 <0.5 < 0.5 < 0.5 < 0.5 < 0.5 < 0.5 < 0.5 < 0.5 0.6

32
2.5. Electron-Positron Pair Production

2.5.1. General Discussion

In this effect, which is the most likely photon

interaction at high energies, a photon disappears in

the field of a charged particle, and an electronpositron pair appears. The cross section k„ for pair

production in the field of a nucleus varies as k,,~Z2

. (2.-26)

The cross section Ke in the field of all the atomic

electrons varies as Z times the square of the unit

charge, or,

Ke ~Z, (2.-27)

and is of minor importance except for the lowest-Z

materials. The ratio Ke/Kn can be set equal to r)/Z

where r) is a slowly varying function of Z and E,

generally close to one, and will be discussed later

in this section.

There have been a number of experimental

studies in which the k„ and Ke cross sections have

been isolated to some extent. For k« data see, for

example, the results by Standil and Shkolnik

[1958], Singh et al. [1959], Rao et al. [1968],

Plimpton and Hammer [1963], Yamazaki and Hollander [1965], and Titus and Levy [1966], and for

Ke data, the results of Criegee [1960] , Sandhu

et al. [1962], and Frei et al. [1964]. Earlier results

for both cross sections have been summarized by

Davisson [1965]. There are additional data which

depend on subtraction of the Compton cross section

cfc from measured total cross sections crtot (see, for

example, Jones [1959, 1960], Wyckoff and Koch

[1960] ) , but the recent Mork correction Acre to cr$N

requires slight revisions in these estimates. These

data still leave wide gaps or contain substantial

uncertainties. For tabulations we rely heavily on

theory, as discussed in the remainder of this section.

2.5.2. Pair Production in the Field of the Nucleus

The threshold for this effect is equal to the

combined rest energies of the created pair 2 me2 (=1.022 MeV). The cross section rises monotonically from zero at threshold, varying approximately

linearly with E, until it levels off near 50 MeV for

high-Z materials and at higher energies for low-Z

materials. At 100, 1000 and 10,000 MeV the cross

section is roughly 75 percent, 95 percent, and 99

percent, respectively, of its high-energy limiting

value.

The values of k„ we present in table 2.-10 and in

section 3 have been revised to incorporate new

screening calculations by Sorenssen [1965, 1966]

and the Mork-Olsen [1965] radiative correction.

However, it is useful to describe first the procedures

and sources of information for the well-established

Table 2.— 10. Scaled cross section kJZ2 for pair production

in the field of the nucleus, based on (Born) evaluated by

Maximon [1968], screening ( Hartree-Fock-Slater) estimates by

Sorenssen [1965, 1966], the Mork-Olsen [1965] radiative correction, and corrections to the Born approximation by empirical

adjustment of the Coulomb correction.

Units are [b/atom]/Z 2

. For unsealed k„ values up to 100 GeV, see tables in section 3.

Photon

energy

[MeV]

iH 6 ^ 13^1 20 Ca 26^e to <£> Oc

1.022 0 0 0 0 0 0

1.5 4.35- 10" 5 4.37- 10“ 5 4.45- 10“ 5 4.62- 10- 5 4.81- 10“ 5 4.92- 10“ 5 2 1.79- lO" 4 1.79- 10- 4 1.81- 10“ 4 1.84- lO" 4 1.88- lO" 4 1.90- 10“ 4 3 5.12- 10“ 4 5.11- 10“ 4 5.13- lO’ 4 5.16- lO' 4 5.19- 10- 4 5.21- 10-4

5 1.1 1

• 10“ 3 1.11- lO" 3 1.11-10-3 1.11- lO” 3 1.10- lO” 3 1.10- lO" 3

10 2.15- 10“ 3 2.14- lO" 3 2.12- lO" 3 2.10-10-3 2.09- lO -3 1 CO <N 0 00 0 20 3.30- lO' 3 3.28- lO- 3 3.23- lO” 3 3.20- lO" 3 3.17- lO” 3 3.15-10- 3 30 3.99- lO" 3 3.95- lO” 3 3.88- lO” 3 3.84- lO- 3 3.79- lO- 3 3.78-10-3

50 4.87- lO" 3 4.76- lO" 3 4.67- lO" 3 4.60- lO" 3 4.54- lO’ 3 4.52- lO" 3 100 6.05- lO” 3 5.76- lO” 3 5.61-10- 3 5.50- lO’ 3 5.42-10-3 5.39-10-3

Photon

energy

[MeV]

42 M° 50^ n 74W 82 Pb 92 U

1.022 0 0 0 0 0

1.5 5.55- 10- 5 6.01 • 10- 5 7.67- 10“ 5 8.27- 10“ 5 9.03- 10" 5 2 2.02- 10- 4 2.10- lO" 4 2.42- 10- 4 2.53- lO' 4 2.68- lO" 4

3 5.33- 10- 4 5.42- 10~ 4 5.74- lO' 4 5.86- 10~ 4 6.01 • 10- 4

5 1.10- lO” 3 1.10- lO" 3 1.09- lO' 3 1.08- lO- 3 1.08- lO’ 3

10 2.03- lO- 3 1.99- lO- 3 1.87- lO" 3 1.83-10"3 1.77- lO" 3 20 3.06- lO" 3 3.00-10-3 2.79- lO" 3 2.72- lO’ 3 2.62- lO" 3 30 3.67-10-3 3.59- 19-3 3.35- lO' 3 3.27- lO” 3 3.16 - lO" 3 50 4.38- lO" 3 4.29- lO" 3 4.00- lO- 3 3.90- lO' 3 3.78- lO" 3 100 5.20- lO" 3 5.08-10-3 4.74-10-3 4.63-10-3 4.48- lO- 3

335 -734 0-69—6 33
White-Grodstein [1957] compilation, and then note

how the present evaluation differs.

White-Grodstein used as an initial approximation the Bethe-Heitler theory done in the Born

approximation (Bethe and Heitler [1934], Heitler

and Sauter [1933], and Racah [1934, 1935]). In the

energy region E < 5 MeV, where screening effects are negligible, cross section values for an un- screened nucleus were obtained from a formula of

Hough [1948], which fits the Bethe-Heitler results

to 0.1 percent. For E>> 5 MeV the differential

Bethe-Heitler formula, including screening based

on the Thomas-Fermi model of the atom (Bethe

and Heitler [1934, eq (36)], also Bethe and Ashkin

[1953, eq (114)]), was integrated numerically

over the energy distribution between the pair

particles to obtain K^lBorn).

Corrections to the Born approximation values were applied at all energies. These corrections were

derived from:

(1) Calculations of Jaeger and Hulme in the energy

range E < 5 MeV,

(2) Calculations of Davies, Bethe and Maximon

for E > 5 MeV, and

(3) Experimental data.

The results of Jaeger and Hulme [1936] and

Jaeger [1936, 1941] were obtained by numerical

solution of the Dirac equation and indicate considerable departures from the Born approximation near

threshold, especially for high-Z elements. For ex- ample, for tin at 3 me2 (= 1.533 MeV) the ratio of

their result to that from formulas based on the

Born approximation is 1.30, while for lead at 3 me2 this ratio is 1.97, dropping to 1.24 at 5.2 me2 (=2.66 MeV). 18 The calculation of Davies, Bethe, and Maximon

[1954] for an unscreened nucleus went beyond the

Born approximation, using Sommerfeld-Maue

[1935] wave functions rather than plane waves. Their results lead to the appearance of a negative

Coulomb correction

28 ZV

-AK

°TM= --j^f(Z), (2.-28)

where /(Z) may be evaluated from the sum

f(Z) = a

2

[ ( 1 + a

2

) - 1 + 0.20206 - 0.0369 a

2 + 0.0083 a

4 -0.002 a6 + • • •], (2.-29)

in which

a = Z/137.

In their approximation (neglect of terms of order

In k/k and 1/A) the Coulomb correction remains the

same whether screening is absent, partial, or complete.

18 Recently 0verba [1967] has extended the Jaeger-Hulme results to include 8 ele- ments 6 C through 92U and energies ranging from 2.001 me2 (1.0225 MeV) to 6.5 me2 (3.32 MeV).

In her tabulations in the energy range E < 5 MeV,

White-Grodstein used the Hough formula to cal- culate /c®w(Born) and then applied graphicallyinterpolated values of the Jaeger-Hulme correction.

In the range E > 5 MeV she fitted the relevant

corrections by a semi-empirical formula

K,i(White-Crodstein)= /^(Born) — Ak%bm

+ Z> 2lj

f^, (2.-30)

k

where the terms /^(Born) and —

A

k

d

kbm were computed as explained above. The additional

term 6

2 (ln k)/k was adjusted to give better agreement with experimental data, particularly those of

Colgate [1952] and Paul [1954] and to provide a smooth transition to the low-energy results of

Jaeger and Hulme.

In the present revision, use was made of a slightly

different semiempirical formula

k„ = \_«n

H (Born, unscreened) — 5hf5

]

• [1 + A (rad. corr.)] — A (empirical) • Ak%bm

, (2.-31)

which, although not necessarily more accurate than

eq. (2.—30), covers the entire energy range from

threshold to the high energy limit. Values of k„

computed using eq (2.— 31) are presented in table

2.-10 in the scaled form kJZ2 for ease of

interpolation.

New data taken into account in this revision are:

(a) the near-threshold expressions by Maximon

[1968] of k„ h (Born, unscreened) as given in

equations (2.-34) and (2.-36),

(b) the screening correction sHFS (in table 2.-13)

calculated by Sorenssen [1965, 1966] using

Hartree-Fock-Slater wave functions (Hanson

et al. [1964]) for 0=Sg^0.3 and the ThomasFermi model of the atom for 0.3 q 8.0

where q is momentum transfer in me units,

(c) the radiative correction of Mork and Olsen

[1965] given in table 2.-11, and

(d) an empirical correction to the Born approximation entered as an energy-dependent cor- rection factor (given in table 2.—11) applied to the high-energy Coulomb correction Ak

bbm

given in table 2.-12, since both corrections vary

approximately as Z4 and are large and of opposite sign near threshold. 19 The latter correction

takes into account additional k„ experimental

data including measurements by Standil and

Shkolnik [1958] and Titus and Levy [1966],

and total attenuation data by Barkan [1956],

Hubei, Roh, and Scheer [1959] and Barlett and

Donahue [1965].

19 Maximon has derived an energy dependence (see table 2.-11) for the Coulomb

correction, giving the modified correction [1 — (2/7) (9Ar* — 6Aj _2 + 4A: -3 )]

• as quoted by Koch [1964] and Sorenssen [1965, 1966], which goes to zero at threshold. However, this improved Coulomb correction still results in a negative theoretical cross section near threshold if no empirical correction term is added.

34
Table 2.-11. Energy-dependent parameters used for evaluating Kn

.

Photon

energy

[MeV]

(Born)

[b/atom]/Z2

Mork-Olsen

radiative

correction

factor [l+A(rad.corr.)]

Empirical

multiplier for Coulomb

correction

Theoretical

multiplier for Coulomb

correction

1.022 0 1.000 0 0

1.5 4.30 -10- 5 (1.011) — 0.0677 0.2778

2 1.772- 10- 4 (1.012) — 0.1286 0.4359

3 5.055- 10-4 (1.012) — 0.1356 0.6061

4 8.205- 10-4 (1.013) -0.0639 0.6971

5 1 . 100 - 10-8 (1.013) + 0.0204 0.7539

6 1.350- lO' 3 (1.013) 0.1216 0.7927

8 1.775- 10-3 (1.013) 0.305 0.8425

10 2.127- lO-3 1.012 0.450 0.8729

15 2.792-10-3 1.012 0.655 0-9144

20 3.278- 10“3 1.011 0.740 0.9354

30 3.977- lO' 3 1.011 0.824 0.9567

40 4.479- 10“ 3 1.011 0.871 0.9674

50 4.872- lO'3 1.011 0.900 0.9739

60 5.194- lO-3 1.011 0.924 0.9782

80 5.705- lO” 3 1.010 0.954 0.9837

100 6. 102 -10-3 1.010 0.976 0.9869

Table 2.-12. Davies-Bethe-Maximon [J954] high-energy

Coulomb correction, — Ak„ bm

, divided by Z

2

. Units are [b/atom]/Z 2

. Z -Ax^V//Z2 z -Ax%BM/Z2

1 -1.15 • 10- 7 18 — 3.684- 10“ 5 4 -1.84 10- 6 19 — 4.097- 10- 5 5 -2.88 10' 6 20 — 4.532- 10 5 6 — 4.15 10“ 6 26 -7.566- 10 5 7 -5.64 10- 6 29 -9.344- lO' 5 8 -7.36 10- 6 42 - 1.884- lO" 4 11 - 1.388 10“ 5 50 -2.591- lO" 4 12 -1.651 10-3 53 -2.876- 10“ 4 13 -1.935 lO' 5 74 — 5.078 lO" 4 14 — 2.241 lO' 5 82 — 5.977 10“ 4 15 — 2.569 lO' 5 92 — 7.119 lO' 4 16 — 2.919 10- 5

The differential Bethe-Heitler Born-approximation cross section, in the high-energy approximation

and for partial screening, can be approximated by

use of a simple and convenient formula derived by

Bernstein [1950]. In this approximation the BetheHeitler screening functions and <£>2 (based on the

Thomas-Fermi atom) are assumed to he equal, and

</?i is fitted by an analytic expression to better than

2 percent. In terms of the photon energy k and the

outgoing electron kinetic energy T, both in me2

units, the resulting formula is

d,K^H (Born )/ dT

4Zh*

137

In (183 Z-1 ' 3

) 7 1 -u

k

T+ 1

x

Kk

(T + 1) (k — T—l)

-1 m\

(2.-32)

where

u =|+[9 In (183 2

-1 '3 )]-1

and

K= 255 Z_1/3

/ (15.6 —f In Z).

This formula can be integrated analytically to give the total pair production cross section:

/c^ w (Born)~

4Z^

137

In (183 Z

-‘/3

C uKA u 2 u 2 u 2K

*{l + T)-6 -I

+ ¥-W-T

X

1 +

uK

In 1+ f+1 -f

-f—

J (2.-33)

If the Bernstein formula (2.-33) is inserted into

eq (2.— 31) we obtain values of k„ which agree

with those in table 2.— 10 and with experimental

data to ~ 5 percent over the energy range

E 5 MeV for Z 29. For lighter materials this

agreement is restricted to higher energies: e.g., for carbon the Bernstein result is lower by ~ 20

percent over the range 5 to 20 MeV but agrees

within ~ 5 percent for E > 50 MeV. However, for

these materials the addition of the contribution

of Compton scattering results in total photon inter35
Table 2.-13. Sorenssen [1965, 1966] screening (Hartree-Fock-S later) corrections, s HFS

, to be subtracted from

(Born) divided by Z2

.

Since sHFS is not a smoothly varying function of Z near ,H. values of sHFS!Z 2 for 2, 3. and 4 are included. Values below lOMeV are extrapolated. Units are [b/atomlIZ 2

.

Photon

energy

[MeV]

iH 2 He 3 Li 4 Be 6 c 13 ^^ 20^-'^-

1.022 0 0 0 0 0 0 0

1.5 — — 1.0 • 10- 7 1.0 - lO " 7 1.0 - 10- 7 3.0 - 10- 7 4.0 • 10- 7 2 — 3.0 - 10- 7 3.0 - 10- 7 3.0 - 10- 7 4.0 - 10- 7 6.0 - 10" 7 8.0 - 10- 7 3 2.0 - 10- 7 8.0 - 10~ 7 9.0 • 10- 7 1.0 - lO - 6 1.1 - lO - 6 1.6 - lO - 6 2.3 - lO - 6

5 8.0 • 10- 7 2.1 - 10- 6 2.3 - lO - 6 2.6 - lO - 6 3.3 - lO -® 5.0 - lO - 6 6.6 - lO - 6

10 4.0 * 10- 5 6.2 • lO - 6 6.7 - lO - 6 7.5 - lO - 8 9.4 • lO " 6 2.01 • lO ” 5 2 . 71 - lO " 5 20 1 . 51 - 1 0“ 5

1 . 65 - 10- 51 . 75 - lO ’ 5 2. 07 - lO ” 5 3 . 07 - 10-8 6 . 60 - 10 -4 8 . 10 - 10" 4 30 to OO o

1 tn 2 . 82 - lO " 5 3 . 11 - lO " 6 4. 30 - lO ” 5 6 . 60 - lO ” 5

1 . 20 - 10“ 41 . 47 - lO ” 4 50 5 . 28 - 10“ 5 5 . 46 - lO

” 6 8 . 20 - lO ” 5

1 . 10 - 1 0- 4 1

o

T—<

IT) 2. 38 - 10" 4 2. 85 - 10 -* 100 1 . 10 - 10- 4

1 . 82 - 10“ 4 2. 70 - 10 -4 3 . 30 - 10- 4 3 . 94 - lO " 45 . 32 - 10“ 4 6 . 1

9

- 1 0- 4

Photon

energy

[MeV]

26 29^U 4 2Mo 50^ n 74W 82^* 92 u

1.022 0 0 0 0 0 0 0

1.5 5.0 -10 - 7 6.0 - 10" 7 8.0 - 10- 7 9.0 • 10 - 7 1.2 - lO - 6 1.3 -10-6 1.4 -lO- 6 2 1.1 - 10-8 1.3 -lO" 6 1.9 -10-« 2.2 - lO " 6 2.8 -lO- 6 2.8 - 10-8 2.9 -lO- 6 3 2.9 • lO - 6 3.2 -lO- 6 4.3 -lO ” 6 4.9 -lO - 6 6.1 -lO- 6 6.4 - lO-® 6.8 -lO - 8 5 8.0 -lO-® 8.6 - lO " 6 1.11- lO ” 5 1.25- lO” 5 1.57- lO " 5 1.67-10-8 1.79- lO " 5

10 3.05-10-8 3.17-10-8 3.85- lO " 5 4.32-10-8 5.40-10-8 5.65- 10- 4 5.91-10-8

20 9.10-10-8 9.43- lO - 5 1.14- 1 0- 4 1.24- lO" 4 1.50- lO” 4 1.56- 10" 4

1 . 66 - 10" 4 30 1.64- lO” 4

1 . 68 - 10- 4 1.98- 1

0

“ 4 2.17- 10 - 4 2.55- 10 - 4 2 . 66 - lO " 4 2.76- lO ” 4 50 3.11- 10 " 4 3.20- 10 “ 4 3.73- lO " 4 4.00- 10 -4 4.59- lO " 4 4.78- lO ” 4 4.96- lO " 4 100 6.64- 10 “ 4 6.76- 10 - 4 7.76- 10 - 4 8 . 20 - 10- 4 9.20- lO " 4 9.41- 10"4 9.74- 10 - 4

action cross sections cr,ot which agree with those

in table 1.—4 within 5 percent.

This differential Bethe-Heitler Born-approximate cross section, without the high energy approximation and with screening disregarded, has

been integrated analytically by Racah [1934, 1936]

and Jost, Luttinger, and Slotnick [1950], but the

resulting expression contains double and single

integrals over elliptic functions. Recently Maximon [1968] has derived two series expansions

for this expression, which he integrated to give

the total cross section k%h

(Born, unscreened).

The resulting two series, which converge rapidly

at low and high energies, respectively, are:

(a) For E ^ 2 MeV

:

, Z2 r| 2tt (kK^w (Born, unscreened) = y^zt — I

(b) For E 5= 2 MeV

:

ZV2 [28

K^w(Born, unscreened) = ]— In (2A) —

+ (f

137 9

6 In (2k) -| + |

In3 (2 A') - ln2 (2A)

218

27

— 7r2 In (2A) + 2£(3) + -^-

2\ 4 k)

2\e

k,

TfnW+

ij

29

9 • 256

In (2 A ) 77

27 • 512

+ (2.-36)

x -.I , 23 2 11 3

. 29

1 +

2

P +

40 P

' +

60 P + %0 P + (2.-34)

where

£( 3 ) = 2

2020569 (2.-37)

where

2A-4

2 + A

- + 2V2k

These two expansions (2.-34) and (2.-36), using

(2.-35) only the terms given here, provide values of

K,f H(Born, unscreened) accurate to within 0.01 per36
cent over the entire energy range from threshold

to arbitrarily high energies.

In addition, Jost, Luttinger, and Slotnick [1950]

have extended their derivation to the case of arbitrary screening. They obtained a formula differential in the momentum transfer which includes

screening effects in terms of the atomic form factor F(q, Z) and which can be numerically integrated to obtain the total cross section k„.

2.5.3. Pair Production in the Field of an Electron

This effect has a threshold of 4 me2 (=2.044

MeV) as required by the sharing, in this case, of

the photon energy and momentum with the target

electron as well as the created electron-positron

pair. The resulting trajectories of the two electrons

and the positron appear as a three-pronged track

in a cloud chamber or photographic emulsion,

hence the name “triplet production” often given

to the process.

An exact theoretical treatment should include

the following effects:

(1) atomic binding of the target electron,

(2) screening by the other atomic electrons and by

the field of the nucleus,

(3) retardation which occurs when the atomic

electron recoil velocity is not negligible in comparison with the velocity of light.

(4) the y — e interaction of the incident photon

with the atomic electron (i.e., virtual Compton

scattering in which the scattered photon gives

rise to an electron-positron pair),

(5) exchange terms resulting from the indistinguishability of the two electrons, and

(6) the radiative corrections.

No one treatment has included all six of these

effects, so numerical values are usually obtained

from a combination of one or more of the following

three principal theories, all of which employ the

Born approximation.

Wheeler and Lamb [1939] used the high energy

approximation and included the above effects (1)

and (2). Ghizzetti [1947] and Borsellino 20 [1947]

included only (3), but Suh and Bethe [1959] have

shown that at high energies their neglect of ex- change (5) is unimportant. Votruba [1948] included

(3), (4) and (5), but his differential cross sections are

so complex that until very recently the required

integrations to obtain the total cross section have

been done only crudely. However, Mork [1967] has

now integrated the Votruba expressions numerically,

and his results are shown in table 2.—14 in the form

of an energy-dependent correction A (triplet) to be

Mork has pointed out that the Borsellino result is identifiable as the leading terms

of the series solution in eq (2.-40) bv Ghizzetti [1947], and that the last Borsellino term should read —21.51, rather than + 21.51, giving

r

2 <28 218

Ke (Borsellino corrected) = ] — In (2A) 137 l 9

' 27

-- [d In3 (2k) -3 In 2 (2A) + 6.84 In (2*) -21.51

jj

for the cross section per electron.

Table 2.-14. The Mork \1967\ correction to the- BorsellinoGhizzetti «e result, obtained by numerical integration of the Votruba differential expressions.

Photon energy

[MeV] A (triplet)

2.044 0.215

2.5 0.608

3 0.765

4 0.895

5 0.932

6 0.959

8 0.996

10 1.0

applied to the Borsellino-Ghizzetti result between

threshold and 10 MeV.

Additional theoretical studies of triplet production have been made by Watson [1947], Nemirovsky [1947, 1948], Reyntjens [1957], Kopylov et al. [1964], Kaufman [1964], and Knasel [1968]. The

most comprehensive survey of the theory is that of

Joseph and Rohrlich [1958] , and more recent results

have been summarized by Gates et al. [1960,

1962], Koch [1964], Davisson [1965], and Olsen

[1968],

In the present tabulation we use values of Ke obtained by combining the Borsellino-Ghizzetti cross

section /<fG (using the Ghizzetti expansion which

includes terms through A -7

), the Mork-Votruba

correction A (triplet), the Wheeler-Lamb screened

cross section k^l in the high-energy and ThomasFermi approximations, the Bethe-Heitler un- screened nuclear-field cross section k^h

, and the

Mork-Olsen radiative correction here assumed to have the value 1.01. From threshold to 10 MeV,

where screening is negligible, we used the

combination

Ke = kTM • A(triplet) -1.01 (2.-38)

for the cross section per electron. At higher energies, as suggested by Mork, we used the combination

Ke={Kr-[/<r(lH)-KfG]} -1.01. (2.-39)

The Ghizzetti [1947] expansion for /<f G is reproduced here for convenience:

,BG - r

2 [28

1+7 1 9“ ln <“>

218

"27~

+- In3 (2A) + 3 In2 (2A)

O

60+ 16a . . .. 123 + 12a + 16A

In (2A) H ^

+'F |

In3 (2A) —4 In2 (2A)

51 +32a . /o; , 123 + 32a + 64A

— In (2A) t

37
+ In2 (2k)

~In (2k)

2915 -288a

216

+ — In (2k)

115

'

432

+

77

36

In (2k) 4

10831'

8640

+

641

300

In (2k) 4

64573"

36000

+

4423

1800

In (2k)

394979"

216000

tiplied the results from eq (2.-39) by the ratio of

these two results for hydrogen. This ratio [eq

(2.-38) divided by eq (2.-39)] varies from 0.857

at 10 MeV to 0.997 at 100 MeV.

Values of Ke from eqs (2.-38) and (— 39), given explicitly in the tables in section 3, are also given in

table 2.— 15 in terms of the scaled ratio

J) = Z (KelKn) (2.-41)

for purposes of interpolation. The total pair production cross section can thus be reconstructed

from tables 2.-10 and -15 as

K = K„ + Ke = Z(Z + 7]) (k„/Z 2

)

. (2.“42)

+ . . .}

(2.-40)

in which the constants

The values in table 2.-15 can be represented to within 5 percent from 10 to 100 MeV and within

±2 percent from 20 to 80 MeV by the empirical

formula

a = — 2.46740 and

£> =—1.80310 r) ~ In ^

- 0.00635 In3

are evaluations of definite integrals over a series

expansion given by Ghizzetti. In addition, to make

the results join smoothly and to correct for the

Wheeler-Lamb high-energy approximation, we mulin which

a = Z/137,

(2.-43)

Table 2.-15. Values of tj = Z (xe/Kn ) relating the triplet cross section Ke to that for nuclear-field pair production.

Here, Ke is the Borsellino [1947]-Ghizzetti [1947] unscreened result corrected for exchange and for y—e interaction near threshold by Mork [1967], for screening using the Wheeler-Lanib [1939] results, and includes a radiative correction factor of 1.01. Using table 2.-10,

K(total) = Z(Z-\-T)) (k,JZ 2

). For explicit values of up to 100' GeV, see tables in section 3.

Photon

energy

[MeV]

iH 6c 13^ 20Ca. 26 Fe 29 Cu

rj = Z-(xe /xn ) 2.044 0 0 0 0 0 0

3 0.0786 0.0787 0.0785 0.0781 0.0775 0.0773

4 0.199 0.200 0.199 0.199 0.199 0.199

5 0.292 0.292 0.293 0.293 0.294 0.294

10 0.543 0.545 0.550 0.555 0.559 0.562 20 0.707 0.71

1

0.721 0.729 0.737 0.741 30 0.779 0.787 0.801 0.811 0.819 0.820

50 0.849 0.868 0.883 0.888 0.890 0.891 100 0.920 0.956 0.963 0.966 0.968 0.968

Photon

energy

[MeV]

42 M° 50^n 74 W 82 Pb 92^-

n = Z-(xel*n) 2.044 0 0 0 0 0

3 0.0755 0.0742 0.0700 0.0687 0.0669

4 0.198 0.197 0.194 0.193 0.191

5 0.295 0.296 0.298 0.299 0.300

10 0.575 0.586 0.624 0.639 0.658 20 0.761 0.773 0.819 0.837 0.861 30 0.833 0.844 0.886 0.901 0.923

50 0.903 0.912 0.954 0.973 0.994 100 0.983 0.994 1.034 1.048 1.068

38
and k is the photon energy in me2 units. Below

10 MeV, Ke is less than 2 percent of (Ttou and experimental estimates (see, for example, the recent

results of Frei, Staub, and Stiissi [1964]) still contain uncertainties too large for confirmation of

present theory.

2.6. Photonuclear Absorption

This effect consists of nuclear interactions ini- tiated by the absorption of a photon. The most likely

result of such an interaction is the emission of a

single neutron, but one must also consider the emission of charged particles, gamma rays, or more than one neutron. Available experimental and theoretical information on such interactions is discussed

in review articles by DeSabbata [1957, 1959],

Levinger [1960], Fuller and Hayward [1962], Hayward [1963], Brenig [1965], and Danos and

Fuller [1965].

The most characteristic feature of the cross section for nuclear absorption of photons is the “giant

resonance.” This is a broad peak in the absorption

cross section centered at about 24 MeV for light

nuclei, decreasing in energy with increasing mass

number to about 12 MeV for the heaviest stable

nuclei. The width ‘T” (energy difference between

the points at which the cross section drops to one

half its maximum value) varies from about 3 MeV

to 9 MeV depending on the detailed properties of

individual nuclei.

When studied with finer resolution the gross

“resonance” is found to have considerable substructure. A prominent feature of this sub-structure,

for nuclei having large permanent deformations, is a splitting of the giant resonance into two main

peaks. In general, those nuclei having either large

permanent deformations or large “dynamic deformations” (resulting from the vibrational nature of the

nuclear ground state) have their giant resonances

spread over the widest energy range.

Table 2.-16 gives the gross parameters of the

giant resonance for a representative group of nuclei

throughout the periodic table. From these parameters the giant resonance can be approximately

reconstructed by assuming that it has the shape of a Lorentz line (see, e.g., Fuller and Hayward

[1962], eg. (2.5), p. 117):

°"ph -n- {E) “ cr

° (E0

2 — E2

) + E2 T

2

' (2.-44)

As indicated in table 2.-16, the magnitude of

the photonuclear absorption cross section, even at the resonance peak energy, E<>, is small in comparison with the sum of the competing “electronic”

cross sections discussed in sections 2.3 to 2.5, and

in no case contributes more than 10 percent to the

total cross section. However, photonuclear absorption can be of considerable importance in shielding

and irradiation technology whenever photon energies

are present which exceed reaction threshold

energies such as those indicated in table 2.-16.

In shielding technology (see, e.g., NBS Handbook

97 [1964] and Hubbell and Spencer [1964]) nuclear

absorption of photons is important because neutrons

are produced in a large fraction of the reactions

(about 40 to 100 percent probability depending on

the photon energy and the mass number of the

particular nucleus). These neutrons are usually

far more penetrating than the incident photons.

Of importance in irradiation technology (see, e.g.,

Table 2.-16. Photonuclear giant resonance cross section parameters3

Nucleus

Threshold

energies Eo, energy

at o-ph. n. peak

cro, value

of O-ph. at peak

T, peak

width at

Percent

of “electronic’’ Refs.2

(y, n) (y, p)

half- max.cross

section

at Eo

!2C MeV

18.7 MeV16.0 MeV

3 23.

blatom

4 0.018 MeV

3.6 %5.9 63 Bu 3

27A

13.1 8.3 3 21.5 4 .038 9.0 3.9 64 Do 2

40Ca 15.7 8.3 3 20.5 4 .100 4.5 5.2 66 Do 2

63Cu 10.8 6.1 17.0 5 .070 8.0 2.0 64 Fu 1

90Zr 12.0 8.4 17.0 5 .180 4.5 3.0 67 Be 2

1 27J 9.1 6.2 15.2 5 .210 5.7 2.3 66 Br 1

165 Ho 8.0 6.1 3 14.0 6 .220 8.5 1.7 65 Am 1

181 Ta 7.6 6.2 3 14.0 6 .280 6.5 1.8 63 Br 1 208p b 7.4 8.0 13.6 5 .495 3.8 2.7 64 Ha 2

235U 6.1 7.6 3 12.2 7 .500 7.0 2.4 64 Bo 3

1 This table was supplied by E. G. Fuller.

2 References (as given in the Photonuclear Data Index): 63 Br 1 Bramblett, R. L., Caldwell, J. T., Auchampaugh, G. F., Fultz S. C.: Phys. Rev. 129 , 2723 (1963). 63 Bu 3 Burgov, N. A., Danilyan, G. V., Dolbilkin. B. S., Lazareva, L. E., Nikolaev, F. A.; Zhur. Eksp. i Teoret.

Fiz. 45, 1693 (1963); Soviet Phys. JETP 18, 1159

(1964). 64 Bo 3 Bowman, C. D., Auchampaugh. G. F., Fultz, S. C.; Phys. Rev. 133 , B676 (1964). 64 Do 2 Dolbilkin, B. S., Zapevalov, V. A., Korin, V. I., Lazareva, L. E., Nikolaev. F. A.; PICNS—64 1060 (1964). 64 Fu 1 Fultz, S. C., Bramblett, R. L., Caldwell, J. T., Harvey,

R. R.: Pbys. Rev. 133 , B1149 (1964). 64 Ha 2 Harvey, R. R., Caldwell, J. T., Bramblett, R. L., Fultz, S. C.; Phys. Rev. 136, B126-131 (1964). 65 Am 1 Ambler, E., Fuller, E. G., Marshak, H.; Phys. Rev. 138 , B117 (1965). 66 Br 1 Bramblett, R. L., Caldwell, J. T., Berman, B. L., Harvey, R. R., Fultz, S. C.; Phys. Rev. 148, B1198

(1966). 66 Do 2 Dolbilkin, B. S., Zapevalov, V. A., Korin, V. I., Lazareva, L. E., Nikolaev, F. A.; Izv. Akad. Nauk fiz. 30,

349 (1966); Bull. Acad. Sci. USSR — Phys. 30 , 354

(1966). 67 Be 2 Berman, B. L., Caldwell, J. T., Harvey, R. R., Kelly, M. A., Bramblett, R. L., Fultz, S. C.: Phys. Rev. 162,1098(1967).

3 Cross section has structure. Energy given is approximate mean energy for photon absorption.

4 Total nuclear absorption cross section at E0 . 5 Maximum absorption cross section resulting in production

of neutrons. For these nuclei this is a good approximation to the

total nuclear absorption cross section.

6 Deformed nuclei. Absorption cross section has two peaks.

Comments under footnote 5 apply.

7 Includes photofission cross section. Comments under loot- notes 5 and 6 apply.

39
Manowitz et al. [1964] and DeProost et al. [1966]) as well as in shielding is the radioactivity which

results from the photodisintegration of the nucleus

in which the photon was absorbed or from the capture in other nuclei of the reaction products.

An initial attempt at a systematic photonuclear

cross section compilation (in the form of graphs)

has been made by Hunt et al. [196?] for use in food

irradiator design studies. Parameters describing

gross features of measured cross sections for photonuclear reactions have been tabulated by Goryachev

[1964].

However, the best source of data for individual

nuclei is at present the technical literature. Available data in the literature can be located by means

of the NBS Photonuclear Data Index (Baggett et al. [1966] and Collins et al. [1967]) which is an annotated index and bibliography of references containing experimental data on photonuclear reactions.

Each index entry gives specific quantitative data

about the type of information available in each

reference. The source of data used to compile this

index is the NBS Photonuclear Data File. This file consists of data sheets containing abstracts of the

significant data (both numerical and graphical)

from each reference. These data sheets, as well as

a reprint collection of all references abstracted,

are on deposit at the Photonuclear Data Center at the National Bureau of Standards.

3. Tabulation of Cross Sections for Elements and Compounds

This section contains photon interaction cross sections and attenuation coefficients as described

in sections 1 and 2. The data are presented by ele- ment, following the format of White-Grodstein

[1957] and Davisson [1965] except that total cross

sections are given in barns/atom in addition to the mass attenuation coefficient in cm2 /g. Similar

data (all in cm2 /g) for some compounds and mixtures of interest in dosimetry (Evans [1968]) have

been added.

In tables 3.—1 to 3.-23 the first column lists the

photon energy in MeV. In this and in other columns

the sign and following two digits at the end of

each entry indicate the power of ten by which

the preceding part of the entry is to be multiplied.

A pair of successive identical energies, the second

of which is preceded by K, L,, L2 , or L3 , marks

the presence of an “absorption edge” discontinuity in the photoelectric and total cross section columns.

The second column, labeled “scattering, with

coherent,” is the sum {(Jc30 + (Tr) of the Compton

(incoherent) collision cross section corrected

for electron binding and the Rayleigh (coherent)

scattering cross section. This sum is based on

values calculated by Storm and Israel [1967]

(see sec. 2.4.2). The third column, labeled “scattering, without coherent,” is the free-electron

Compton collision cross section (Z X crc) [b/atom]

where or, including the Mork [1968] radiative and

double-Compton corrections Aa^1

, is given in table

2 .- 8. The fourth column, labeled “photoelectric,"

is the photoeffect cross section rpe derived from

experimental and theoretical values by procedures described in section 2.3. The fifth column,

labeled “pair production in field of nucleus,”

contains values of k„ from eq (2.-31), and the

sixth column, labeled “pair production in field

of electrons,” contains values of k> from eqs

(2.-38) and (2.-39).

The seventh and eighth columns, labeled “total,

with coherent” and “total, without coherent,"

are sums crtot over columns 2, 4, 5, and 6, and

over columns 3, 4, 5, and 6, respectively. The

conversion factor at the bottom of each page

(also in table 1

. —1) has been used to convert the

total cross section values (b/atom) in columns

7 and 8 into the corresponding mass attenuation

coefficients g/p(cm2/g) in columns 9 and 10. Values

of p,/p in the last column are identical with those

in table 1.-4. Estimates of uncertainties for vari- ous ranges of E and Z are given in section 1.4. Tables 3.-24 to 3.-36 for compounds and mixtures were derived from values in tables 3.-1 to 3.-23 using eq (1.-6) and the fractions-by-weight

Wi in table 1.—3. Possible errors from use of the

“mixture rule” as employed here are discussed

in the last paragraph of section 1.3.

40
Table 3.-1. HYDROGEN, Z=1

Photon

energy

Scattering PhotoelectricPair production Total Total

With

coherent Withoutcoherent Nuclearfield Electronfield With

coherent Withoutcoherent Withcoherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm'2/g cm-/g

1.00-02 6.39-01 6.40-01 4.57-03 6.44-01 6.45-01 3.85-01 3.85-01

1.50-02 6.28-01 6.29-01 1.13-03 6.30-01 6.30-01 3.76-01 3.76-01 2.00-02 6.17-01 6.18-01 4. 19-04 6.18-01 6.18-01 3.69-01 3.69-01 3.00-02 5.97-01 1.03-04 5.98-01 3.57-01 4.00-02 5.79—01 3.84-05 5.79-01 3.46-01 5.00-02 5.61-01 1.78-05 5.61-01 3.35-01- 6.00-02 5.46-01 9.51-06 5.46-01 3.26-01 8.00-02 5.17-01 3.55-06 5.17-01 3.09-01

1.00-01 4.93-01 1.66-06 4.93-01 2.94-01

1.50-01 4.44—01 4.23-07 4.44-01 2.65-01

2.00-01 4.06-01 1 .64—07 4.06-01 2.43-01

3.00-01 3.53-01 4.51-08 3.53-01 2.11-01

4.00-01 3.17-01 1.91-08 3.17-01 1.89-01 5.00-01 2.89-01 1.02-08 2.89-01 1.73-01 6.00-01 . 2.67-01 6.35-09 2.68-01 1.60-01 8.00-01 2.35-01 3.20-09 2.35-01 1.40-01 1.00+00 2.11-01 1.99-09 2.11-01 1.26-01 1.50+00 1.72-01 9.25-10 4.43-05 1.72-01 1.03-01 2.00+00 1.46-01 5.90-10 1.77-04 1.46-01 8.75-02 3.00+00 1.15-01 3.32-10 5.11-04 4.02-05 1.16-01 6.91-02 4.00+00 9.62-02 2.28-10 8.30-04 1.65-04 9.72-02 5.81-02

5.00+00 8.31-02 1.75-10 1.11-03 3.25-04 8.45-02 5.05-02

6.00+00 7.34—02 1.40-10 1.36-03 4.99-04 7.53-02 4.50-02

8.00+00 6.01-02 1.00-10 1.79-03 8.54^-04 6.27-02 3.75-02

1.00+01 5.11-02 7.89-11 2.14-03 1.17-03 5.45-02 3.25-02

1.50+01 3.79-02 2.79-03 1.82-03 4.25-02 2.54-02

2.00+01 3.04-02 3.28-03 2.33-03 3.60-02 2.15-02

3.00+01 2.21-02 3.97-03 3.11-03 2.92-02 1.74-02

4.00+01 1.76-02 4.46-03 3.68-03 2.57-02 1.54-02

5.00+01 1.47-02 4.85-03 4.14-03 2.37-02 1.41-02

6.00+01 1.26-02 5.17-03 4.51-03 2.23-02 1.33-02

8.00+01 9.97-03 5.66-03 5.10-03 2.07-02 1.24-02

1.00+02 8.28-03 6.04-03 5.56-03 1.99-02 1.19-02

1.50+02 5.89-03 6.69-03 6.39-03 1.90-02 1.13-02 2.00+02 4.62-03 7.12-03 6.95-03 1.87-02 1.12-02 3.00+02 3.28-03 7.65-03 7.70-03 1.86-02 1.11-02 4.00+02 2.56-03 7.97-03 8.20-03 1.87-02 1.12-02 5.00+02 2.12-03 8.19-03 8.55-03 1.89-02 1.13-02 6.00+02 1.82-03 8.35-03 8.82-03 1.90-02 1.13-02 8.00+02 1.42-03 8.57-03 9.21-03 1.92-02 1.15-02

1.00+03 1.17-03 8.71-03 9.47-03 1.94-02 1.16-02

1.50+03 8.16-04 8.93-03 9.88-03 1.96-02 1.17-02 2.00+03 6.31-04 9.04-03 1.01-02 1.98-02 1.18-02 3.00+03 4.39-04 9.16-03 1.04-02 2.00-02 1.20-02 4.00+03 3.39-04 9.24-03 1.06-02 2.01-02 1.20-02 5.00+03 2.77-04 9.27-03 1.06-02 2.02-02 1.21-02 6.00+03 2.35-04 9.31-03 1.07-02 2.03-02 1.21-02 8.00+03 1.81-04 9.35-03 1.08-02 2.03-02 1.22-02 1.00+04 1.48-04 9.37-03 1.09-02 2.04-02 1.22-02

1.50+04 1.02-04 9.41-03 1.09-02 2.05-02 1.22-02 2.00+04 7.85-05 9.43-03 1.10-02 2.05-02 1.23-02 3.00+04 5.41-05 9.45-03 1.10-02 2.06-02 1.23-02 4.00+04 4.16-05 9.46-03 1.11-02 2.06-02 1.23-02 5.00+04 3.39-05 9.47-03 1.11-02 2.06-02 1.23-02 6.00+04 2.86-05 9.47-03 1.11-02 2.06-02 1.23-02 8.00+04 2.19-05 9.48-03 1.11-02 2.06-02 1.23-02

1.00+05 1.78-05 9.48-03 1.11-02 2.06-02 1.23-02

(b/atom) x .597500= cmz/g

41
Table 3.-2. BERYLLIUM, Z=4

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclearfield Electronfield Withcoherent Without

coherent Withcoherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm 2/g cm'2 /g 1.00-02 3.42+00 2.56+00 5.46+00 8.88+00 8.02+00 5.93-01 5.36-01

1.50-02 3.01+00 2.52+00 1.49+00 4.50+00 4.01+00 3.00-01 2.68-01 2.00-02 2.78+00 2.47+00 6.12-01 3.39+00 3.08+00 2.27-01 2.06-01 3.00-02 2.54+00 2.39+00 1.68-01 2.70+00 2.56+00 1.81-01 1.71-01 4.00-02 2.40+00 2.31+00 6.45-02 2.47+00 2.38+00 1.65-01 1.59-01 5.00-02 2.31+00 2.25400 3.06-02 2.34+00 2.28+00 1.56-01 1.52-01 6.00-02 2.23+00 2.18400 1.67-02 2.24+00 2.20+00 1.50-01 1.47-01 8.00-02 2.09+00 2.07+00 6.44-03 2.10+00 2.08+00 1.40-01 1.39-01

1.00-01 1.99+00 1.97+00 3.04-03 1.99+00 1.97+00 1.33-01 1.32-01

1.50-01 1.78400 1.77400 8.01-04 1.78+00 1.77+00 1.19-01 1.19-01 2.00-01 1.63400 3.15-04 1.63+00 1.09-01 3.00-01 1.41400 8.83-05 1.41+00 9.45-02

4.00-01 1.27400 3.76-05 1.27+00 8.47-02

5.00-01 1.16+00 2.01-05 1.16+00 7.73-02

6.00-01 1.07400 1.26-05 1.07+00 7.15-02

8.00-01 9.40-01 6.32-06 9.41-01 6.29-02

1.00400 8.45-01 3.91-06 8.46-01 5.65-02

1.50400 6.87-01 1.83-06 7.10-04 6.88-01 4.60-02

2.00400 5.86-01 1.16-06 2.84—03 5.89-01 3.94-02

3.00400 4.61-01 6.55-07 8.17-03 1.61-04 4.70-01 3.14-02

4.00400 3.85-01 4.48-07 1.33-02 6.61-04 3.99-01 2.66-02

5.00400 3.32-01 3.44-07 1.78-02 1.30-03 3.51-01 2.35-02

6.00400 2.94-01 2.75-07 2.18-02 2.00-03 3.17-01 2.12-02

8.00400 2.40-01 1.97-07 2.86-02 3.42-03 2.72-01 1.82-02

1.00401 2.05-01 1.55-07 3.41-02 4.67-03 2.43-01 1.63-02

1.50401 1.51-01 4.46-02 7.27-03 2.03-01 1.36-02

2.00401 1.21-01 5.23-02 9.34-03 1.83-01 1.22-02

3.00401 8.85-02 6.32-02 1.24-02 1.64-01 1.10-02

4.00401 7.03-02 7.09-02 1.47-02 1.56-01 1.04-02

5.00401 5.87-02 7.67-02 1.66-02 1.52-01 1.02-02

6.00401 5.06-02 8.12-02 1.80-02 1.50-01 1.00-02

8.00401 3.99-02 8.81-02 2.04—02 1.48-01 9.91-03

1.00402 3.31-02 9.31-02 2.22-02 1.48-01 9.92-03

1.50402 2.36-02 1.01-01 2.53-02 1.50-01 1.00-02 2.00402 1.85-02 1.07-01 2.74-02 1.52-01 1.02-02 3.00402 1.31-02 1.13-01 3.02-02 1.56-01 1.04-02 4.00402 1.03-02 1.17-01 3.20-02 1.59-01 1.06-02 5.00402 8.49-03 1.20-01 3.33-02 1.61-01 1.08-02 6.00402 7.27-03 1.21-01 3.43-02 1.63-01 1.09-02 8.00402 5.68-03 1.24-01 3.59-02 1.66-01 1.11-02

1.00403 4.67-03 1.26-01 3.69-02 1.68-01 1.12-02

1.50403 3.26-03 1.28-01 3.87-02 1.70-01 1.14-02 2.00403 2.52-03 1.30-01 3.98-02 1.72-01 1.15-02 3.00403 1.76-03 1.31-01 4.11-02 1.74-01 1.16-02 4.00403 1.35-03 1.32-01 4.19-02 1.75-01 1.17-02 5.00403 1.11-03 1.33-01 4.24-02 1.76-01 1.18-02 6.00403 9.40-04 1.33-01 4.28-02 1.77-01 1.18-02 8.00403 7.24-04 1.34-01 4.32-02 1.77-01 1.19-02 1.00404 5.91-04 1.34-01 4.35-02 1.78-01 1.19-02 1.50404 4.08-04 1.34-01 4.38-02 1.79-01 1.19-02 2.00404 3.14—04 1.35-01 4.40-02 1.79-01 1.20-02 3.00404 2.17-04 1.35-01 4.42-02 1.79-01 1.20-02 4.00404 1.66-04 1.35-01 4.43-02 1.79-01 1.20-02 5.00404 1.35-04 1.35-01 4.44-02 1.79-01 1.20-02 6.00404 1.14-04 1.35-01 4.44-02 1.80-01 1.20-02 8.00404 8.78-05 1.35-01 4.44-02 1.80-01 1.20-02

1.00405 7.14-05 1.35-01 4.45-02 1.80-01 1.20-02

(b/atom) x .066830 = cm2/g

42
Table 3.-3. BORON, Z=5

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclearfield Electronfield Withcoherent Withoutcoherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm 2/g cm2/g 1.00-02 4.61+00 3.20+00 1.63+01 2.09+01 1.95+01 1.16+00 1.09+00

1.50-02 3.95+00 3.14+00 4.36+00 8.31+00 7.50+00 4.63-01 4.18-01 2.00-02 3.61+00 3.09+00 1.68+00 5.29+00 4.77+00 2.95-01 2.66-01 3.00-02 3.25+00 2.99+00 4.52-01 3.70+00 3.44+00 2.06-01 1.92-01 4.00-02 3.04+00 2.89+00 1.84-01 3.23+00 3.08+00 1.80-01 1.71-01 5.00-02 2.91+00 2.81+00 8.80-02 3.00+00 2.89+00 1.67-01 1.61-01 6.00-02 2.80+00 2.73+00 4.86-02 2.85+00 2.78+00 1.59-01 1.55-01 8.00-02 2.63+00 2.59+00 1.89-02 2.64+00 2.60+00 1.47-01 1.45-01

1.00-01 2.49+00 2.46+00 8.97-03 2.50+00 2.47+00 1.39-01 1.38-01 1.50-01 2.23+00 2.22+00 2.38-03 2.23+00 2.22+00 1.24-01 1.24-01 2.00-01 2.04+00 2.03+00 9.41-04 2.04+00 2.03+00 1.14-01 1.13-01 3.00-01 1.77+00 1.77+00 2.65-04 1.77-4)0 1.77+00 9.84-02 9.85-02

4.00-01 1.58+00 1.13-04 1.58+00 8.83-02

5.00-01 1.45+00 6.05-05 1.45+00 8.06-02

6.00-01 1.34+00 3.77-05 1.34+00 7.45-02

8.00-01 1.18+00 1.90-05 1.18+00 6.55-02

1.00+00 1.06+00 1.18-05 1.06+00 5.89-02

1.50+00 8.59-01 5.51-06 1.11-03 8.60-01 • 4.79-02

2.00+00 7.33-01 3.51-06 4.44-03 7.37-01 4.11-02 3.00+00 5.77-01 1.97-06 1.28-02 2.01-04 5.90-01 3.28-02 4.00+00 4.81-01 1.35-06 2.07-02 8.26-04 5.03-01 2.80-02 5.00+00 4.15-01 1.03-06 2.78-02 1.62-03 4.45-01 2.48-02 6.00+00 3.67-01 8.23-07 3.40-02 2.50-03 4.04-01 2.25-02 8.00+00 3.00-01 5.89-07 4.46-02 4.27-03 3.49-01 1.95-02

1.00+01 2.56-01 4.63-07 5.32-02 5.84^-03 3.15-01 1.75-02

1.50+01 1.89-01 6.96-02 9.09-03 2.68-01 1.49-02

2.00+01 1.52-01 8.16-02 1.17-02 2.45-01 1.37-02

3.00+01 1.11-01 9.85-02 1.55-02 2.25-01 1.25-02

4.00+01 8.79-02 1.10-01 1.84-02 2.17-01 1.21-02

5.00+01 7.34-02 1.19-01 2.07-02 2.13-01 1.19-02

6.00+01 6.32-02 1.26-01 2.26-02 2.12-01 1.18-02

8.00+01 4.98-02 1.37-01 2.55-02 2.12-01 1.18-02

1.00+02 4.14-02 1.45-01 2.77-02 2.14-01 1.19-02

1.50+02 2.95-02 1.57-01 3.15-02 2.18-01 1.22-02 2.00+02 2.31-02 1.66-01 3.40-02 2.23-01 1.24-02 3.00+02 1.64-02 1.76-01 3.74-02 2.29-01 1.28-02 4.00+02 1.28-02 1.82-01 3.96-02 2.34-01 1.30-02 5.00+02 1.06-02 1.86-01 4.13-02 2.37-01 1.32-02 6.00+02 1 9.09-03 1.89-01 4.25-02 2.40-01 1.34-02 8.00+02 7.10-03 1.93-01 4.43-02 2.44-01 1.36-02 1.00+03 5.84-03 1.95-01 4.56-02 2.47-01 1.37-02

1.50+03 4.08-03 1.99-01 4.76-02 2.51-01 1.40-02 2.00+03 3.16-03 2.01-01 4.89-02 2.53-01 1.41-02 3.00+03 2.19-03 2.04-01 5.05-02 2.56-01 1.43-02 4.00+03 1.69-03 2.05-01 5.14-02 2.58-01 1.44-02 5.00+03 1.38-03 2.06-01 5.21-02 2.59-01 1.44-02 6.00+03 1.17-03 2.06-01 5.25-02 2.60-01 1.45-02 8.00+03 9.05-04 2.07-01 5.31-02 2.61-01 1.45-02

1.00+04 7.39-04 2.07-01 5.34-02 2.61-01 1.46-02

1.50+04 5.11-04 2.08-01 5.40-02 2.63-01 1.46-02 2.00+04 3.93-04 2.08-01 5.43-02 2.63-01 1.47-02 3.00+04 2.71-04 2.09-01 5.46-02 2.64-01 1.47-02 4.00+04 2.08-04 2.09-01 5.48-02 2.64—01 1.47-02 5.00+04 1.69-04 2.09-01 5.49-02 2.64-01 1.47-02 6.00+04 1.43-04 2.09-01 5.49-02 2.64-01 1.47-02 8.00+04 1.10-04 2.09-01 5.50-02 2.64-01 1.47-02

1.00+05 8.93-05 2.09-01 5.51-02 2.64-01 1.47-02

(b/atom) x .055710 = cm2/g

43
Table 3.-4. CARBON, Z=6

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Withoutcoherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm’/g cm2 /g

' 1:00-02 6.11+00 3.84+00 3.93+01 4.54+01 4.31+01 2.28+00 2.17+00

1.50-02 5.06+00 3.77+00 1.06+01 1.57+01 1.44+01 7.87-01 7.22-01 2.00-02 4.53+00 3.71+00 4.01+00 8.54+00 7.72+00 4.29-01 3.88-01 3.00-02 4.00+00 3.58+00 9.99-01 5.00+00 4.58+00 2.51-01 2.30-01 4.00-02 3.73+00 3.47+00 3.79-01 4.10+00 3.85+00 2.06-01 1.93-01 5.00-02 3.54+00 3.37+00 1.93-01 3.73+00 3.56+00 1.87-01 1.79-01 6.00-02 3.39+00 3.27+00 1.15-01 3.51+00 3.39+00 1.76-01 1.70-01 8.00-02 3.17+00 3.10+00 4.50-02 3.21+00 3.15+00 1.61-01 1.58-01

1.00-01 3.00+00 2.96+00 2.16-02 3.02+00 2.98+00 1.52-01 1.50-01

1.50-01 2.69+00 2.66+00 5.75-03 2.69+00 2.67+00 1.35-01 1.34-01 2.00-01 2.45+00 2.44+00 2.29-03 2.45+00 2.44+00 1.23-01 1.23-01 3.00-01 2.13+00 2.12+00 6.46-04 2.13+00 2.12+00 1.07-01 1.07-01 4.00-01 1.90+00 1.90+00 2.77-04 1.91+00 1.90+00 9.57-02 9.55-02

5.00-01 1.74+00 1.49-04 1.74+00 8.72-02

6.00-01 1.61+00 9.27-05 1.61+00 8.07-02

8.00-01 1.41+00 4.68-05 1.41+00 7.09-02

1.00+00 1.27+00 2.89-05 1.27+00 6.37-02

1.50+00 1.03+00 1.35-05 1.60-03 1.03+00 5.19-02

2.00+00 8.79-01 8.61-06 6.40-03 8.86-01 4.45-02

3.00+00 6.92-01 4.82-06 1.84-02 2.41-04 7.11-01 3.57-02

4.00+00 5.77-01 3.29-06 2.98-02 9.91-04 6.08-01 3.05-02

5.00+00 4.98-01 2.52-06 4.00-02 1.95-03 5.40-01 2.71-02

6.00+00 4.40-01 2.01-06 4.90-02 3.00-03 4.93-01 2.47-02

8.00+00 3.60—01 1.44-06 6.42-02 5.12-03 4.30-01 2.16-02

1.00+01 3.07-01 1.12-06 7.66-02 7.01-03 3.90-01 1.96-02

1.50+01 2.27-01 1.00-01 1.09-02 3.38-01 1.70-02 2.00+01 1.82-01 1.17-01 1.40-02 3.14-01 1.58-02 3.00+01 1.33-01 1.41-01 1.87-02 2.93-01 1.47-02

4.00+01 1.05-01 1.58-01 2.21-02 2.86-01 1.44-02 5.00+01 8.80-02 1.71-01 2.48-02 2.84-01 1.42-02 6.00+01 7.59-02 1.81-01 2.71-02 2.84-01 1.43-02 8.00+01 5.98-02 1.96-01 3.06-02 2.86-01 1.44-02

1.00+02 4.97-02 2.07-01 3.31-02 2.90-01 1.46-02 1.50+02 3.54-02 2.26-01 3.76-02 2.99-01 1.50-02 2.00+02 2.77-02 2.37-01 4.06-02 3.06-01 1.53-02 3.00+02 1.96-02 2.51-01 4.46-02 3.16-01 1.59-02 4.00+02 1.54-02 2.60-01 4.72-02 3.22-01 1.62-02 5.00+02 1.27-02 2.65-01 4.91-02 3.27-01 1.64-02 6.00+02 1.09-02 2.69-01 5.05-02 3.31-01 1.66-02 8.00+02 8.52-03 2.75-01 5.26-02 3.36-01 1.69-02 1.00+03 7.01-03 2.78-01 5.40-02 3.40-01 1.71-02

1.50+03 4.89-03 2.84-01 5.64-02 3.45-01 1.73-02 2.00+03 3.79-03 2.87-01 5.79-02 3.48-01 1.75-02 3.00+03 2.64-03 2.90-01 5.98-02 3.52-01 1.77-02 4.00+03 2.03-03 2.92-01 6.08-02 3.54-01 1.78-02 5.00+03 1.66-03 2.93-01 6.15-02 3.56-01 1.79-02 6.00+03 1.41-03 2.93—01 6.20-02 3.57-01 1.79-02 8.00+03 1.09-03 2.94-01 6.26-02 3.58-01 1.80-02 1.00+04 8.87-04 2.95-01 6.30-02 3.59-01 1.80-02 1.50+04 6.13-04 2.96-01 6.36-02 3.60-01 1.81-02 2.00+04 4.71-04 2.96-01 6.40-02 3.61-01 1.81-02 3.00+04 3.25-04 2.97-01 6.43-02 3.62-01 1.82-02 4.00+04 2.49-04 2.97-01 6.45-02 3.62-01 1.82-02 5.00+04 2.03-04 2.97-01 6.46-02 3.62-01 1.82-02 6.00+04 1.72-04 2.97-01 6.47-02 3.62-01 1.82-02 8.00+04 1.32-04 2.98-01 6.48-02 3.63-01 1.82-02

1.00+05 1.07-04 2.98-01 6.49-02 3.63-01 1.82-02

(b/atom) x .050240 = cm2/g

44
Table 3.-5. NITROGEN, Z= 7

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclearfield Electronfield Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm~/g cm-/g

1.00-02 8.03+00 4.48+00 7.86+01 8.66+01 8.31+01 3.73+00 3.57+00

1.50-02 6.38+00 4.40+00 2.10+01 2.74+01 2.54+01 1.18+00 1.09+00 2.00-02 5.60+00 4.33+00 8.26+00 1.39+01 1.26+01 5.96-01 5.41-01 3.00-02 4.83+00 4.18+00 2.23+00 7.06+00 6.41+00 3.04-01 2.76-01 4.00-02 4.44+00 4.05+00 8.78-01 5.31+00 4.93+00 2.29-01 2.12-01 5.00-02 4.18+00 3.93+00 4.25-01 4.61+00 4.35+00 1.98-01 1.87-01 6.00-02 4.00+00 3.82+00 2.38-01 4.24+00 4.06+00 1.82-01 1.74-01 8.00-02 3.73+00 3.62+00 9,40-02 3.82+00 3.72+00 1.64-01 1.60-01

1.00-01 3.52+00 3.454-00 4.54-02 3.56+00 3.49+00 1.53-01 1.50-01

1.50-01 3.13+00 3.11+00 1.22-02 3.15+00 3.12+00 1.35-01 1.34-01 2.00-01 2.86+00 2.85+00 4.85-03 2.86+00 2.85+00 1.23-01 1.23-01 3.00-01 2.48+00 2.48+00 1.38-03 2.49+00 2.48+00 1.07-01 1.06-01 4.00-01 2.22+00 5.89-04 2.22+00 9.54—02

5.00-01 2.03+00 3.16-04 2.03+00 8.71-02

6.00-01 1.87+00 1.97-04 1.87+00 8.05-02

8.00-01 1.65+00 9.94-05 1.65+00 7.08-02

1.00+00 1.48+00 6.15-05 1.48+00 6.36-02

1.50+00 1.20+00 2.88-05 2.19-03 1.21+00 5.18-02

2.00+00 1.03+00 1.84-05 8.71-03 1.03+00 4.45-02

3.00+00 8.07-01 1.03-05 2.50-02 2.82-04 8.33-01 3.58-02 4.00+00 6.73-01 6.99-06 4.06-02 1.16-03 7.15-01 3.07-02

5.00+00 5.81-01 5.36-06 5.44-02 2.27-03 6.38-01 2.74-02 6.00+00 5. 14—01 4.27-06 6.67-02 3.50-03 5.84-01 2.51-02

8.00+00 4.20-01 3.06-06 8.73-02 5.98-03 5.14-01 2.21-02

1.00+01 3.58-01 2.39-06 1.04-01 8.17-03 4.70-01 2.02-02

1.50+01 2.65-01 1.36-01 1.27-02 4.14-01 1.78-02 2.00+01 2.13-01 1.59-01 1.63-02 3.88-01 1.67-02

3.00+01 1.55-01 1.92-01 2.18-02 3.68-01 1.58-02

4.00+01 1.23-01 2.14-01 2.58-02 3.63-01 1.56-02

5.00+01 1.03-01 2.32-01 2.90-02 3.63-01 1.56-02

6.00+01 8.85-02 2.45-01 3.16-02 3.65-01 1.57-02

8.00+01 6.98-02 2.66-01 3.56-02 3.71-01 1.60-02

1.00+02 5.97-02 2.81-01 3.85-02 3.79-01 1.63-02

1.50+02 4.13-02 3.06-01 4.37-02 3.91-01 1.68-02 2.00+02 3.23-02 3.21-01 4.71-02 4.01-01 1.72-02 3.00+02 2.29-02 3.40-01 5.17-02 4.14-01 1.78-02 4.00+02 1.79-02 3.51-01 5.47-02 4.23-01 1.82-02 5.00+02 1.49-02 3.58-01 5.68-02 4.30-01 1.85-02 6.00+02 1 .27-02 3.63-01 5.84-02 4.35-01 1.87-02 8.00+02 9.94--03 3.70-01 6.08-02 4.41-01 1.90-02

1.00+03 8.18-03 3.75-01 6.24-02 4.46-01 1.92-02

1.50+03 5.71-03 3.82-01 6.51-02 4.53-01 1.95-02 2.00+03 4.42-03 3.86-01 6.68-02 4.57-01 1.96-02 3.00+03 3.07-03 3.90-01 6.89-02 4.62-01 1.99-02 4.00+03 2.37-03 3.92-01 7.00-02 4.64-01 2.00-02

5.00+03 1.94-03 3.93-01 7.07-02 4.66-01 2.00-02

6.00+03 1.64-03 3.94-01 7.13-02 4.67-01 2.01-02

8.00+03 1.27-03 3.95-01 7.20-02 4.69-01 2.02-02

1.00+04 1.03-03 3.96-01 7.24-02 4.70-01 2.02-02

1.50+04 7.15-04 3.97-01 7.31-02 4.71-01 2.03-02

2.00+04 5.50-04 3.98-01 7.34-02 4.72-01 2.03-02

3.00+04 3.79-04 3.99-01 7.38-02 4.73-01 2.03-02

4.00+04 2.91-04 3.99-01 7.40-02 4.73-01 2.03-02

5.00+04, 2.37-04 3.99-01 7.41-02 4.73-01 2.04-02

6.00+04 2.00-04 3.99-01 7.42-02 4.74-01 2.04-02

8.00+04 1 .54—04 3.99-01 7.43-02 4.74-01 2.04-02

1.00+05 1.25-04 3.99-01 7.43-02 4.74-01 2.04-02

(b/atom) x .043000= cm2/g

45
Table 3.-6. OXYGEN, Z=8

Photon

energy

Scattering Photoelectric

Pair production Total Total \

With

coherent Withoutcoherent Nuclear

field Electron

field Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm2/g 1.00-02 1.06+01 5.12+00 1.43+02 1.54+02 1.48+02 5.78+00 5.58+00

1.50-02 8.00+00 5.03+00 3.81+01 4.61+01 4.31+01 1.74+00 1.62+00 2.00-02 6.84+00 4.94+00 1.51+01 2.19+01 2.00+01 8.26-01 7.54-01 3.00-02 5.74+00 4.78+00 4.13+00 9.87+00 8.91+00 3.72-01 3.35-01 4.00-02 5.20+00 4.63+00 1.64+00 6.84+00 6.27+00 2.57-01 2.36-01 5.00-02 4.87+00 4.49+00 8.00-01 5.67+00 5.29+00 2.13-01 1.99-01 6.00-02 4.63+00 4.36+00 4.48-01 5.08+00 4.81+00 1.91-01 1.81-01 8.00-02 4.29+00 4.14+00 1.78-01 4.47+00 4.32+00 1.68-01 1.62-01 1.00-01 4.05+00 3.94+00 8.54-02 4.13+00 4.03+00 1.56-01 1.52-01

1.50-01 3.60+00 3.55+00 2.32-02 3.62+00 3.57+00 1.36-01 1.34-01 2.00-01 3.27+00 3.25+00 9.30-03 3.28+00 3.26+00 1.24-01 1.23-01 3.00-01 2.84+00 2.83+00 2.65-03 2.84+00 2.83+00 1.07-01 1.07-01 4.00-01 2.54+00 2.53+00 1.13-03 2.54+00 2.54+00 9.57-02 9.54-02

5.00-01 2.32+00 2.31+00 6.11-04 2.32+00 2.31+00 8.73-02 8.71-02

6.00-01 2.15+00 2.14+00 3.82-04 2.15+00 2.14+00 8.08-02 8.06-02

8.00-01 1.88+00 1.92-04 1.88+00 7.08-02

1.00+00 1.69+00 1.19-04 1.69+00 6.37-02

1.50+00 1.37+00 5.57-05 ' 2.86-03 1.38+00 5.18-02

2.00+00 1.17+00 3.54-05 1.14-02 1.18+00 4.46-02

3.00+00 9.23-01 1.98-05 3.27-02 3.22-04 9.56-01 3.60-02

4.00+00 7.69-01 1.35-05 5.30-02 1.32-03 8.24-01 3.10-02

5.00+00 6.65-01 1.03-05 7.11-02 2.60-03 7.38-01 2.78-02

6.00+00 5.87-01 8.22-06 8.70-02 3.99-03 6.78-01 2.55-02

8.00+00 4.80-01 5.88-06 1.14-01 6.83-03 6.01-01 2.26-02

1.00+01 4.09-01 4.61-06 1.36-01 9.34-03 5.54-01 2.09-02

1.50+01 3.03-01 1.77-01 1.45-02 4.95-01 1.86-02 2.00+01 2.43-01 2.08-01 1.87-02 4.69-01 1.77-02 3.00+01 1.77-01 2.50-01 2.49-02 4.52-01 1.70-02 4.00+01 1.41-01 2.79-01 2.95-02 4.49-01 1.69-02

5.00+01 1.17-01 3.01-01 3.31-02 4.52-01 1.70-02 6.00+01 1.01-01 3.19-01 3.61-02 4.56-01 1.72-02

8.00+01 7.98-02 3.46-01 4.05-02 4.66-01 1.75-02

1.00+02 6.62-02 3.65-01 4.39-02 4.75-01 1.79-02

1.50+02 4.72-02 3.97-01 4.97-02 4.94-01 1.86-02 2.00+02 3.70-02 4.17-01 5.36-02 5.08-01 1.91-02 3.00+02 2.62-02 4.40-01 5.87-02 5.25-01 1.98-02 4.00+02 2.05-02 4.54-01 6.21-02 5.37-01 2.02-02

5.00+02 1.70-02 4.63-01 6.44-02 5.45-01 2.05-02

6.00+02 1.45-02 4.70-01 6.62-02 5.51-01 2.07-02

8.00+02 1.14-02 4.79-01 6.88-02 5.59-01 2.10-02

1.00+03 9.34-03 4.84-01 7.07-02 5.65-01 2.12-02

1.50+03 6.53-03 4.93-01 7.37-02 5.73-01 2.16-02

2.00+03 5.05-03 4.98-01 7.56-02 5.78-01 2.18-02

3.00+03 3.51-03 5.02-01 7.78-02 5.84-01 2.20-02

4.00+03 2.71-03 5.05-01 7.90-02 5.87-01 2.21-02

5.00+03 2.22-03 5.07-01 7.98-02 5.89-01 2.22-02

6.00+03 1.88-03 5.08-01 8.04-02 5.90-01 2.22-02

8.00+03 1.45-03 5.09-01 8.11-02 5.92-01 2.23-02

1.00+04 1.18-03 5.10-01 8.16-02 5.93-01 2.23-02

1.50+04 8.17-04 5.12-01 8.23-02 5.95-01 2.24-02

2.00+04 6.28-04 5.12-01 8.27-02 5.96-01 2.24-02

3.00+04 4.33-04 5.13-01 8.31-02 5.97-01 2.25-02

4.00+04 3.33-04 5.13-01 8.33-02 5.97-01 2.25-02

5.00+04 2.71-04 5.14-01 8.34-02 5.97-01 2.25-02

6.00+04 2.29-04 5.14-01 8.35-02 5.98-01 2.25-02

8.00+04 1.75-04 5.14-01 8.37-02 5.98-01 2.25-02

1.00+05 1.43-04 5.14-01 8.38-02 5.98-01 2.25-02

(b/atom) x .037640 = cm2/?

46
Table 3.-7. SODIUM, Z=ll

Photon

energy.

Scattering PhotoelectricPair production Total Total

With

coherent Withoutcoherent Nuclearfield Electronfield Withcoherent Withoutcoherent With

coherent Withoutcoherent

MeV blatom blatom b/atom blatom b/atom b/atom b/atom cm2/g cm'2/g 1.00-02 2.19+01 7.04+00 5.69+02 5.91+02 5.76+02 1.55+01 1.51+01 1.50-02 1.49+01 6.92+00 1.60+02 1.75+02 1.67+02 4.58+00 4.37+00

2.00-02 1.18+01 6.80+00 6.48+01 7.66+01 7.16+01 2.01+00 1.88+00 3.00-02 9.11+00 6.57+00 1.78+01 2.69+01 2.44+01 7.05-01 6.39-01 4.00-02 7.90+00 6.37+00 7.18+00 1.51+01 1.35+01 3.95-01 3.55-01 5.00-02 7.19+00 6.18+00 3.53+00 1.07+01 9.71+00 2.81-01 2.54-01 6.00-02 6.73+00 6.00+00 1.99+00 8.72+00 7.99+00 2.28-01 2.09-01 8.00-02 6.11+00 5.69+00 7.92-01 6.90+00 6.48+00 1.81-01 1.70-01

1.00-01 5.69+00 5.42+00 3.85-01 6.08+00 5.80+00 1.59-01 1.52-01

1.50-01 5.01+00 4.88+00 1.06-01 5.11+00 4.99+00 1.34—01 1.31-01 2.00-01 4.54+00 4.47+00 4.29-02 4.58+00 4.51+00 1.20-01 1.18-01 3.00-01 3.92+00 3.89+00 1.24-02 3.93+00 3.90+00 1.03-01 1.02-01 4.00-01 3.50+00 3.48+00 5.31-03 3.50+00 3.49+00 9.18-02 9.14-02

5.00-01 3.19+00 3.18+00 2.86-03 3.19+00 3.18+00 8.36-02 8.34-02

6.00-01 2.95+00 2.94+00 1.78-03 2.95+00 2.95+00 7.74—02 7.72-02

8.00-01 2.59+00 9.01-04 2.59+00 6.78-02

1.00+00 2.33+00 5.58-04 2.33+00 6.09-02

1.50+00 1.89+00 2.61-04 5.46-03 1.90+00 4.97-02 2.00+00 1.61+00 1.67-04 2.16-02 1.63+00 4.28-02

3.00+00 1.27+00 9.25-05 6.19-02 4.43-04 1.33+00 3.49-02 4.00+00 1.06+00 6.28-05 1.00-01 1.82-03 1.16+00 3.04—02 5.00+00 9.14-01 4.79-05 1.34-01 3.57-03 1.05+00 2.76-02 6.00+00 8.08-01 3.82-05 1.64-01 5.49-03 9.77-01 2.56-02 8.00+00 6.61-01 2.73-05 2.15-01 9.40-03 8.85-01 2.32-02

1.00+01 5.63-01 2.14-05 2.56-01 1.28-02 8.31-01 2.18-02

1.50+01 4.16-01 3.34-01 2.00-02 7.70-01 2.02-02

2.00+01 3.34-01 3.90-01 2.57-02 7.50-01 1.96-02

3.00+01 2.43-01 4.69-01 3.42-02 7.47-01 1.96-02

4.00+01 1.93-01 5.24-01 4.05-02 7.58-01 1.99-02

5.00+01 1.61-01 5.65-01 4.55-02 7.72-01 2.02-02

6.00+01 1.39-01 5.98-01 4.94-02 7.87-01 2.06-02

8.00+01 1.10-01 6.47-01 5.53-02 8.12-01 2.13-02

1.00+02 9.11-02 6.82-01 5.98-02 8.33-01 2.18-02

1.50+02 6.48-02 7.39-01 6.75-02 8.72-01 2.28-02

2.00+02 5.08-02 7.74-01 7.27-02 8.97-01 2.35-02

3.00+02 3.60-02 8.14-01 7.95-02 9.30-01 2.44-02

4.00+02 2.82-02 8.38-01 8.38-02 9.50-01 2.49-02

5.00+02 2.34-02 8.53-01 8.69-02 9.64—01 2.52-02

6.00+02 2.00-02 8.65-01 8.92-02 9.74-01 2.55-02

8.00+02 1.56-02 8.79-01 9.26-02 9.87-01 2.59-02

1.00+03 1.28-02 8.88-01 9.50-02 9.96-01 2.61-02

1.50+03 8.97-03 9.03-01 9.89-02 1.01+00 2.65-02

2.00+03 6.94—03 9.10-01 1.01-01 1.02+00 2.67-02

3.00+03 4.83-03 9.18-01 1.04-01 1.03+00 2.69-02

4.00+03 3.73-03 9.23-01 1.05-01 1.03+00 2.70-02

5.00+03 3.05-03 9.26-01 1.06-01 1.04+00 2.71-02

6.00+03 2.58-03 9.28-01 1.07-01 1.04+00 2.72-02

8.00+03 1.99-03 9.30-01 1.08-01 1.04+00 2.72-02

1.00+04 1.63-03 9.31-01 1.08-01 1.04+00 2.73-02

1.50+04 1.12-03 9.34-01 1.09-01 1.04+00 2.74-02 2.00+04 8.64-04 9.36-01 1.10-01 1.05+00 2.74-02

3.00+04 5.96-04 9.36-01 1.10-01 1.05+00 2.74-02

4.00+04 4.57-04 9.37-01 1.10-01 1.05+00 2.75-02

5.00+04 3.72-04 9.38-01 1.11-01 1.05+00 2.75-02

6.00+04 3.15-04 9.38-01 1.11-01 1.05+00 2.75-02

8.00+04 2.41-04 9.38-01 1.11-01 1.05+00 2.75-02

1.00+05 1.96-04 9.38-01 1.11-01 1.05+00 2.75-02

(b/atom) x . 026200 = cm2/g

47
Table 3.-8. MAGNESIUM, Z=12

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electronfield Withcoherent Withoutcoherent With

coherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm2/g 1.00-02 2.60+01 7.68+00 8.13+02 8.39+02 8.21+02 2.08+01 2.03+01

1.50-02 1.75+01 7.55+00 2.34+02 2.52+02 2.42+02 6.23+00 5.98+00

2.00-02 1.37+01 7.41+00 9.60+01 1.10+02 1.03+02 2.72+00 2.56+00

3.00-02 1.03+01 7.17+00 2.67+01 3.70+01 3.39+01 9.18-01 8.39-01 4.00-02 8.87+00 6.94+00 1.07+01 1.96+01 1.76+01 4.85-01 4.37-01 5.00-02 8.02+00 6.74+00 5.28+00 1.33+01 1.20+01 3.29-01 2.98-01 6.00-02 7.46+00 6.55+00 2.97+00 1.04+01 9.52+00 2.58-01 2.36-01 8.00-02 6.73+00 6.21+00 1.19+00 7.92+00 7.40+00 1.96-01 1.83-01

1.00-01 6.25+00 5.91+00 5.81-01 6.83+00 6.49+00 1.69-01 1.61-01

1.50-01 5.48+00 5.32+00 1.60-01 5.64+00 5.48+00 1.40-01 1.36-01 2.00-01 4.96+00 4.88+00 6.48-02 5.03+00 4.94+00 1.25-01 1.22-01 3.00-01 4.28+00 4.24+00 1.87-02 4.30+00 4.26+00 1.06-01 1.06-01 4.00-01 3.82+00 3.80+00 8.08-03 3.83+00 3.81+00 9.49-02 9.44-02

5.00-01 3.48+00 3.47+00 4.35-03 3.49+00 3.48+00 8.64-02 8.61-02

6.00-01 3.22+00 3.21+00 2.72-03 3.22+00 3.21+00 7.97-02 7.96-02

8.00-01 2.83+00 2.82+00 1.37-03 2.83+00 2.82+00 7.01-02 6.99-02

1.00+00 2.54+00 2.54+00 8.50-04 2.54+00 2.54+00 6.28-02 6.29-02

1.50+00 2.06+00 3.99-04 6.52-03 2.07+00 5.12-02

2.00+00 1.76+00 2.53-04 2.58-02 1.79+00 4.42-02

3.00+00 1 .38+00 1.40-04 7.36-02 4.83-04 1.46+00 3.61-02

4.00+00 1.15+00 9.53-05 1.19-01 1.98-03 1.28+00 3.16-02

5.00+00 9.97-01 7.27-05 1.60-01 3.89-03 1.16+00 2.87-02

6.00+00 8.81-01 5.79-05 1.95-01 5.99-03 1.08+00 2.68-02

8.00+00 7.21-01 4.14-05 2.55-01 1.02-02 9.86-01 2.44-02

1.00+01 6. 14—01 3.23-05 3.04-01 1.40-02 9.32-01 2.31-02

1.50+01 4.54—01 3.96-01 2.18-02 8.73-01 2.16-02

2.00+01 3.65-01 4.63-01 2.80-02 8.56-01 2.12-02

3.00+01 2.66-01 5.57-01 3.73-02 8.60-01 2.13-02

4.00+01 2.11-01 6.22-01 4.42-02 8.77-01 2.17-02

5.00+01 1.76-01 6.71-01 4.95-02 8.97-01 2.22-02

6.00+01 1.52-01 7.10-01 5.37-02 9.15-01 2.27-02

8.00+01 1.20-01 7.67-01 6.02-02 9.47-01 2.35-02

1.00+02 9.93-02 8.09-01 6.50-02 9.73-01 2.41-02

1.50+02 7.07-02 8.76-01 7.34-02 1.02+00 2.53-02

2.00+02 5.54-02 9.16-01 7.91-02 1.05+00 2.60-02

3.00+02 3.93-02 9.64-01 8.63-02 1.09+00 2.70-02

4.00+02 3.08-02 9.91-01 9.10-02 1.11+00 2.76-02

5.00+02 2.55-02 1.01+00 9.43-02 1.13+00 2.80-02

6.00+02 2.18-02 1.02+00 9.67-02 1.14+00 2.83-02

8.00+02 1.70-02 1.04+00 1.00-01 1.16+00 2.87-02

1.00+03 1.40-02 1.05+00 1.03-01 1.17+00 2.90-02

1.50+03 9.79-03 1.07+00 1.07-01 1.18+00 2.93-02

2.00+03 7.58-03 1.08+00 1.10-01 1.19+00 2.96-02

3.00+03 5.27-03 1.09+00 1.12-01 1.20+00 2.98-02

4.00+03 4.07-03 1.09+00 1.14-01 1.21+00 3.00-02

5.00+03 3.33-03 1.10+00 1.15-01 1.21+00 3.01-02

6.00+03 2.82-03 1.10+00 1.16-01 1.22+00 3.02-02

8.00+03 2.17-03 1.10+00 1.17-01 1.22+00 3.02-02

1.00+04 1.77-03 1.10+00 1.17-01 1.22+00 3.03-02

1.50+04 1.23-03 1.11+00 1.18-01 1.23+00 3.03-02

2.00+04 9.42-04 1.11+00 1.18-01 1.23+00 3.04-02

3.00+04 6.50-04 1.11+00 1.19-01 1.23+00 3.04-02

4.00+04 4.99-04 1.11+00 1.19-01 1.23+00 3.05-02

5.00+04 4.06-04 1.11+00 1.19-01 1.23+00 3.05-02

6.00+04 3.43-04 1.11+00 1.20-01 1.23+00 3.05-02

8.00+04 2.63-04 1.11+00 1.20-01 1.23+00 3.05-02

1.00+05 2.14-04 1.11+00 1.20-01 1.23+00 3.05-02

(b/atom) x .024770= cm2 /g

48
Table 3.-9. ALUMINUM, Z=I3

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Withoutcoherent Nuclear

field Electronfield With

coherent Without

coherent With

coherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g

1.00-02 3.04+01 8.32+00 1.15+03 1.18+03 1.16+03 2.63+01 2.58+01

1.50-02 2.03+01 8.17+00 3.35+02 3.55+02 3.43+02 7.93+00 7.66+00

2.00-02 1.57+01 8.03+00 1.37+02 1 .53+02 1.45+02 3.41+00 3.24+00

3.00-02 1.17+01 7.77+00 3.85+01 5.02+01 4.63+01 1.12+00 1.03+00 4.00-02 9.89+00 7.52+00 1.55+01 2.54+01 2.30+01 5.67-01 5.14-01 5.00-02 8.88+00 7.30+00 7.65+00 1.65+01 1.49+01 3.69-01 3.34-01 6.00-02 8.22+00 7.09+00 4.33+00 1.25+01 1.14+01 2.80-01 2.55-01 8.00-02 7.38+00 6.72+00 1.73+00 9.11+00 8.45+00 2.03-01 1.89-01

1.00-01 6.83+00 6.41+00 8.45-01 7.67+00 7.25+00 1.71-01 1.62-01

1.50-01 5.96+00 5.77+00 2.33-01 6.19+00 6.00+00 1.38-01 1.34-01 2.00-01 5.39+00 5.28+00 9.53-02 5.49+00 5.38+00 1.22-01 1.20-01 3.00-01 4 . 64+00 4.60+00 2.76-02 4.67+00 4.62+00 1.04^-01 1.03-01 4.00-01 4.14+00 4.12+00 1 . 19—02 4.15+00 4.13+00 9.27-02 9.22-02

5.00-01 3.78+00 3.76+00 6.43-03 3.78+00 3.77+00 8.44-02 8.41-02

6.00-01 3.49+00 3.48+00 4.02-03 3.49+00 3.48+00 7.80-02 7.77-02

8.00-01 3.06+00 3.06+00 2.04-03 3.06+00 3.06+00 6.84-02 6.83-02

1.00+00 2.75+00 2.75+00 1.26-03 2.75+00 2.75+00 6.13-02 6.14-02

1.50+00 2.23+00 5.89-04 7.68-03 2.24+00 5.00-02

2.00+00 1.91+00 3.73-04 3.03-02 1.94+00 4.32-02

3.00+00 1.50+00 2.07-04 8.65-02 5.23-04 1.59+00 3.54-02

4.00+00 1.25+00 1.41-04 1.40-01 2.15-03 1.39+00 3.11-02 5.00+00 1.08+00 1.07-04 1.87-01 4.22-03 1.27+00 2.84-02

6.00+00 9.54—01 8.53-05 2.29-01 6.49-03 1.19+00 2.66-02

8.00+00 7.81-01 6.09-05 2.99—01 1.11-02 1.09+00 2.44-02

1.00+01 6.65-01 4.76-05 3.57-01 1.52-02 1.04+00 2.31-02

1.50+01 4.92-01 4.65-01 2.36-02 9.80-01 2.19-02

2.00+01 3.95-01 5.43-01 3.03-02 9.68-01 2.16-02

3.00+01 2.88-01 6.52-01 4.04^-02 9.81-01 2.19-02

4.00+01 2.29—01 7.29-01 4.79-02 1.01+00 2.24-02

5.00+01 1.91-01 7.86-01 5.36-02 1.03+00 2.30-02

6.00+01 1.64-01 8.31-01 5.81-02 1.05+00 2.35-02

8.00+01 1.30-01 8.98-01 6.51-02 1.09+00 2.44-02

1.00+02 1.08-01 9.46-01 7.03-02 1.12+00 2.51-02

1.50+02 7.66-02 1.02+00 7.93-02 1.18+00 2.63-02

2.00+02 6.01-02 1.07+00 8.53-02 1.21+00 2.71-02

3.00+02 4.26-02 1.13+00 9.31-02 1.26+00 2.82-02

4.00+02 3.33-02 1.16+00 9.81-02 1.29+00 2.88-02

5.00+02 2.76-02 1.18+00 1.02-01 1.31+00 2.92-02

6.00+02 2.36-02 1.19+00 1.04-01 1.32+00 2.95-02

8.00+02 1.85-02 1.22+00 1.08-01 1.34+00 3.00-02

1.00+03 1.52-02 1.23+00 1.11-01 1.35+00 3.02-02

1.50+03 1.06-02 1.25+00 1.15-01 1.37+00 3.07-02

2.00+03 8.21-03 1.26+00 1.18-01 1.38+00 3.09-02

3.00+03 5.71-03 1.27+00 1.21-01 1.40+00 3.12-02

4.00+03 4.40-03 1.28+00 1.22-01 1.40+00 3.13-02

5.00+03 3.60-03 1.28+00 1.23-01 1.41+00 3. 14^-02 6.00+03 3.05-03 1.28+00 1.24-01 1.41+00 3.15-02

8.00+03 2.35-03 1.29+00 1.25-01 1.41+00 3.16-02

1.00+04 1.92-03 1.29+00 1.26-01 1.42+00 3.16-02

1.50+04 1.33-03 1.29+00 1.27-01 1.42+00 3.17-02

2.00+04 1 .02-03 1.29+00 1.27-01 1.42+00 3.17-02

3.00+04 7.0+-04 1.30+00 1.28-01 1.42+00 3.18-02

4.00+04 5.40-04 1.30+00 1.28-01 1.43+00 3.18-02

5.00+04 4.40—04 1.30+00 1.28-01 1.43+00 3.18-02

6.00+04 3.72-04 1.30+00 1.28-01 1.43+00 3.18-02

8.00+04 2.85-04 1.30+00 1.28-01 1.43+00 3.18-02

1.00+05 2.32-04 1.30+00 1.28-01 1.43+00 3.19-02

(b/atorn) x .022320 = cm2

/j'

49
Table 3.-10. SILICON, Z=14

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electronfield Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm2 /g cm'2 /g 1.00-02 3.50+01 8.97+00 1.56+03 1.59+03 1.57+03 3.42+01 3.36+01

1.50-02 2.34+01 8.80+00 4.56+02 4.79+02 4.65+02 1.03+01 9.97+00

2.00-02 1.78+01 8.65+00 1.87+02 2.05+02 1.96+02 4.39+00 4.19+00

3.00-02 1.31+01 8.36+00 5.29+01 6.60+01 6.13+01 1.41+00 1.31+00 4.00-02 1.10+01 8.10+00 2.15+01 3.25+01 2.96+01 6.96-01 6.35-01 5.00-02 9.79+00 7.86+00 1.06+01 2.04+01 1.85+01 4.37-01 3.96-01 6.00-02 9.01+00 7.64+00 6.00+00 1.50+01 1.36+01 3.22-01 2.92-01 8.00-02 8.04+00 7.24+00 2.42+00 1.05+01 9.66+00 2.24-01 2.07-01

1.00-01 7.41+00 6.90+00 1.19+00 8.60+00 8.09+00 1.84-01 1.73-01

1.50-01 6.44+00 6.21+00 3.29-01 6.77+00 6.54+00 1.45-01 1.40-01 2.00-01 5.82+00 5.69+00 1 .34—01 5.96+00 5.82+00 1.28-01 1.25-01 3.00-01 5.01+00 4.95+00 3.91-02 5.05+00 4.99+00 1.08-01 1.07-01 4.00-01 4.47+00 4.43+00 1.69-02 4.49+00 4.45+00 9.62-02 9.54-02

5.00-01 4.07+00 4.05+00 9.15-03 4.08+00 4.06+00 8.75-02 8.70-02

6.00-01 3.76+00 3.75+00 5.72-03 3.77+00 3.75+00 8.08-02 8.05-02

8.00-01 3.29+00 3.29+00 2.89-03 3.30+00 3.29+00 7.07-02 7.06-02

1.00+00 2.96+00 1.79-03 2.96+00 6.35-02

1.50+00 2.40+00 8.36-04 8.94-03 2.41+00 5.18-02

2.00+00 2.05+00 5.30-04 3.52-02 2.09+00 4.48-02

3.00+00 1.61+00 2.93-04 1.00-01 5.63-04 1.72+00 3.68-02

4.00+00 1.35+00 1.99-04 1.62-01 2.31-03 1.51+00 3.24-02

5.00+00 1.16+00 1.42-04 2.17-01 4.54-03 1.38+00 2.97-02

6.00+00 1.03+00 1.21-04 2.67-01 6.99-03 1.30+00 2.79-02

8.00+00 8.41-01 8.61-05 3.47-01 1.20-02 1.20+00 2.57-02

1.00+01 7.16-01 6.74-05 4.13-01 1.63-02 1.15+00 2.46-02

1.50+01 5.30-01 5.38-01 2.55-02 1.09+00 2.34-02

2.00+01 4.25-01 6.28-01 3.27-02 1.09+001 2.33-02

3.00+01 3.10-01 7.55-01 4.35-02 1.11+00 2.38-02

4.00+01 2.46-01 8.43-01 5.16-02 1.14+00 2.45-02

5.00+01 2.05-01 9.13-01 5.76-02 1.18+00 2.52-02

6.00+01 1.77-01 9.61-01 6.25-02 1.20+00 2.57-02

8.00+01 1.40-01 1.04+00 6.99-02 1.25+00 2.67-02

1.00+02 1.16-01 1.09+00 7.55-02 1.28+00 2.75-02

1.50+02 8.25-02 1.18+00 8.51-02 1.35+00 2.89-02

2.00+02 6.47-02 1.24+00 9.16-02 1.39+00 2.99-02

3.00+02 4.58-02 1.30+00 9.98-02 1.45+00 3.10-02

4.00+02 3.59-02 1.34+00 1.05-01 1.48+00 3.17-02

5.00+02 2.97-02 1.36+00 1.09-01 1.50+00 3.22-02

6.00+02 2.55-02 1.38+00 1.12-01 1.52+00 3.25-02

8.00+02 1.9<M)2 1.40+00 1.16-01 1.54+00 3.30-02

1.00+03 1.63-02 1.42+00 1.19-01 1.55+00 3.33-02

1.50+03 1.14-02 1.44+00 1.23-01 1.58+00 3.38-02

2.00+03 8.84-03 1.45+00 1.26-01 1.59+00 3.41-02

3.00+03 6.15-03 1.47+00 1.29-01 1.60+00 3.44^-02 4.00+03 4.74-4)3 1.47+00 1.31-01 1.61+00 3.45-02

5.00+03 3.88-03 1.48+00 1.32-01 1.61+00 3.46-02

6.00+03 3.29-03 1.48+00 1.33-01 1.62+00 3.47-02

8.00+03 2.53-03 1.49+00 1.34-01 1.62+00 3.48-02

1.00+04 2.07-03 1.49+00 1 .34—01 1.63+00 3.48-02

1.50+04 1.43-03 1.49+00 1.35-01 1.63+00 3.49-02

2.00+04 1.10-03 1.49+00 1.36-01 1.63+00 3.50-02

3.00+04 7.58-04 1.50+00 1.36-01 1.63+00 3.50-02

4.00+04 5.82-04 1.50+00 1.37-01 1.64+00 3.51-02

5.00+04 4.74—04 1.50+00 1.37-01 1.64+00 3.51-02

6.00+04 4.01-04 1.50+00 1.37-01 1.64+00 3.51-02

8.00+04 3.07-04 1.50+00 1.37-01 1.64+00 3.51-02

1.00+05 2.50-04 1.50+00 1.37-01 1.64+00 3.51-02

(b/atom) x .021440 = cm^g

50
Table 3.-11. PHOSPHORUS, Z=15

Photon

energy

Scattering PhotoPair production Total Total

With

coherent Withoi

cohere!

electric Nuclear

field Electron

field Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm'2 /g cm'2 /g 1.00-02 3.99+01 9.61+00 2.06+03 2.10+03 2.07+03 4.08+01 4.02+01

1.50-02 2.66+01 9.43+00 6.10+02 6.37+02 6.19+02 1.24+01 1.20+01 2.00-02 2.02+01 9.27+00 2.53+02 2.73+02 2.62+02 5.31+00 5.10+00

3.00-02 1.46+01 8.96+00 7.10+01 8.56+01 8.00+01 1.66+00 1.55+00 4.00-02 1.21+01 8.68+00 2.89+01 4.10+01 3.76+01 7.97-01 7.31-01 5.00-02 1.07+01 8.42+00 1.44+01 2.51+01 2.28+01 4.89-01 4.44-01 6.00-02 9.84+00 8.18+00 8.16+00 1.80+01 1.63+01 3.50-01 3.18-01 8.00-02 8.71+00 7.76+00 3.31+00 1.20+01 1.11+01 2.34-01 2.15-01

1.00-01 8.00+00 7.39+00 1.61+00 9.61+00 9.00+00 1.87-01 1.75-01

1.50-01 6.93+00 6.65+00 4.53-01 7.39+00 7.11+00 1.44-01 1.38-01 2.00-01 6.25+00 6.10+00 1.85-01 6.44+00 6.28+00 1.25-01 1.22-01 3.00-01 5.38+00 5.30+00 5.41-02 5.43+00 5.36+00 1.06-01 1.04—01 4.00-01 4.79+00 4.75+00 2.35-02 4.81+00 4.78+00 9.36-02 9.28-02

5.00-01 4.36+00 4.34+00 1.27-02 4.37+00 4.35+00 8.50-02 8.46-02

6.00-01 4.03+00 4.01+00 7.95-03 4.03+00 4.02+00 7.84-02 7.82-02

8.00-01 3.54+00 3.53+00 4.01-03 3.54+00 3.53+00 6.88-02 6.86-02

1.00+00 3.17+00 2.49-03 3.17+00 6.17-02

1.50+00 2.58+00 1.17-03 1.03-02 2.59+00 5.03-02

2.00+00 2.20+00 7.36-04 4.05-02 2.24+00 4.36-02

3.00+00 1.73+00 4.07-04 1.15-01 6.04-04 1.85+00 3.59-02

4.00+00 1.44+00 2.76-04 1.86-01 2.48-03 1.63+00 3.17-02

5.00+00 1.25+00 2.11-04 2.49-01 4.87-03 1.50+00 2.92-02

6.00+00 1.10+00 1.67-04 3.04-01 7.49-03 1.41+00 2.75-02

8.00+00 9.01-01 1.19-04 3.98-01 1.28-02 1.31+00 2.55-02

1.00+01 7.67-01 9.32-05 4.73-01 1.75-02 1.26+00 2.45-02

1.50+01 5.68-01 6.16-01 2.73-02 1.21+00 2.36-02

2.00+01 4.56-01 7.20-01 3.50-02 1.21+00 2.35-02

3.00+01 3.32-01 8.66-01 4.66-02 1.24+00 2.42-02

4.00+01 2.64-4)1 9.67-01 5.52-02 1.29+00 2.50-02

5.00+01 2.20-01 1.04+00 6.17-02 1.32+00 2.57-02

6.00+01 1.90-01 1.10+00 6.68-02 1.36+00 2.64-02

8.00+01 1.50-01 1.19+00 7.47-02 1.41+00 2.74-02

1.00+02 1.24-01 1.25+00 8.06-02 1.45+00 2.83-02

1.50+02 8.84-02 1.35+00 9.09-02 1.53+00 2.98-02

2.00+02 6.93-02 1.41+00 9.78-02 1.58+00 3.07-02

3.00+02 4.91-02 1.49+00 1.06-01 1.64+00 3.19-02

4.00+02

| 3.85-02 1.53+00 1.12-01 1.68+00 3.27-02

5.00+02 3.18-02 1.56+00 1.16-01 1.71+00 3.32-02

6.00+02 2.73-02 1.58+00 1.19-01 1.72+00 3.35-02

8.00+02 2.13-02 1.60+00 1.23-01 1.75+00 3.40-02

1.00+03 1.75-02 1.62+00 1.26-01 1.77+00 3.44-02

1.50+03 1.22-02 1.65+00 1.31-01 1.79+00 3.48-02

2.00+03 9.47-03 1.66+00 1.34-01 1.81+00 3.51-02

3.00+03 6.58-03 1.68+00 1.37-01 1.82+00 3.54-02

4.00+03 5.08-03 1.69+00 1.39-01 1.83+00 3.56-02

5.00+03 4.16-03 1.69+00 1.40-01 1.84+00 3.57-02 6.00+03 3.52-03 1.70+00 1.41-01 1.84+00 3.58-02

8.00+03 2.71-03 1.70+00 1.42-01 1.85+00 3.59-02

1.00+04 2.22-03 1.70+00 1.43-01 1.85+00 3.59-02

1.50+04 1.53-03 1.71+00 1.44-01 1.85+00 3.60-02

2.00+04 1.18-03 1.71+00 1.44-01 1.86+00 3.61-02

3.00+04 8.12-04 1.71+00 1.45-01 1.86+00 3.61-02

4.00+04 6.24-04 1.71+00 1.45-01 1.86+00 3.61-02

5.00+04 5.08-04 1.71+00 1.45-01 1.86+00 3.62-02

6.00+04 4.29-04 1.71+00 1.45-01 1.86+00 3.62-02

8.00+04 3.29-04 1.71+00 1.46-01 1.86+00 3.62-02

1.00+05 2.68-04 1.72+00 1.46-01 1.86+00 3.62-02

(b/atom) x .019440 = cm2 /g

51
Table 3.-12. SULFUR, Z=16

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Withoutcoherent Nuclearfield Electronfield Withcoherent Without

coherent With

coherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm 2 /g 1.00-02 4.52+01 1.02+01 2.67+03 2.72+03 2.68+03 5.10+01 5.03+01

1.50-02 3.03+01 1.01+01 8.00+02 8.30+02 8.10+02 1.56+01 1.52+01 2.00-02 2.28+01 9.89+00 3.32+02 3.55+02 3.42+02 6.66+00 6.42+00

3.00-02 1.62+01 9.56+00 9.40+01 1.10+02 1.04+02 2.07+00 1.94+00 4.00-02 1.33+01 9.26+00 3.82+01 5.15+01 4.75+01 9.68-01 8.91-01 5.00-02 1.17+01 8.98+00 1.91+01 3.08+01 2.81+01 5.79-01 5.27-01 6.00-02 1.07+01 8.73+00 1.08+01 2.15+01 1.95+01 4.04—01 3.67-01 8.00-02 9.41+00 8.28+00 4.40+00 1.38+01 1.27+01 2.59-01 2.38-01

1.00-01 8.61+00 7.88+00 2.16+00 1.08+01 1.00+01 2.02-01 1.89-01

1.50-01 7.43+00 7.10+00 6.10-01 8.04+00 7.71+00 1.51-01 1.45-01 2.00-01 6.69+00 6.50+00 2.51-01 6.94+00 6.75+00 1.30-01 1.27-01 3.00-01 5.73+00 5.66+00 7.35-02 5.81+00 5.73+00 1.09-01 1.08-01 4.00-01 5.11+00 5.07+00 3.19-02 5.14+00 5.10+00 9.66-02 9.58-02

5.00-01 4.66+00 4.63+00 1.73-02 4.67+00 4.65+00 8.78-02 8.72-02

6.00-01 4.30+00 4.28+00 1.08-02 4.31+00 4.29+00 8.10-02 8.06-02

8.00-01 3.77+00 3.76+00 5.48-03 3.77+00 3.77+00 7.09-02 7.08-02

1. 001-00 3.39+00 3.38+00 3.39-03 3.40+00 3.39+00 6.38-02 6.36-02

1.50+00 2.74+00 2.75+00 1.59-03 1.18-02 2.76+00 2.76+00 5.18-02 5.19-02

2.00+00 2.34+00 1.00-03 4.62-02 2.39+00 4.49-02

3.00+00 1.84+00 5.53-04 1.31-01 6.44—04 1.98+00 3.71-02

4.00+00 1.54+00 3.74—04 2.12-01 2.64—03 1.75+00 3.29-02

5.00+00 1.33+00 2.86-04 2.83-01 5.19-03 1.62+00 3.04—02

6.00+00 1.17+00 2.27-04 3.46-01 7.99-03 1.53+00 2.87-02

8.00+00 9.61-01 1.62-04 4.52-01 1.37-02 1.43+00 2.68-02

1.00+01 8.18-01 1.26-04 5.38-01 1.87-02 1.38+00 2.58-02

1.50+01 6.06-01 7.00-01 2.91-02 1.34+00 2.51-02

2.00+01 4.86-01 8.18-01 3.73-02 1.34+00 2.52-02

3.00+01 3.54-01 9.83-01 < 4.98-02 1.39+00 2.61-02

4.00+01 2.81-01 1.10+00 5.88-02 1.44+00 2.70-02

5.00+01 2.35-01 1.18+00 6.57-02 1.48+00 2.78-02

6.00+01 2.02-01 1.25+00 7.11-02 1.52+00 2.86-02

8.00+01 1.60-01 1.35+00 7.95-02 1.59+00 2.98-02

1.00+02 1.33-01 1.42+00 8.58-02 1.64+00 3.07-02

1.50+02 9.43-02 1.53+00 9.67-02 1.72+00 3.24—02

2.00+02 7.39-02 1.60+00 1.04-01 1.78+00 3.34-02

3.00+02 5.24-02 1.68+00 1.13-01 1.85+00 3.48-02

4.00+02 4.10-02 1.73+00 1.19-01 1.89+00 3.56-02

5.00+02 3.40-02 1.77+00 1.23-01 1.92+00 3.61-02

6.00+02 2.91-02 1.79+00 1.26-01 1.95+00 3.65-02

8.00+02 2.27-02 1.82+00 1.31-01 1.97+00 3.70-02

1.00+03 1.87-02 1.84+00 1.34—01 1.99+00 3.74-02

1.50+03 1.30-02 1.87+00 1.39-01 2.02+00 3.80-02

2.00+03 1.01-02 1.89+00 1.42-01 2.04+00 3.83-02

3.00+03 7.02-03 1.90+00 1.45-01 2.06+00 3.86-02

4.00+03 5.42-03 1.91+00 1.47-01 2.06+00 3.88-02

5.00+03 4.43-03 1.92+00 1.49-01 2.07+00 3.89-02

6.00+03 3.76-03 1.92+00 1.49-01 2.08+00 3.90-02

8.00+03 2.90-03 1.93+00 1.50-01 2.08+00 3.91-02

1.00+04 2.37-03 1.93+00 1.51-01 2.08+00 3.91-02

1.50+04 1.63-03 1.94+00 1.52-01 2.09+00 3.92-02

2.00+04 1.26-03 1.94+00 1.53-01 2.09+00 3.93-02

3.00+04 8.66-04 1.94+00 1.53-01 2.09+00 3.93-02

4.00+04 6.65-04 1.94+00 1.54-01 2.10+00 3.94-02 | 5.00+04 5.42-04 1.94+00 1.54-01 2.10+00 3.94-02

6.00+04 4.58-04 1.94+00 1 .54—01 2.10+00 3.94-02

8.00+04 3.51-04 1.94+00 1.54-01 2.10+00 3.94-02 I 1.00+05 2.86-04 1.94+00 1.54-01 2.10+00 3.94-02

(b/atom) x .018780 = cm2 /g

52
Table 3.-13. ARGON, Z=18

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Withoutcoherent Nuclear

field Electron

field Withcoherent Without

coherent With

coherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm'2 /g cm2 /g

1.00-02 5.66+01 1.15+01 4.22+03 4.28+03 4.23+03 6.45+01 6.38+01

1.50-02 3.84+01 1.13+01 1.28+03 1.32+03 1.29+03 1.99+01 1.95+01 2.00-02 2.87+01 1.11+01 5.37+02 5.66+02 5.48+02 8.53+00 8.27+00

3.00-02 1.97+01 1.08+01 1.54+02 1.74+02 1.65+02 2.62+00 2.48+00

4.00-02 1.59+01 1.04+01 6.34+01 7.93+01 7.38+01 1.20+00 1.11+00 5.00-02 1.38+01 1.01+01 3.17+01 4.55+01 4.18+01 6.87-01 6.30-01 6.00-02 1.25+01 9.82+00 1.80+01 3.05+01 2.78+01 4.60-01 4.20-01 8.00-02 1.09+01 9.31+00 7.40+00 1.83+01 1.67+01 2.75-01 2.52-01

1.00-01 9.87+00 8.87+00 3.65+00 1.35+01 1.25+01 2.04-01 1.89-01

1.50-01 8.44+00 7.98+00 1.05+00 9.49+00 9.03+00 1.43-01 1.36-01 2.00-01 7.58+00 7.324-00 4.34-01 8.01+00 7.75+00 1.21-01 1.17-01 3.00-01 6.48+00 6.364-00 1.28-01 6.61+00 6.49+00 9.96-02 9.79-02

4.00-01 5.77+00 5.704-00 5.57-02 5.82+00 5.76+00 8.78-02 8.68-02

5.00-01 5.24+00 5.21+00 3.01-02 5.27+00 5.24+00 7.95-02 7.90-02

6.00-01 4.84+00 4.82+00 1.89-02 4.86+00 4.84+00 7.33-02 7.29-02

8.00-01 4.24+00 4.23+00 9.60-03 4.25+00 4.24+00 6.41-02 6.40—02' 1.00+00 3.82+00 3.80+00 5.95-03 3.82+00 3.81+00 5.76-02 5. 75-02 1 1.50+00 3.10+00 3.09+00 2.77-03 1.51-02 3.11+00 3.11+00 4.70-02 4.69-02

2.00+00 2.64+00 1.75-03 5.88-02 2.70+00 4.07-02 3.00+00 2.08+00 9.6^—04 1.66-01 7.24-04 2.24+00 3.38-02

4.00+00 1.73+00 6.52-04 2.68-01 2.97-03 2.00+00 3.02-02

5.00+00 1.49400 4.96-04 3.58-01 5.84-03 1.86+00 2.80-02 6.00+00 1.32+00 3.94-04 4.38-01 8.98-03 1.77+00 2.67-02 8.00+00 1.08+00 2.81-04 5.71-01 1.54-02 1.67+00 2.51-02

1.00+01 9.21-01 2.19-04 6.79-01 2.10-02 1.62+00 2.44-02

1.50+01 6.81-01 8.84-01 3.27-02 1.60+00 2.41-02

2.00+01 5.47-01 1.03+00 4.20-02 1.62+00 2.44^02

3.00+01 3.98-01 1.24+00 5.60-02 1.69+00 2.55-02

4.00+01 3.16-01 1.38+00 6.60-02 1.76+00 2.66-02

5.00+01 2.64-01 1.49+00 7.36-02 1.83+00 2.75-02

6.00+01 2.28-01 1.57+00 7.98-02 1.88+00 2.84-02

8.00+01 1.79-01 1.69+00 8.90-02 1.96+00 2.96-02

1.00+02 1.49-01 1.78+00 9.60-02 2.03+00 3.06-02

1.50+02 1.06-01 1.94+00 1.08-01 2.16+00 3.25-02

2.00+02 8.32-02 2.02+00 1.16-01 2.22+00 3.34-02

3.00+02 5.89-02 2.12+00 1.26-01 2.31+00 3.48-02

4.00+02 4.62-02 2.18+00 1.33-01 2.36+00 3.56-02

5.00+02 3.82-02 2.22+00 1.37-01 2.39+00 3.61-02

6.00+02 3.27-02 2.25+00 1.41-01 2.42+00 3.65-02

8.00+02 2.56-02 2.29+00 1.46-01 2.46+00 3.71-02

1.00+03 2.10-02 2.31+00 1.49—01 2.48+00 3.75-02

1.50+03 1.47-02 2.35+00 1.55-01 2.52+00 3.80-02

2.00+03 1.14-02 2.37+00 1.58-01 2.54+00 3.82-02

3.00+03 7.90-03 2.39+00 1.62-01 2.56+00 3.86-02

4.00+03 6.10-03 2.40+00 1.64-01 2.57+00 3.87-02

5.00+03 4.99-03 2.41+00 1.65-01 2.58+00 3.89-02

6.00+03 4.23-03 2.41+00 1.66-01 2.58+00 3.89-02

8.00+03 3.26-03 2.42+00 1.67-01 2.59+00 3.91-02

1.00+04 2.66-03 2.42+00 1.68-01 2.60+00 3.91-02

1.50+04 1.84-03 2.43+00 1.69-01 2.60+00 3.92-02

2.00+04 1.41-03 2.43+00 1.69-01 2.60+00 3.93-02

3.00+04 9.75-04 2.44+00 1.70-01 2.61+00 3.93-02

4.00+04 7.48-04 2.44+00 1.70-01 2.61+00 3.93-02

5.00+04 6.09-04 2.44+00 1.71-01 2.61+00 3.93-02

6.00+04, 5.15-04 2.44+00 1.71-01 2.61+00 3.94-02

8.00+04 3.95-04 2.44+00 1.71-01 2.61+00 3.94-02

1.00+05: 3.21-04 2.44+00 1.71-01 2.61+00 3.94—02

(b/atom) x .015080 = cm2/g

53
Table 3.-14. POTASSIUM, Z=19

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Withoutcoherent Nuclearfield Electron

field Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g 1.00-02 6.22+01 1.22+01 5.19+03 5.25+03 5.20+03 8.09+01 8.01+01

1.50-02 4.25+01 1.19+01 1.58+03 1.63+03 1.60+03 2.50+01 2.46+01 2.00-02 3.17+01 1.17+01 6.69+02 7.01+02 6.81+02 1.08+01 1.05+01 3.00-02 2.17+01 1.13+01 1.93+02 2.14+02 2.04+02 3.30+00 3.14+00

4.00-02 1.73+01 1.10+01 7.94+01 9.67+01 9.04+01 1.49+00 1.39+00 5.00-02 1.49+01 1.07+01 3.98+01 5.47+01 5.05+01 8.43-01 7.77-01 6.00-02 1.35+01 1.04+01 2.29+01 3.64+01 3.33+01 5.60-01 5.12-01 8.00-02 1.16+01 9.83+00 9.40+00 2.10+01 1.92+01 3.24-01 2.96-01

1.00-01 1.05+01 9.36+00 4.65+00 1.52+01 1.40+01 2.33-01 2.16-01

1.50-01 8.95+00 8.43+00 1.34+00 1.03+01 9.77+00 1.58-01 1.50-01 2.00-01 8.02+00 7.72+00 5.57-01 8.58+00 8.28+00 1.32-01 1.28-01 3.00-01 6.85+00 6.72+00 1.64-01 7.01+00 6.88+00 1.08-01 1.06-01 4.00-01 6.09+00 6.02+00 7.17-02 6.16+00 6.09+00 9.49-02 9.38-02

5.00-01 5.54+00 5.50+00 3.89-02 5.58+00 5.53+00 8.59-02 8.52-02

6.00-01 5.12+00 5.08+00 2.44-02 5.14+00 5.11+00 7.92-02 7.87-02

8.00-01 4.48+00 4.47+00 1.24-02 4.49+00 4.48+00 6.92-02 6.90-02

1.00+00 4.03+00 4.02+00 7.68-03 4.04+00 4.02+00 6.21-02 6.20-02

1.50+00 3.27+00 3.26+00 3.58-03 1.69-02 3.29+00 3.28+00 5.06-02 5.06-02

2.00+00 2.78+00 2.26-03 6.56-02 2.85+00 4.39-02

3.00+00 2.19+00 1.24-03 1.86-01 7.65-04 2.38+00 3.66-02

4.00+00 1.83+00 8.39-04 2.99-01 3.14-03 2.13+00 3.28-02

5.00+00 1.58+00 6.38-04 3.99-01 6.17-03 1.98+00 3.06-02

6.00+00 1.39+00 5.06-04 4.87-01 9.49-03 1.89+00 2.91-02

8.00+00 1.14+00 3.60-04 6.35-01 1.62-02 1.79+00 2.76-02

1.00+01 9.72-01 2.80-04 7.56-01 2.22-02 1.75+00 2.70-02

1.50+01 7.19-01 9.83-01 3.46-02 1.74+00 2.68-02

2.00+01 5.77-01 1.15+00 4.43-02 1.77+00 2.73-02

3.00+01 4.20-01 1.38+00 5.91-02 1.86+00 2.86-02

4.00+01 3.34-01 1.54+00 6.96-02 1.94+00 2.99-02

5.00+01 2.79-01 1.65+00 7.76-02 2.01+00 3.10-02

6.00+01 2.40-01 1.75+00 8.40-02 2.07+00 3.19-02

8.00+01 1.89-01 1.88+00 9.38-02 2.17+00 3.34-02

1.00+02 1.57-01 1.98+00 1.01-01 2.24+00 3.45-02

1.50+02 1.12-01 2.16+00 1.14-01 2.39+00 3.68-02

2.00+02 8.78-02 2.24+00 1.22-01 2.45+00 3.77-02

3.00+02 6.22-02 2.36+00 1.33-01 2.55+00 3.93-02

4.00+02 4.87-02 2.42+00 1.40-01 2.61+00 4.02-02

5.00+02 4.03-02 2.46+00 1.44-01 2.65+00 4.08-02

6.00+02 3.45-02 2.50+00 1.48-01 2.68+00 4.12-02

8.00+02 2.70-02 2.54+00 1.53-01 2.72+00 4.19-02

1.00+03 2.22-02 2.57+00 1.57-01 2.75+00 4.23-02

1.50+03 1.55-02 2.61+00 1.63-01 2.79+00 4.29-02

2.00+03 1.20-02 2.63+00 1.66-01 2.80+00 4.32-02

3.00+03 8.34—03 2.65+00 1.70-01 2.83+00 4.36-02

4.00+03 6.44-03 2.66+00 1.72-01 2.84+00 4.38-02

5.00+03 5.26-03 2.67+00 1.73-01 2.85+00 4.39-02

6.00+03 4.46-03 2.68+00 1.74-01 2.86+00 4.40-02

8.00+03 3.44-03 2.69+00 1.75-01 2.87+00 4.41-02

1.00+04 2.81-03 2.69+00 1.76-01 2.87+00 4.42-02

1.50+04 1.94-03 2.70+00 1.77-01 2.88+00 4.43-02

2.00+04 1.49-03 2.70+00 1.78-01 2.88+00 4.43-02

3.00+04 1.03-03 2.70+00 1.78-01 2.88+00 4.44-02

4.00+04 7.90-04 2.71+00 1.79-01 2.89+00 4.45-02

5.00+04 6.43-04 2.71+00 1.79-01 2.89+00 4.45-02

6.00+04 5.44-04 2.71+00 1.79-01 2.89+00 4.45-02

8.00+04 4.17-04 2.71+00 1.79-01 2.89+00 4.45-02

1.00+05 3.39-04 2.71+00 1.79-01 2.89+00 4.45-02

(b/atom) x .015400 = cm2 /g

54
Table 3.-15. CALCIUM, Z=20

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Withoutcoherent Nuclear

field Electronfield Withcoherent Withoutcoherent Withcoherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm2 /g cm2/g 1.00-02 6.78+01 1.28+01 6.35+03 6.42+03 6.36+03 9.65+01 9.56+01

1.50-02 4.68+01 1.26+01 1.96+03 2.00+03 1.97+03 3.01+01 2.96+01 2.00-02 3.40+01 1.24+01 8.27+02 8.62+02 8.39+02 1.30+01 1.26+01 3.00-02 2.36+01 1.19+01 2.42+02 2.66+02 2.54+02 3.99+00 3.82+00

4.00-02 1.87+01 1.16+01 9.98+01 1.19+02 1.11+02 1.78+00 1.67+00

5.00-02 1.61+01 1.12+01 5.03+01 6.64+-01 6.15+01 9.98-01 9.25-01 6.00-02 1.44+01 1.09+01 2.87+01 4.31+01 3.96+01 6.48-01 5.95-01 8.00-02 1.24+01 1.03+01 1.19+01 2.43+01 2.22+01 3.65-01 3.34-01

1.00-01 1.12+01 9.85+00 5.89+00 1.71+01 1.57+01 2.56-01 2.37-01

1.50-01 9.47+00 8.87+00 1.70+00 1.12+01 1.06+01 1.68-01 1.59-01 2.00-01 8.47+00 8.13+00 7.09-01 9.17+00 8.84+00 1.38-01 1.33-01 3.00-01 7.22+00 7.07+00 2.10-01 7.43+00 7.28+00 1.12-01 1.09-01 4.00-01 6.42+00 6.33+00 9.19-02 6.51+00 6.43+00 9.79-02 9.66-02

5.00-01 5.84+00 5.79+00 4.98-02 5.89+00 5.84+00 8.85-02 8.78-02

6.00-01 5.39+00 5.35+00 3.13-02 5.42+00 5.38+00 8.14-02 8.09-02

8.00-01 4.72+00 4.70+00 1.59-02 4.74+00 4.72+00 7.12-02 7.09—02: 1.00+00 4.24+00 4.23+00 9.87-03 4.25+00 4.24+00 6.39-02 6.37—02, 1.50+00 3.44+00 3.44+00 4.58-03 1.88-02 3.46+00 3.46+00 5.20-02 5.20—02] 2.00+00 2.93+00 2.93+00 2.90-03 7.30-02 3.01+00 3.01+00 4.53-02 4.52-02

3.00+00 2.31+00 1.59-03 2.06-01 8.05-04 2.51+00 3.78-02 4.00+00 1.92+00 1.07-03 3.31-01 3.30-03 2.26+00 3.40-02

5.00+00 1.66+00 8.16-04 4.42-01 6.49-03 2.11+00 3.17-02

6.00+00 1.47+00 6.46-04 5.40-01 9.98-03 2.02+00 3.03-02

8.00+00 1.20+00 4.60-04 7.03-01 1.71-02 1.92+00 2.89-02

1.00+01 1.02+00 3.59-04 8.36-01 2.33-02 1.88+00 2.83-02

1.50+01 7.57-01 1.09+00 3.64-02 1.88+00 2.83-02

2.00+01 6.08-01 1.27+00 4.67-02 1.92+00 2.89—02| 3.00+01 4.42-01 1.52+00 6.22-02 2.03+00 3.05-02

4.00+01 3.52-01 1.70+00 7.32-02 2.12+00 3.19-02

5.00+01 2.93-01 1.83+00 8.16-02 2.20+00 3.31-02

6.00+01 2.53-01 1.93+00 8.83-02 2.27+00 3.42-02

8.00+01 1.99-01 2.08+00 9.85-02 2.38+00 3.58-02

1.00+02 1.66-01 2.19+00 1.06-01 2.46+00 3.70-02

1.50+02 1.18-01 2.39+00 1.20-01 2.62+00 3.94-02

2.00+02 9.24-02 2.48+00 1.28-01 2.70+00 4.05-02

3.00+02 6.55-02 2.60+00 1.39-01 2.81+00 4.22-02

4.00+02 5.13-02 2.67+00 1.46-01 2.87+00 4.32-02

5.00+02 4.25-02 2.72+00 1.51-01 2.92+00 4.38-02

6.00+02 3.64-02 2.76+00 1.55-01 2.95+00 4.43-02

8.00+02 2.84-02 2.81+00 1.69-01 2.99+00 4.50-021 1.00+03 2.34-02 2.84+00 1.64-01 3.03+00 4.55-02

1.50+03 1.63-02 2.88+00 1.70-01 3.07+00 4.61-02

2.00+03 1.26-02 2.90+00 1.74-01 3.09+00 4.64—02

3.00+03 8.78-03 2.93+00 1.78-01 3.12+00 4.68-02

4.00+03 6.78-03 2.94+00 1.80-01 3.13+00 4.70-02

5.00+03 5.54-03 2.95+00 1.81-01 3.14+00 4.72-02

6.00+03 4.70-03 2.96+00 1.82-01 3.14+00 4.73-02

8.00+03 3.62-03 2.97+00 1.83-01 3.15+00 4.74-02

1.00+04 2.96-03 2.97+00 1.84-01 3.16+00 4.75-02

1.50+04 2.04-03 2.98+00 1.85-01 3.17+00 4.76-02

2.00+04 1.57-03 2.98+00 1.86-01 3.17+00 4.77-02

3.00+04 1.08-03 2.99+00 1.86-01 3.17+00 4.77-02

4.00+04 8.31-04 2.99+00 1.87-01 3.18+00 4.77-02

5.00+04 6.77-04 2.99+00 1.87-01 3.18+00 4.78-02

6.00+04 5.72-04 2.99+00 1.87-01 3.18+00 4.78-02

8.00+04 4.39-04 2.99+00 1.87-01 3.18+00 4.78-02

1.00+05 3.57-04 2.99+00 1.87-01 3.18+00 4.78-02

(b/atom) x .015030= cm2/g

55
Table 3.-16. IRON, Z=26

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Withoutcoherent Withcoherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g

1.00-02 1.23+02 1.67+01 1.59+04 1.60+04 1.59+04 1.73+02 1.72+02

1.50-02 8.05+01 1.63-hOl 5.15+03 5.23+03 5.17+03 5.64+01 5.57+01 2.00-02 5.98+01 1.61+01 2.31+03 2.37+03 2.33+03 2.55+01 2.51+01 3.00-02 3.89+01 1.55+01 7.15+02 7.54+02 7.31+02 8.13+00 7.88+00

4.00-02 2.94+01 1.50+01 3.06+02 3.35+02 3.21+02 3.62+00 3.46+00

5.00-02 2.43+01 1.46+01 1.56+02 1.80+02 1.71+02 1.94+00 1.84+00 6.00-02 2.12+01 1.42+01 9.04+01 1.12+02 1.05+02 1.20+00 1.13+00 8.00-02 1.76+01 1.34+01 3.76+01 5.52+01 540+01 5.95-01 5.50-01

1.00-01 1.54+01 1.28+01 1.89+01 3.43+01 3.17+01 3.70-01 3.42-01

1.50-01 1.27+01 1.15+01 5.52+00 1.82+01 1.71+01 1.96-01 1.84-01 2.00-01 1.12+01 1.06+01 2.33+00 1.35+01 1.29+01 1.46-01 1.39-01 3.00-01 9.50+00 9.19+00 6.98-01 1.02+01 9.89+00 1.10-01 1.07-01 4.00-01 8.41+00 8.24+00 3.09-01 8.72+00 8.54+00 9.40-02 9.21-02

5.00-01 7.62+00 7.52+00 1.69-01 7.79+00 7.69+00 8.40-02 8.29-02

6.00-01 7.03+00 6.96+00 1.07-01 7.14+00 7.06+00 7.69-02 7.62-02

8.00-01 6.15+00 6.11+00 5.44-02 6.21+00 6.17+00 6.69-02 6.65-02

1.00+00 5.52+00 5.50+00 3.38-02 5.55+00 5.53+00 5.99-02 5.96-02

1.50+00 4.48+00 4.47+00 1.56-02 3.32-02 4.53+00 4.51+00 4.88-02 4.87-02

2.00+00 3.81+00 9.81-03 1.26-01 3.95+00 4.25-02

3.00+00 3.00+00 5.35-03 3.50-01 1.05-03 3.35+00 3.62-02

4.00+00 2.50+00 3.61-03 5.61-01 4.30-03 3.07+00 3.31-02

5.00+00 2.16+00 2.73-03 7.46-01 8.44-03 2.92+00 3.14-02

6.00+00 1.91+00 2.16-03 9.08-01 1.30-02 2.83+00 3.05-02

8.00+00 1.56+00 1.53-03 1.18+00 2.22-02 2.77+00 2.98-02

1.00+01 1.33+00 1.19-03 1.40+00 3.04-02 2.76+00 2.98-02

1.50+01 9.84-01 7.00-04 1.82+00 4.73-02 2.85+00 3.07-02

2.00+01 7.90-01 5.00-04 2.13+00 6.07-02 2.98+00 3.21-02

3.00+01 5.75-01 2.55+00 8.06-02 3.20+00 3.45-02

4.00+01 4.57-01 2.84+00 9.45-02 3.39+00 3.65-02

5.00+01 3.81-01 3.06+00 1.05-01 3.54+00 3.82-02

6.00+01 3.29-01 3.22+00 1.13-01 3.67+00 3.95-02

8.00+01 2.59-01 3.48+00 1.27-01 3.86+00 4.16-02

1.00+02 2.15-01 3.65+00 1.36-01 4.01+00 4.32-02

1.50+02 1.53-01 3.94+00 1.53-01 4.25+00 4.58-02

2.00+02 1.20-01 4.12+00 1.64—01 4.40+00 4.75-02

3.00+02 8.51-02 4.32+00 1.78-01 4.58+00 4.94-02

4.00+02 6.67-02 4.44+00 1.86-01 4.69+00 5.06-02

5.00+02 5.52-02 4.52+00 1.92-01 4.77+00 5.14-02

6.00+02 4.73-02 4.57+00 1.97-01 4.82+00 5.19-02

8.00+02 3.69-02 4.65+00 2.04-01 4.89+00 5.27-02

1.00+03 3.04-02 4.69+00 2.09-01 4.93+00 5.32-02

1.50+03 2.12-02 4.77+00 2.16-01 5.00+00 5.39-02

2.00+03 1.64-02 4.80+00 2.20-01 5.04+00 5.43-02

3.00+03 1.14-02 4.84H-00 2.24-01 5.08+00 5.48-02

4.00+03 8.81-03 4.86+00 2.26-01 5.10+00 5.50-02

5.00+03 7.20-03 4.88+00 2.28-01 5.11+00 5.51-02

6.00+03 6.11-03 4.89+00 2.29-01 5.13+00 5.52-02

8.00+03 4.71-03 4.90+00 2.31-01 5.14+00 5.54-02

1.00+04 3.84-03 4.91+00 2.31-01 5.14+00 5.55-02

1.50+04 2.66-03 4.92+00 2.33-01 5.16+00 5.56-02

2.00+04 2.04-03 4.93+00 2.33-01 5.16+00 5.56-02

3.00+04 1.41-03 4.93+00 2.34-01 5.17+00 5.57-02

4.00+04 1.08-03 4.93+00 2.35-01 5.17+00 5.57-02

5.00+04 8.80-04 4.94+00 2.35-01 5.17+00 5.58-02

6.00+04 7.44-04 4.94+00 2.35-01 5.17+00 5.58-02

8.00+04 5.70-04 4.94+00 2.35-01 5.17+00 5.58-02

1.00+05 4.64—04 4.94+00 2.36-01 5.17+00 5.58-02

(b/atom) x .010780 = cm2 /g

56
Table 3.-17. COPPER, Z=29

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Withoutcoherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm*/g 1.00-02 1.66+02 1.86+01 2.35+04 2.37+04 2.35+04 2.24+02 2.23+02

1.50-02 1.06+02 1.82+01 7.72+03 7.83+03 7.74+03 7.42+01 7.33+01 2.00-02 7.70+01 1.79+01 3.46+03 3.54+03 3.48+03 3.35+01 3.30+01 3.00-02 4.92+01 1.73+01 1.11+03 1.15+03 1.12+03 1.09+01 1.06+01 4.00-02 3.64+01 1.68+01 4.80+02 5.16+02 4.97+02 4.89+00 4.71+00

5.00-02 2.96+01 1.63+01 2.47+02 2.77+02 2.63+02 2.62+00 2.50+00

6.00-02 2.55+01 1.58+01 1.45+02 1.71+02 1.61+02 1.62+00 1.52+00 8.00-02 2.07+01 1.50+01 6.08+01 8.14+01 7.58+01 7.72-01 7.18-01

1.00-01 1.79+01 1.43+01 3.08+01 4.87+01 4.51+01 4.61-01 4.27-01

1.50-01 1.45+01 1.29+01 9.04+00 2.36+01 2.19+01 2.23-01 2.08-01 2.00-01 1.27+01 1.18+01 3.80+00 1.65+01 1.56+01 1.57-01 1.48-01 3.00-01 1.07+01 1.02+01 1.15+00 1.18+01 1.14+01 1.12-01 1.08-01 4.00-01 9.42+00 9.19+00 5.12-01 9.93+00 9.70+00 9.41-02 9.19-02

5.00-01 8.54+00 8.39+00 2.81-01 8.82+00 8.67+00 8.36-02 8.22-02

6.00-01 7.86+00 7.76+00 1.77-01 8.04+00 7.94+00 7.62-02 7.52-02

8.00-01 6.87+00 6.82+00 9.11-02 6.96+00 6.91+00 6.60-02 6.55-02

1.00+00 6.16+00 6.13+00 5.65-02 6.22+00 6.19+00 5.89-02 5.86-02

1.50+00 4.99+00 4.98+00 2.61-02 4.23-02 5.06+00 5.05+00 4.80-02 4.79-02

2.00+00 4.25+00 4.25+00 1.63-02 1.58-01 4.43+00 4.43+00 4.20-02 4.19-02

3.00+00 3.35+00 3.34+00 8.88-03 4.38-01 1.17-03 3.79+00 3.79+00 3.60-02 3.59-02

4.00+00 2.79+00 5.96-03 6.98-01 4.79-03 3.50+00 3.32-02 5.00+00 2.41+00 4.50-03 9.28-01 9.41-03 3.35+00 3.18-02 6.00+00 2.13+00 3.56-03 1.13+00 1.45-02 3.28+00 3.10-02 8.00+00 1.74+00 2.52-03 1.46+00 2.48-02 3.23+00 3.06-02

1.00+01 1.48+00 1.95-03 1.74+00 3.39-02 3.25+00 3.08-02

1.50+01 1.10+00 1.20-03 2.25+00 5.27-02 3.41+00 3.23-02

2.00+01 8.81-01 9.00-04 2.63+00 6.77-02 3.58+00 3.39-02

3.00+01 6.41-01 6.00-04 3.15+00 8.97-02 3.89+00 3.68-02

4.00+01 5.10—01 4.00-04 3.51+00 1.05-01 4.13+00 3.91-02

5.00+01 4.25-01 3.78+00 1.17-01 4.32+00 4.10-02

6.00+01 3.67-01 3.99+00 1.26-01 4.48+00 4.25-02

8.00+01 2.89-01 4.30+00 1.41-01 4.73+00 4.48-02

1.00+02 2.40-01 4.52+00 1.51-01 4.91+00 4.65-02

1.50+02 1.71-01 4.87+00 1.70-01 5.21+00 4.94-02

2.00+02 1.34-01 5.08+00 1.82-01 5.39+00 5.11-02

3.00+02 9.50-02 5.32+00 1.97-01 5.61+00 5.32-02

4.00+02 7.44-02 5.46+00 2.06-01 5.74+00 5.44-02

5.00+02 6.16-02 5.55+00 2.13-01 5.83+00 5.52-02

6.00+02 5.27-02 5.62+00 2.18-01 5.89+00 5.58-02

8.00+02 4.12-02 5.71+00 2.25-01 5.97+00 5.66-02

1.00+03 3.39-02 5.77+00 2.30-01 6.03+00 5.72-02

1.50+03 2.37-02 5.85+00 2.38-01 6.11+00 5.79-02

2.00+03 1.83-02 5.89+00 2.42-01 6.15+00 5.83-02

3.00+03 1.27-02 5.94+00 2.47-01 6.20+00 5.88-02

4.00+03 9.83-03 5.97+00 2.49-01 6.23+00 5.90-02

5.00+03 8.03-03 5.98+00 2.51-01 6.24+00 5.91-02

6.00+03 6.81-03 5.99+00 2.52-01 6.25+00 5.93-02

8.00+03 5.25-03 6.01+00 2.54-01 6.26+00 5.94-02

1.00+04 4.29-03 6.01+00 2.55-01 6.27+00 5.95-02

1.50+04 2.96-03 6.03+00 2.56-01 6.29+00 5.96-02

2.00+04 2.28-03 6.03+00 2.57-01 6.29+00 5.96-02

3.00+04 1.57-03 6.05+00 2.58-01 6.31+00 5.98-02

4.00+04 1.21-03 6.05+00 2.58-01 6.31+00 5.98-02

5.00+04 9.82-04 6.05+00 2.58-01 6.31+00 5.98-02

6.00+04 8.30-04 6.05+00 2.58-01 6.31+00 5.98-02

8.00+04 6.36-04 6.05+00 2.59-01 6.31+00 5.98-02

1.00+05 5.18-04 6.05+00 2.59-01 6.31+00 5.98-02

(b/atom) x .009478 = cm2 /g

57
Table 3.-18. MOLYBDENUM, Z=42

Photon

energy

Scattering Pair production Total Total

With

coherent Without

coherent

electric Nuclear

field Electron

field Withcoherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g 1.00-02 3.77+02 2.69+01 1.34+04 1.37+04 1.34+04 8.62+01 8.40+01

1.50-02 2.46+02 2.64+01 4.24+03 4.49+03 4.27+03 2.82+01 2.68+01 2.00-02 1.74+02 2.59+01 1.84+03 2.01+03 1.87+03 1.26+01 1.17+01 K 2.00-02 1.74+02 2.59+01 1.28+04 1.30+04 1.29+04 8.17+01 8.08+01 3.00-02 1.07+02 2.51+01 4.48+03 4.59+03 4.51+03 2.88+01 2.83+01 4.00-02 7.64+01 2.43+01 2.04+03 2.12+03 2.07+03 1.33+01 1.30+01 5.00-02 5.94+01 2.36+01 1.09+03 1.15+03 1.11+03 7.20+00 6.97+00

6.00-02 4.90+01 2.29+01 6.54+02 7.03+02 6.77+02 4.41+00 4.25+00

8.00-02 3.71+01 2.17+01 2.85+02 3.22+02 3.06+02 2.02+00 1.92+00

1.00-01 3.06+01 2.07+01 1.47+02 1.78+02 1.68+02 1.11+00 1.05+00

1.50-01 2.32+01 1.86+01 4.50+01 6.82+01 6.36+01 4.28-01 3.99—01

2.00-01 1.97+01 1.71+01 1.93+01 3.90+01 3.64+01 2.45-01 2.28-01

3.00-01 1.60+01 1.48+01 6.02+00 2.21+01 2.09+01 1.39-01 1.31-01 4.00-01 1.39+01 1.33+01 2.74+00 1.67+01 1.60+01 1.05-01 1.01-01 5.00-01 1.25+01 1.22+01 1.53+00 1.41+01 1.37+01 8.83-02 8.59-02

6.00-01 1.16+01 1.12+01 9.80-01 1.25+01 1.22+01 7.88-02 7.67-02

8.00-01 1.00+01 9.88+00 5.04-01 1.05+01 1.04+01 6.61-02 6.52-02

1.00+00 8.97+00 8.88+00 3.13-01 9.29+00 9.19+00 5.83-02 5.77-02

1.50+00 7.25+00 7.21+00 1.43-01 9.99-02 7.49+00 7.46+00 4.70-02 4.68-02

2.00+00 6.17+00 6.16+00 8.84-02 3.54-01 6.62+00 6.60+00 4.15-02 4.14—02

3.00+00 4.84+00 4.84+00 4.77-02 9.40-01 1.69-03 5.83+00 5.83+00 3.66-02 3.66-02

4.00+00 4.05+00 4.04+00 3.18-02 1.47+00 6.94-03 5.56+00 5.55+00 3.49-02 3.48-02

5.00+00 3.50+00 3.49+00 * 2.39-02 1.94+00 1.36-02 5.47+00 5.47+00 3.44-02 3.43-02

6.00+00 3.08+00 1.88-02 2.34+00 2.10-02 5.46+00 3.43-02

8.00+00 2.52+00 1.31-02 3.01+00 3.59-02 5.58+00 3.50-02

1.00+01 2.15+00 1.02-02 3.55+00 4.90-02 5.76+00 3.62-02

1.50+01 1.59+00 6.39-03 4.59+00 7.64-02 6.27+00 3.93-02

2.00+01 1.28+00 4.65-03 5.36+00 9.78-02 6.74+00 4.23-02

3.00+01 9.29-01 3.01-03 6.43+00 1.28-01 7.49+00 4.70-02

4.00+01 7.38-01 2.22-03 7.15+00 1.50-01 8.04+00 5.05-02

5.00+01 6.16-01 1.76—03 7.69+00 1.66-01 8.47+00 5.32-02

6.00+01 5.31-01 1.46-03 8.10+00 1.79-01 8.82+00 5.53-02

8.00+01 4.19-01 1.08-03 8.72+00 1.99-01 9.34+00 5.86-02

1.00+02 3.48-01 8.65-04 9.14+00 2.15-01 9.71+00 6.09-02

1.50+02 2.48-01 9.83+00 2.40-01 1.03+01 6.48-02

2.00+02 1.94-01 1.02+01 2.56-01 1.07+01 6.72-02

3.00+02 1.38-01 1.07+01 2.76-01 1.12+01 7.00-02 4.00+02 1.08-01 1.10+01 2.89-01 1.14+01 7.16-02 5.00+02 8.92-02 1.12+01 2.97-01 1.16+01 7.27-02 6.00+02 7.63-02 1.13+01 3.04-01 1.17+01 7.35-02 8.00+02 5.96-02 1.15+01 3.14-01 1.19+01 7.45-02

1.00+03 4.91-02 1.16+01 3.20-01 1.20+01 7.53-02

1.50+03 3.43-02 1.18+01 3.30-01 1.21+01 7.62-02 2.00+03 2.65-02 1.19+01 3.35-01 1.22+01 7.67-02 3.00+03 1.84-02 1.20+01 3.41-01 1.23+01 7.73-02 4.00+03 1.42-02 1.20+01 3.44-01 1.24+01 7.77-02 5.00+03 1.16-02 1.20+01 3.46-01 1.24+01 7.79-02 6.00+03 9.87-03 1.21+01 3.48-01 1.24+01 7.80-02 8.00+03 7.60-03 1.21+01 3.50-01 1.24+01 7.81-02

1.00+04 6.21-03 1.21+01 3.51-01 1.25+01 7.83-02

1.50+04 4.29-03 1.22+01 3.53-01 1.25+01 7.85-02

2.00+04 3.30-03 1.22+01 3.54-01 1.25+01 7.85-02

3.00+04 2.27-03 1.22+01 3.55-01 1.25+01 7.86-02

4.00+04 1.75-03 1.22+01 3.55-01 1.25+01 7.86-02 5.00+04 1.42-03 1.22+01 3.55-01 1.25+01 7.86-02 6.00+04 1.20-03 1.22+01 3.56-01 1.25+01 7.87-02 8.00+04 9.22-04 1.22+01 3.56-01 1.25+01 7.88-02

1.00+05 7.50-04 1.22+01 3.56-01 1.25+01 7.88-02

(b/atom) x .006277 = cm2 /g

58
Table 3.-19. TIN, Z=50

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclearfield Electron

field Withcoherent Withoutcoherent Withcoherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g 1.00-02 5.38+02 3.20+01 2.73+04 2.79+04 2.74+04 1.41+02 1.39+02

1.50-02 3.60+02 3.14+01 8.91+03 9.27+03 8.94+03 4.70+01 4.53+01 2.00-02 2.59+02 3.09+01 3.95+03 4.21+03 3.98+03 2.13+01 2.02+01 2.92-02 1.61+02 2.99+01 1.33+03 1.49+03 1.36+03 7.54+00 6.88+00

K 2.92-02 1.61+02 2.99+01 8.57+03 8.73+03 8.60+03 4.43+01 4.37+01

3.00-02 1.56+02 2.99+01 7.98+03 8.14+03 8.01+03 4.13+01 4.07+01 4.00-02 1.10+02 2.89+01 3.70+03 3.81+03 3.73+03 1.94+01 1.89+01 5.00-02 8.44+01 2.81+01 2.02+03 2.10+03 2.04+03 1.07+01 1.04+01 6.00-02 6.85+01 2.73+01 1.22+03 1.29+03 1.25+03 6.53+00 6.32+00

8.00-02 5.02+01 2.59+01 5.45+02 5.95+02 5.71+02 3.02+00 2.90+00

1.00-01 4.05+01 2.46+01 2.90+02 3.31+02 3.15+02 1.68+00 1.60+00

1.50-01 2.96+01 2.22+01 9.15+01 1.21+02 1.14+02 6.14-01 5.77-01

2.00-01 2.45+01 2.03+01 4.02+01 6.47+01 6.06+01 3.28-01 3.07-01

3.00-01 1.96+01 1.77+01 1.28+01 3.24+01 3.05+01 1.64-01 1.55-01 4.00-01 1.69+01 1.58+01 5.93+00 2.28+01 2.18+01 1.16-01 1.10-01 5.00-01 1.51+01 1.45+01 3.50+00 1.86+01 1.80+01 9.46-02 9.11-02

6.00-01 1.39+01 1.34+01 2.20+00 1.61+01 1.56+01 8.16-02 7.91-02

8.00-01 1.20+01 1.18+01 1.15+00 1.32+01 1.29+01 6.69-02 6.55-02

1.00+00 1.07+01 1.06+01 6.90-01 1.14+01 1.13+01 5.78-02 5.71-02

1.50+00 8.65+00 8.59+00 3.13-01 1.53-01 9.12+00 9.06+00 4.63-02 4.59-02

2.00+00 7.36+00 7.33+00 1.93-01 5.23-01 8.08+00 8.04+00 4.10-02 4.08-02 3.00+00 5.77+00 5.77+00 1.05-01 1.35+00 2.01-03 7.24+00 7.23+00 3.67-02 3.67-02

4.00+00 4.82+00 4.81+00 6.93-02 2.10+00 8.26-03 7.00+00 6.98+00 3.55-02 3.54-02 5.00+00 4.16+00 4.15+00 5.18-02 2.74+00 1.62-02 6.97+00 6.96+00 3.54-02 3.53-02

6.00+00 3.68+00 3.67+00 4.05-02 3.29+00 2.50-02 7.03+00 7.03+00 3.57-02 3.57-02 8.00+00 3.00+00 2.83-02 4.21+00 4.27-02 7.28+00 3.69-02

1.00+01 2.56+00 2.18-02 4.95+00 5.84-02 7.58+00 3.85-02

1.50+01 1.89+00 1.37-02 6.38+00 9.09-02 8.37+00 4.25-02

2.00+01 1.52+00 9.94-03 7.44+00 1.16-01 9.08+00 4.61-02

3.00+01 1.11+00 6.41-03 8.92400 1.52-01 1.02+01 5.17-02

4.00+01 8.79-01 4.73-03 9.92+00 1.77-01 1.10+01 5.57-02

5.00+01 7.34—01 3.75-03 1.07+01 1.96-01 1.16+01 5.88-02

6.00+01 6.32-01 3.10-03 1.12+01 2.11-01 1.21+01 6.13-02

8.00+01 4.98-01 2.31-03 1.21+01 2.35-01 1.28+01 6.51-02

1.00+02 4. 14—01 1.84-03 1.27+01 2.52-01 1.33+01 6.77-02

1.50+02 2.95-01 1.36+01 2.81-01 1.42+01 7.21-02

2.00+02 2.31-01 1.42+01 3.00-01 1.47+01 7.48-02

3.00+02 1.64-01 1.49+01 3.23-01 1.54+01 7.80-02 4.00+02 1.28-01 1.53+01 3.38-01 1.57+01 7.98-02

5.00+02 1.06-01 1.55+01 3.48-01 1.60+01 8.10-02

6.00+02 9.09-02 1.57+01 3.56-01 1.61+01 8.19-02

8.00+02 7.10-02 1.59+01 3.67-01 1.64+01 8.31-02

1.00+03 5.84-02 1.61+01 3.74-01 1.65+01 8.38-02

1.50+03 4.08-02 1.63+01 3.84-01 1.67+01 8.49-02

2.00+03 3.16-02 1.64+01 3.90-01 1.69+01 8.56-02

3.00+03 2.19-02 1.66+01 3.97-01 1.70+01 8.62-02

4.00+03 1.69-02 1.66+01 4.00-01 1.70+01 8.65-02

5.00+03 1.38-02 1.67+01 4.03-01 1.71+01 8.67-02

6.00+03 1.17-02 1.67+01 4.04-01 1.71+01 8.68-02

8.00+03 9.05-03 1.67+01 4.06-01 1.72+01 8.70-02

1.00+04 7.39-03 1.68+01 4.08-01 1.72+01 8.71-02

1.50+04 5.11-03 1.68+01 4.10-01 1.72+01 8.73-02

2.00+04 3.93-03 1.68+01 4.11-01 1.72+01 8.7+-02

3.00+04 2.71-03 1.68+01 4.12-01 1.73+01 8.75-02

4.00+04 2.08-03 1.68+01 4.12-01 1.73+01 8.76-02

5.00+04 1.69-03 1.69+01 4.13-01 1.73+01 8.77-02

6.00+04 1.43-03 1.69+01 4.13-01 1.73+01 8.77-02

8.00+04 1.10-03 1.69+01 4.13-01 1.73+01 8.77-02

1.00+05 8.93-03 1.69+01 4.14-01 1.73+01 8.77-02

(b/atom) x .005074= cm2

/

g

59
Table 3.-20. IODINE, Z=53

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Without

coherent W ith coherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm2/g cm2/g 1.00-02 6.07+02 3.39+01 3.33+04 3.39+04 3.33+04 1.61+02 1.58+02 1.50-02 4.05+02 3.33+01 1.12+04 1.16+04 1.13+04 5.52+01 5.34+01 2.00-02 2.94+02 3.28+01 5.18+03 5.47+03 5.21+03 2.60+01 2.47+01 3.00-02 1.77+02 3.17+01 1.65+03 1.83+03 1.68+03 8.67+00 7.98+00 3.32-02 1.56+02 3.13+01 1.24+03 1.40+03 1.27+03 6.62+00 6.03+00

K 3.32-02 1.56+02 3.13+01 7.52+03 7.68+03 7.55+03 3.64+01 3.58+01 4.00-02 1.23+02 3.07+01 4.66+03 4.79+03 4.69+03 2.27+01 2.23+01 5.00-02 9.48+01 2.98+01 2.57+03 2.66+03 2.60+03 1.26+01 1.23+01 6.00-02 7.69+01 2.89+01 1.56+03 1.64+03 1.59+03 7.78+00 7.55+00

8.00-02 5.58+01 2.74+01 7.14+02 7.69+02 7.41+02 3.65+00 3.52+00

1.00-01 4.46+01 2.61+01 3.77+02 4.22+02 4.03+02 2.00+00 1.91+00

1.50-01 3.21+01 2.35+01 1.18+02 1.50+02 1.42+02 7.14-01 6.74-01

2.00-01 2.64+01 2.15+01 5.21+01 7.85+01 7.36+01 3.72-01 3.49-01

3.00-01 2.09+01 1.87+01 1.66+01 3.76+01 3.53+01 1.78-01 1.68-01 4.00-01 1.80+01 1.68+01 7.71+00 2.57+01 2.45+01 1.22-01 1.16-01 5.00-01 1.62+01 1.53+01 4.40+00 2.06+01 1.97+01 9.76-02 9.36-02

6.00-01 t. 48+01 1.42+01 2.83+00 1.76+01 1.70+01 8.35-02 8.07-02

8.00-01 1.28+01 1.25+01 1.46+00 1.42+01 1.39+01 6.76-02 6.61-02

1.00+00 1.13+01 1.12+01 9.11-01 1.23+01 1.21+01 5.81-02 5.75-02

1.50+00 9.18+00 9.10+00 4.13-01 1.78-01 9.77+00 9.70+00 4.64-02 4.60-02

2.00+00 7.80+00 7.77+00 2.54-01 5.98-01 8.65+00 8.62+00 4.11-02 4.09-02

3.00+00 6.12+00 6.11+00 1.36-01 1.53+00 2.13-03 7.79+00 7.78+00 3.70-02 3.69-02

4.00+00 5.12+00 5.10+00 8.97-02 2.36+00 8.76-03 7.57+00 7.56+00 3.59-02 3.59-02

5.00+00 4.41+00 4.40+00 6.70-02 3.08+00 1.72-02 7.57+00 7.56+00 3.59—02 3.59-02

6.00+00 3.90+00 3.89+00 5.25-02 3.69+00 2.65-02 7.66+00 7.66+00 3.64-02 3.63-02

8.00+00 3.18+00 3.66-02 4.70+00 4.53-02 7.96+00 3.78-02

1.00+01 2.71+00 2.82-02 5.52+00 6.19-02 8.32+00 3.95-02

1.50+01 2.01+00 1.76-02 7.10+00 9.64-02 9.22+00 4.38-02

2.00+01 1.61+00 1.28-02 8.29+00 1.23-01 1.00+01 4.76-02

3.00+01 1.17+00 8.25-03 9.95+00 1.60-01 1.13+01 5.36-02

4.00+01 9.32-01 6.09-03 1.11+01 1.87-01 1.22+01 5.78-02

5.00+01 7.78-01 4.83-03 1.19+01 2.07-01 1.29+01 6.11-02

6.00+01 6.70-01 3.99-03 1.25+01 2.23-01 1.34+01 6.37-02

8.00+01 5.28-01 2.97-03 1.35+01 2.48-01 1.42+01 6.76-02

1.00+02 4.39-01 2.37-03 1.41+01 2.6(5—01 1.48+01 7.04-02

1.50+02 3.12-01 1.52+01 2.97-01 1.58+01 7.50-02 2.00+02 2.45-01 1.58+01 3.16-01 1.64+01 7.78-02 3.00+02 1.74-01 1.66+01 3.40-01 1.71+01 8.11-02

4.00+02 1.36-01 1.70+01 3.56-01 1.75+01 8.30-02

5.00+02 1.12-01 1.73+01 3.67-01 1.77+01 8.42-02

6.00+02 9.63-02 1.75+01 3.75-01 1.79+01 8.51-02

8.00+02 7.52-02 1.78+01 3.86-01 1.82+01 8.64-02

1.00+03 6.19-02 1.79+01 3.94-01 1.84+01 8.71-02

1.50+03 4.32-02 1.82+01 4.05-01 1.86+01 8.84-02

2.00+03 3.35-02 1.83+01 4.11-01 1.88+01 8.90-02

3.00+03 2.33-02 1.84+01 4.17-01 1.89+01 8.96-02

4.00+03 1.80-02 1.85+01 4.21-01 1.90+01 9.00-02

5.00+03 1.47-02 1.86+01 4.23-01 1.90+01 9.02-02

6.00+03 1. 24-02 1.86+01 4.25-01 1.90+01 9.04-02

8.00+03 9.59-03 1.86+01 4.27-01 1.91+01 9.05-02

1.00+04 7.83-03 1.87+01 4.29-01 1.91+01 9.06-02

1.50+04 5.41-03 1.87+01 4.31-01 1.91+01 9.08-02

2.00+04 4.16-03 1.87+01 4.32-01 1.92+01 9.10-02

3.00+04 2.87-03 1.88+01 4.33-01 1.92+01 9.11-02

4.00+04 2.20-03 1.88+01 4.33-01 1.92+01 9.11-02

5.00+04 1.79-03 1.88+01 4.34-01 1.92+01 9.11-02

6.00+04 1.52-03 1.88+01 4.34-01 1.92+01 9.12-02

8.00+04 1.16-03 1.88+01 4.34-01 1.92+01 9.12-02

1.00+05 9.46-04 1.88+01 4.35-01 1.92+01 9.12-02

(b/atom) x .004746 = cm2 /g

60
Table 3.-21. TUNGSTEN, Z = 74

Photon

energy

Scattering PhotoelectricPair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Withoutcoherent Withcoherent Withoutcoherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm2 /g cm2/g 1.00-02 1.38+03 4.74+61 2.78+04 2.92+04 2.78+04 9.55+61 9.12+01

1.02-02 1.35+03 4.74+61 2.63+04 2.77+64 2.64+04 9.07+61 8.64+01

L, 1.02-02 1.35+03 4.74+61 7.04+04 7.18+04 7.05+04 2.35+62 2.31+02

1.15-02 1.20+03 4.71+01 5.06+04 5.17+04 5.06+04 1.70+02 1.66+02 U 1.15-02 1.20+03 4.71+01 7.05+04 7.17+64 7.05+04 2.35+02 2.31+02

1.21-02 1.14+03 4.70+61 6.17+04 6.29+04 6.18+04 2.06+62 2.02+02

L, 1.21-02 1.14+03 4.70+61 7.45+04 7.56+04 7.45+04 2.48+62 2.44+02

1.50-02 8.99+02 4.65+61 4.25+04 4.34+04 4.25+04 1.42+02 1.39+02 2.00-02 6.39+02 4.57+61 1.98+04 2.05+04 1.99+04 6.70+61 6.51+01 3.00-02 3.88+02 4.42+61 6.62+03 7.01+03 6.67+03 2.30+01 2.18+01 4.00-02 2.65+02 4.28+01 3.00+03 3.26+03 3.04+03 1.07+61 9.97+00

5.00-02 1.96+62 4.16+01 1.61+03 1.80+03 1.65+03 5.91+00 5.40+00

6.00-02 1.54+02 4.04+01 9.61+02 1.12+03 1.00+03 3.65+00 3.28+00

6.95-02 1.28+02 3.93+01 6.32+02 7.60+02 6.71+62 2.49+00 2.20+00 K 6.95-02 1.28+02 3.93+01 3.33+03 3.46+03 3.37+03 1.13+01 1.10+01 8.00-02 1.07+02 3.83+01 2.30+03 2.41+03 2.34+63 7.89+00 7.66+00

1.00-01 8.13+01 3.65+01 1.27+03 1.35+63 1.31+03 4.43+60 4.29+00

1.50-01 5.38+01 3.28+61 4.26+02 4.80+02 4.59+02 1.57+60 1.50+00

2.00-01 4.20+01 3.01+01 1.95+02 2.37+62 2.25+02 7.77-01 7.38-01

3.00-01 3.15+01 2.62+01 6.60+01 9.75+61 9.22+01 3.20-01 3.02-01

4.00-01 2.65+01 2.34+01 3.14+01 5.79+01 5.48+01 1.90-01 1.80-01 5.00-01 2.34+01 2.14+01 1.81+01 4.15+01 3.95+01 1.36-01 1.29-01 6.00-01 2.12+01 1.98+01 1.17+01 3.29+01 3.15+01 1.08-01 1.03-01 8.00-01 1.82+01 1.74+01 6.20+00 2.44+01 2.36+01 7.99-62 7.73-02

1.00+00 1.61+01 1.56+01 3.88+00 2.00+01 1.95+01 6.54-02 6.39-02

1.50+00 1.30+01 1.27+01 1.77+00 4.28-61 1.52+01 1.49+01 4.97-62 4.88-02

2.00+00 1.09+01 1.08+01 1.06+00 1.32+60 1.33+01 1.32+01 4.37-02 4.34-02

3.00+00 8.57+00 8.53+00 5.58-01 3.15+00 2.98-03 1.23+01 1.22+01 4.02-62 4.01-62

4.00+00 7.16+00 7.12+60 3.62-01 4.67+60 1.22-02 1.22+01 1.22+01 4.00-02 3.98-02

5.00+00 6.17+00 6.15+00 2.68-01 5.96+00 2.40-02 1.24+61 1.24+01 4.07-62 4.06-02

6.00+00 5.45+00 5.43+00 2.08-01 7.02+60 3.69-02 1.27+61 1.27+01 4.16-02 4.16-02

8.00+00 4.45+00 4.44+60 1.44-01 8.76+60 6.32-02 1.34+01 1.34+01 4.39-62 4.39-02

1.00+01 3.80+00 3.78+00 1.10-01 1.02+01 8.64-02 1.42+01 1.41+01 4.64-02 4.63-62

1.50+01 2.80+00 6.88-02 1.30+01 1.34-01 1.60+01 5.24-02

2.00+01 2.25+00 4.97-02 1.51+61 1.69-01 1.76+01 5.77-02

3.00+01 1.64+00 3.20-02 1.82+01 2.19-61 2.01+01 6.59-02

4.00+01 1.30+00 2.36-02 2.03+61 2.55-01 2.19+01 7.16-02

5.00+01 1.09+00 1.87-02 2.18+01 2.83-01 2.32+01 7.60-02

6.00+61 9.35-01 1.55-02 2.30+61 3.05-01 2.42+01 7.94-02

8.00+01 7.38-01 1.15-02 2.47+01 3.38-01 2.58+01 8.45-02

1.00+02 6.13-01 9.20-63 2.59+01 3.62-01 2.69+01 8.81-02

1.50+02 4.36-01 2.78+01 4.02-61 2.87+01 9.39-02

2.00+62 3.42-01 2.90+61 4.27-01 2.98+01 9.76-02

3.00+62 2.42-01 3.03+61 4.59-01 3.11+01 1.02-01 4.00+02 1.90-61 3.11+01 4.80-01 3.18+01 1.04-01 5.00+02 1.57-01 3.16+01 4.94-01 3.23+01 1.06-01 6.00+02 1.34-01 3.20+61 5.04-01 3.26+01 1.07-61 8.00+02 1.05-01 3.24+01 5.18-01 3.31+01 1.08-61 1.00+03 8.64'—02 3.27+01 5.27-01 3.34+01 1.09-01 1.50+63 6. 04-02 3.32+01 5.40-01 3.38+01 1.11-01 2.00+63 4.67-02 3.34+01 5.48-01 3.40+01 1.11-01 3.00+63 3.25-02 3.37+61 5.56-01 3.43+01 1.12-01 4.60+63 2.51-02 3.38+61 5.60-01 3.44+01 1.13-01 5.00+63 2.05-02 3.39+61 5.63-01 3.45+01 1.13-01 6.06+03 1.74-02 3.40+01 5.65-01 3.45+01 1.13-01 8.00+03 1.34-02 3.40+01 5.68-01 3.46+01 1.13-01 1.00+04 1.09-02 3.41+01 5.70-01 3.47+01 1.14-01 1.50+04 7.56-03 3.41+01 5.72-01 3.47+01 1.14-01 2.00+64 5.81-63 3.42+01 5.73-01 3.48+01 1.14-61 3.00+04 4.01-03 3.42+01 5.75-61 3.48+01 1.14-01 4.00+04 3.08-03 3.42+61 5.76-01 3.48+01 1.14-01 5.00+04 2.51-03 3.43+01 5.76-01 3.48+01 1.14-01 6.00+04 2.12-03 3.43+01 5.76-01 3.48+01 1.14—01 8.00+04 1.62-03 3.43+01 5.77-01 3.48+01 1.14-01

1.00+65 1.32-03 3.43+01 5.77-01 3.48+01 1.14-01

(b/atom) x .003276 = cm2 /n 61
Table 3.-22. LEAD, Z=82

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electronfield With

coherent Without

coherent With

coherent Without

coherent

MeV b/atom b/atom b/atom b/atom b/atom b/atom b/atom cm-/g cm-/g 1.00-02 1.73+03 5.25+01 4.40+04 4.57+04 4.41+04 1.33+02 1.28+02

1.30-02 1.34+03 5.19+01 2.20+04 2.33+04 2.20+04 6.78+01 6.41+01 L3 1.30-02 1.34+03 5.19+01 5.58+04 5.71+04 5.59+04 1.66+02 1.62+02

1.50-02 1.15+03 5.16+01 3.84+04 3.96+04 3.85+04 1.15+02 1.12+02

1.52-02 1.13+03 5.15+01 3.75+04 3.86+04 3.76+04 1.12+02 1.09+02 U 1.52-02 1.13+03 5.15+01 4.90+04 5.01+04 4.91+04 1.46+02 1.43+02

1.59-02 1.08+03 5.14+01 4.35+04 4.46+04 4.36+04 1.30+02 1.27+02

L, 1.59-02 1.08+03 5.14+01 5.29+04 5.40+04 5.29+04 1.57+02 1.54+02 2.00-02 8.17+02 5.07+01 2.86+04 2.95+04 2.87+04 8.57+01 8.34+01 3.00-02 4.91+02 4.90+01 9.71+03 1.02+04 9.76+03 2.97+01 2.84+01 4.00-02 3.36+02 4.75+01 4.47+03 4.81+03 4.52+03 1.40+01 1.31+01 5.00-02 2.48+02 4.60+01 2.44+03 2.68+03 2.48+03 7.81+00 7.22+00 6.00-02 1.94+02 4.47+01 1.48+03 1.67+03 1.52+03 4.87+00 4.43+00

8.00-02 1.32+02 4.24+01 6.70+02 8.03+02 7.13+02 2.33+00 2.07+00

8.80-02 1.16+02 4.16+01 5.15+02 6.31+02 5.56+02 1.83+00 1.62+00 K 8.80-02 1.16+02 4.16+01 2.45+03 2.56+03 2.49+03 7.45+00 7.23+00

1.00-01 9.93+01 4.04+01 1.76+03 1.86+03 1.80+03 5.40+00 5.23+00

1.50-01 6.39+01 3.64+01 6.14+02 6.78+02 6.51+02 1.97+00 1.89+00

2.00-01 4.92+01 3.33+01 2.92+02 3.41+02 3.25+02 9.91-01 9.45-01

3.00-01 3.61+01 2.90+01 1.03+02 1.39+02 1.32+02 4.04-01 3.83-01

4.00-01 3.00+01 2.60+01 4.96+01 7.96+01 7.56+01 2.31-01 2.20-01

5.00-01 2.63+01 2.37+01 2.92+01 5.55+01 5.29+01 1.61-01 1.54-01 6.00-01 2.37+01 2.19+01 1.92+01 4.29+01 4.11+01 1.25-01 1.20-01 8.00-01 2.03+01 1.93+01 1.02+01 < 3.04+01 2.95+01 8.85-02 8.56-02

1.00+00 1.79+01 1.73+01 6.39+00 2.43+01 2.37+01 7.08-02 6.90-02

1.50+00 1.43+01 1.41+01 2.89+00 5.66-01 1.78+01 1.75+01 5.17-02 5.10-02

2.00+00 1.22+01 1.20+01 1.77+00 1.70+00 1.57+01 1.55+01 4.55-02 4.50-02

3.00+00 9.51+00 9.46+00 9.14-01 3.94+00 3.30-03 1.44+01 1.43+01 4.18-02 4.16-02

4.00+00 7.94+00 7.89+00 5.89-01 5.77+00 1.35-02 1.43+01 1.43+01 4.16-02 4.14-02

5.00+00 6.84+00 6.81+00 4.34-01 7.30+00 2.66-02 1.46+01 1.46+01 4.24-02 4.24-02

6.00+00 6.04+00 6.02+00 3.36-01 8.54+00 4.09-02 1.50+01 1.49+01 4.35-02 4.34-02

8.00+00 4.93+00 4.92+00 2.31-01 1.05+01 7.00-02 1.58+01 1.58+01 4.59-02 4.59-02

1.00+01 4.20+00 4.19+00 1.78-01 1.22+01 9.57-02 1.67+01 1.67+01 4.84-02 4.84-02

1.50+01 3.10+00 1.12-01 1.55+01 1.48-01 1.89+01 5.48-02

2.00+01 2.49+00 8.10-02 1.81+01 1.86-01 2.09+01 6.06-02

3.00+01 1.81+00 5.20-02 2.18+01 2.42-01 2.39+01 6.96-02

4.00+01 1.44+00 3.80-02 2.43+01 2.81-01 2.60+01 7.57-02

5.00+01 1.20+00 3.00-02 2.61+01 3.11-01 2.77+01 8.04-02

6.00+01 1.04+00 2.50-02 2.75+01 3.35-01 2.89+01 8.41-02

8.00+01 8.18-01 1.80-02 2.96+01 3.71-01 3.08+01 8.96-02

1.00+02 6.79-01 1.41-02 3.10+01 3.97-01 3.21+01 9.34-02

1.50+02 4.83-01 3.33+01 4.41-01 3.43+01 9.96-02

2.00+02 3.79-01 3.48+01 4.68-01 3.56+01 1.03-01 3.00+02 2.69-01 3.64+01 5.03-01 3.71+01 1.08-01 4.00+02 2.10-01 3.73+01 5.25-01 3.80+01 1.11-01 5.00+02 1 . 74—01 3.79+01 5.40-01 3.86+01 1.12-01 6.00+02 1.49-01 3.83+01 5.51-01 3.90+01 1.13-01 8.00+02 1.16-01 3.89+01 5.66-01 3.96+01 1.15-01 1.00+03 9.58-02 3.92+01 5.76-01 3.99+01 1.16-01 1.50+03 6.69-02 3.98+01 5.90-01 4.04+01 1.18-01 2.00+03 5.18-02 4.00+01 5.98-01 4.07+01 1.18-01 3.00+03 3.60-02 4.04+01 6.07-01 4.10+01 1.19-01 4.00+03 2.78-02 4.05+01 6.12-01 4.12+01 1.20-01 5.00+03 2.27-02 4.06+01 6.15-01 4.13+01 1.20-01 6.00+03 1.93-02 4.07+01 6.17-01 4.13+01 1.20-01 8.00+03 1.48-02 4.08+01 6.20-01 4.14+01 1.20-01 1.00+04 1.21-02 4.09+01 6.21-01 4.15+01 1.21-01 1.50+04 8.37-03 4.09+01 6. 24-01 4.16+01 1.21-01 2.00+04 6.44-03 4.10+01 6.25-01 4.16+01 1.21-01 3.00+04 4.44-03 4.10+01 6.27-01 4.16+01 1.21-01 4.00+04 3.41-03 4.10+01 6.28-01 4.17+01 1.21-01 5.00+04 2.78-03 4.11+01 6.28-01 4.17+01 1.21-01 6.00+04 2.35-03 4.11+01 6.28-01 4.17+01 1.21-01 8.00+04 1.80-03 4.11+01 6.29-01 4.17+01 1.21-01 1.00+05 1.46-03 4.11+01 6.29-01 4.17+01 1.21-01

(b/atom) x .002907 = cm2

/g; 62
Table 3.-23. URANIUM, Z=92

Photon

energy

Scattering Photoelectric

Pair production Total Total

With

coherent Without

coherent Nuclear

field Electron

field Withcoherent Without

coherent Withcoherent Without

coherent

MeV b/atom b/atom bjatom b/atom b/atom b/atom b/atom cm'l/g cmr/g 1.00-02 2.17+03 5.89+01 6.84+04 7.05+04 6.84+04 1.78+02 1.73+02 1.50-02 1.47+03 5.79+01 2.38+04 2.53+04 2.38+04 6.39+01 6.03+01

1.72-02 1.27+03 5.74+01 1.68+04 1.81+04 1.69+04 4.58+01 4.28+01 U 1.72-02 1.27+03 5.74+01 4.06+04 4.19+04 4.07+04 1.06+02 1.03+02 2.00-02 1.07+03 5.68+01 2.70+04 2.81+04 2.71+04 7.10+01 6.85+01 2.09-02 1.01+03 5.67+01 2.38+04 2.48+04 2.38+04 6.27+01 6.03+01 U 2.09-02 1.01+03 5.67+01 3.38+04 3.48+04 3.38+04 8.80+01 8.56+01

2.18—02 9.61+02 5.65+01 3.06+04 3.15+04 3.06+04 7.98+01 7.75+01

L, 2.18-02 9.61+02 5.65+01 3.53+04 3.63+04 3.54+04 9.18+01 8.95+01 3.00-02 6.36+02 5.50+01 1.56+04 1.62+04 1.56+04 4.10+01 3.96+01 4.00-02 4.36+02 5.32+01 7.35+03 7.79+03 7.40+03 1.97+01 1.87+01 5.00-02 3.22+02 5.16+01 4.07+03 4.39+03 4.12+03 1.11+01 1.04+01 6.00-02 2.51+02 5.02+01 2.50+03 2.75+03 2.55+03 6.96+00 6.45+00

8.00-02 1.68+02 4.76+01 1.16+03 1.32+03 1.20+03 3.35+00 3.04+00

1.00-01 1.25+02 4.53+01 6.31+02 7.56+02 6.77+02 1.91+00 1.71+00

1.16-01 1.05+02 4.38+01 4.26+02 5.31+02 4.70+02 1.34+00 1.19+00 K 1.16-01 1.05+02 4.38+01 1.82+03 1.92+03 1.86+03 4.86+00 4.71+00

1.50-01 7.80+01 4.08+01 9.36+02 1.01+03 9.77+02 2.56+00 2.47+00

2.00-01 5.88+01 3.74+01 4.48+02 5.07+02 4.85+02 1.28+00 1.23+00

3.00-01 4.21+01 3.25+01 1.59+02 2.01+02 1.92+02 5.09-01 4.85-01 4.00-01 3.45+01 2.91+01 7.87+01 1.13+02 1.08+02 2.86-01 2.73-01

5.00-01 3.01+01 2.66+01 4.64+01 7.65+01 7.30+01 1.93-01 1.85-01 6.00-01 2.70+01 2.46+01 3.06+01 5.76+01 5.52+01 1.46-01 1.40-01 8.00-01 2.29+01 2.16+01 1.65+01 3.94+01 3.81+01 9.97-02 9.64^-02 1.00+00 2.03+01 1.94+01 1.04+01 3.07+01 2.98+01 7.76-02 7.54-02

1.50+00 1.61+01 1.58+01 4.73+00 7.77-01 2.17+01 2.13+01 5.48-02 5.39-02

2.00+00 1.37+01 1.35+01 2.84+00 2.26+00 1.88+01 1.86+01 4.75-02 4.70-02

3.00+00 1.07+01 1.06+01 1.49+00 5.09+00 3.70-03 1.73+01 1.72+01 4.38-02 4.35-02

4.00+00 8.91+00 8.85+00 9.58-01 7.32+00 1.52-02 1.72+01 1.71+01 4.35-02 4.34-02

5.00+00 7.68+00 7.64+00 7.02-01 9.16+00 2.99-02 1.76+01 1.75+01 4.45-02 4.44-02

6.00+00 6.78+00 6.75+00 5.43-01 1.06+01 4.59-02 1.80+01 1.80+01 4.55-02 4.54-02

8.00+00 5.55+00 5.52+00 3.75-01 1.30+01 7.86-02 1.90+01 1.89+01 4.80-02 4.79-02

1.00+01 4.72+00 4.71+00 2.88-01 1.49+01 1.07-01 2.00+01 2.00+01 5.06-02 5.06-02

1.50+01 3.48+00 1.80-01 1.88+01 1.65-01 2.27+01 5.73-02

2.00+01 2.80+00 1.31-01 2.20+01 2.08-01 2.51+01 6.36-02

3.00+01 2.04+00 8.50-02 2.66+01 2.69-01 2.90+01 7.33-02

4.00+01 1.62+00 6.20-02 2.96+01 3.13-01 3.16+01 7.99-02

5.00+01 1.35+00 5.00-02 3.18+01 3.46-01 3.36+01 8.50-02

6.00+01 1.16+00 4.00-02 3.36+01 3.73-01 3.51+01 8.89-02

8.00+01 9.17-01 3.00-02 3.61+01 4.12-01 3.75+01 9.48-02

1.00+02 7.62-01 2.40-02 3.77+01 4.41-01 3.89+01 9.84-02

1.50+02 5.42-01 4.07+01 4.89-01 4.17+01 1.06-01 2.00+02 4.25-01 4.24+01 5.19-01 4.34+01 1.10-01 3.00+02 3.01-01 4.44-f01 5.57-01 4.53+01 1.15-01 4.00+02 2.36-01 4.56+01 5.81-01 4.64+01 1.17-01 5.00+02 1.95-01 4.63+01 5.98-01 4.71+01 1.19-01 6.00+02 1.67-01 4.69+01 6.09-01 4.76+01 1.21-01 8.00+02 1.31-01 4.75+01 6.25-01 4.83+01 1.22-01 1.00+03 1.07-01 4.80+01 6.36-01 4.88+01 1.23-01 1.50+03 7.50-02 4.87+01 6.51-01 4.94+01 1.25-01 2.00+03 5.81-02 4.90+01 6.60-01 4.97+01 1.26-01 3.00+03 4.04-02 4.94+01 6.69-01 5.01+01 1.27-01 4.00+03 3.12-02 4.96+01 6.74-01 5.03+01 1.27-01 5.00+03 2.55-02 4.97+01 6.78-01 5.04+01 1.28-01 6.00+03 2.16-02 4.98+01 6.80-01 5.05+01 1.28-01 8.00+03 1.67-02 5.00+01 6.83-01 5.07+01 1.28-01 1.00+04 1.36-02 5.00+01 6.85-01 5.07+01 1.28-01 1.50+04 9.40-03 5.01+01 6.88-01 5.08+01 1.29-01 2.00+04 7.22-03 5.02+01 6.89-01 5.09+01 1.29-01 3.00+04 4.98-03 5.02+01 6.91-01 5.09+01 1.29-01 4.00+04 3.83-03 o. 03+01 6.92-01 5.10+01 1.29-01 5.00+04 3.11-03 5.03+01 6.92-01 5.1P+01 1.29-01 6.00+04 2.63-03 5.03+01 6.92-01 5.10+01 1.29-01 8.00+04 2.02-03 5.03+01 6.93-01 5.10+01 1.29-01 1.00+05 1.64-03 5.04+01 6.93-01 5.11+01 1.29-01

(b/alom) x .002530 = cm2 /g 63
Table 3.-24. WATER, H2 0

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Withoutcoherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2lg cm2lg cm2/g cm2/g cm2lg cm2lg cm2/g 1.00-02 3.97-01 2.14—01 4.78+00 5.18+00 4.99+00

1.50-02 3.09-01 2.10-61 1.27+00 1.58+00 1.48+00

2.00-02 2.70-01 2.67-61 5.05-01 7.75-01 7.11-01

3.00-02 2.32-01 2.00-01 1.38-01 3.70-01 3.38-01

4.00-02 2.13-01 1.93-01 5.48-02 2.67-01 2.48-01

5.00-62 2.00-01 1.88-01 2.67-02 2.27-01 2.14-01

6.00-02 1.91-01 1.82-61 1.50-02 2.06-01 1.97-01

8.00-02 1.78-01 1.73-61 5.95-03 1.84-01 1.79-01

1.00-01 1.68-01 1.65-01 2.85-03 1.71-01 1.68-01

1.50-01 1.50-01 1.48-01 7.76-04 1.51-01 1.49-01

2.00-01 1.37-61 1.36-01 3.11-04 1.37-01 1.36-01

3.00-01 1.19-61 1.18-01 8.86-05 1.19-01 1.18-01

4.00-01 1.06-61 1.06-01 3.78-05 1.06-01 1.06-01

5.00-01 9.68-02 9.67-02 2.04-05 9.68-02 9.67-02

6.00-01 8.96-02 8.95-02 1.28-05 8.96-02 8.95-02

8.00-01 7.86-02 6.42-06 7.86-02

1.00+00 7.06-02 3.98-06 7.07-02

1.50+00 5.74-02 1.86-06 9.86-05 5.75-02

2.00+00 4.90-02 1.18-06 3.93-04 4.94-02

3.00+00 3.85-02 6.62-07 1.13-03 1.34-05 3.97-02

4.00+00 3.22-02 4.51-07 1.83-03 5.52-05 3.40-02

5.00+00 2.78-02 3.44-07 2.45-03 1.09-04 3.03-02

6.00+00 2.45-02 2.75-07 3.00-03 1.67-04 2.77-02

8.06+60 2.01-02 1.97-07 3.93-03 2.86-04 2.43-02

1.00+61 1.71-02 1.54-07 4.69-03 3.90-04 2.22-02

1.50+01 1.27-02 6.11-03 6.08-04 1.94-02

2.00+01 1.02-02 7.16-03 7.80-04 1.81-02

3.00+01 7.40-03 8.63-03 1.04-03 1.71-02

4.06+01 5.88-03 9.63-03 1.23-03 1.67-02

5.00+01 4.91-03 1.04-02 1.38-03 1.67-02

6.00+01 4.22-03 1.10-02 1.51-03 1.67-02

8.00+01 3.33-03 1.19-02 1.70-03 1.70-02

1.00+02 2.77-03 1.26-02 1.84-03 1.72-02

1.56+02 1.97-03 1.37-02 2.09-03 1.78-02

2.00+02 1.54-03 1.44-02 2.26-03 1.82-02

3.06+02 1.09-03 1.52-02 2.48-03 1.88-02

4.06+02 8.57-04 1.57-02 2.62-03 1.92-02

5.00+02 7.10-04 1.60-02 2.73-03 1.95-02

6.06+02 6.08-04 1.63-02 2.80-03 1.97-02

8.00+02 4.75-04 1.66-02 2.92-03 2.00-02

1.00+03 3.90-04 1.68-02 3.00-03 2.02-02

1.50+63 2.73-04 1.71-02 3.12-03 2.05-02

2.00+63 2.11-64 1.72-02 3.20-03 2.06-02

3.00+03 1.47-64 1.74-02 3.30-03 2.08-02

4.00+03 1.13-04 1.75-02 3.35-03 2.10-02

5.00+63 9.26-05 1.76-02 3.38-03 2.10-02

6.00+03 7.86-05 1.76-02 3.40-03 2.11-02

8.00+63 6.05-05 1.77-02 3.43-03 2.11-02

1.00+04 4.94-05 1.77-02 3.45-03 2.12-02

1.50+04 3.41-05 1.77-02 3.48-03 2.13-02

2.00+04 2.62-05 1.78-02 3.50-03 2.13-02

3.00+04 1.81-05 1.78-02 3.52-03 2.13-02

4.00+04 1.39-05 1.78-02 3.52-03 2.13-02

5.00+04 1.13-05 1.78-02 3.53-03 2.13-02

6.00+04 9.57-06 1.78-02 3.53-03 2.14—02

8.00+04 7.33-06 1.78-02 3.54-03 2.14-02

1.06+05 5.97-06 1.78-02 3.54-03 2.14-02

64
Table 3.-25. SILICON DIOXIDE, Si02

Photon

energy

Scattering Photoelectric

Pair pr< duction Total

With

coherent Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2/g cm2

//; cm2 /g cm2/g cm2/g cm2/g 1.00-62 5.64-01 1.93-01 1.85+01 1.90+01 1.87+01

1.50-02 3.95-01 1.89-01 5.33+00 5.73+00 5.52+00

2.00-02 3.16-01 1.86-01 2.18+00 2.49+00 2.36+00

3.00-02 2.46-01 1.80-01 6.13-01 8.59-01 7.93-01

4.00-02 2.14-01 1.74-01 2.48-01 4.63-01 4.22-01

5.00-02 1.96-01 1.69-01 1.22-01 3.18-01 2.91-01

6.00-02 1.83-01 1.64-01 6.91-02 2.52-01 2.33-01

8.00-02 1.67-01 1.56-01 2.78-02 1.94-01 1.83-01

1.00-01 1.55-01 1.48-01 1.36-02 1.69-01 1.62-01

1.50-01 1.37-01 1.33-01 3.76-03 1.40-01 1.37-01

2.00-01 1.24-01 1.22-01 1.53-03 1.26-01 1.24-01

3.00-01 1.07-01 1.06-01 4.45-04 1.08-01 1.07-01

4.00-01 9.57-02 9.52-02 1.92-04 9.59-02 9.54-02

5.00-01 8.73-02 8.70-02 1.04-04 8.74-02 8.71-02

6.00-01 8.07-02 8.05-02 6.50-05 8.08-02 8.05-02

8.00-01 7.07-02 3.28-05 7.07-02

1.00+00 6.36-02 2.03-05 6.36-02

1.50+00 5.16-02 9.49-06 1.47-04 5.18-02

2.00+00 4.41-02 6.02-06 5.81-04 4.47-02

3.00+00 3.47-02 3.33-06 1.66-03 1.21-05 3.63-02

4.00+00 2.89-02 2.26-06 2.69-03 4.97-05 3.17-02

5.00+00 2.50-02 1.63-06 3.60-03 9.76-05 2.87-02

6.00+00 2.21-02 1.38-06 4.42-03 1.50-04 2.66-02

8.00+00 1.81-02 9.81-07 5.76-03 2.57-04 2.41-02

1.00+01 1.54—02 7.68-07 6.86-03 3.51-04 2.26-02

1.50+01 1.14-02 8.94-03 5.47-04 2.09-02

2.00+01 9. 14—03 1.05-02 7.02-04 2.03-02

3.00+01 6.65-03 1.26-02 9.35-04 2.02-02

4.00+01 5.28-03 1.40-02 1.11-03 2.04-02

5.00+01 4.41-03 1.52-02 1.24-03 2.08-02

6.00+01 3.80-03 1.60-02 1.35-03 2.12-02

8.00+01 3.00-03 1.73-02 1.51-03 2.18-02

1.00+02 2.49-03 1.83-02 1.64-03 2.24-02

1.50+02 1.77-03 1.98-02 1.85-03 2.34-02

2.00+02 1.39-03 2.07-02 1.99-03 2.41-02

3.00+02 9.85-04 2.19-02 2.18-03 2.50-02

4.00+02 7.71-04 2.25-02 2.30-03 2.56-02

5.00+02 6.39-04 2.29-02 2.38-03 2.60-02

6.00+02 5.47-04 2.33-02 2.45-03 2.62-02

8.00+02 4.27-04 2.37-02 2.54-03 2.66-02

1.00+03 3.51-04 2.39-02 2.61-03 2.69-02

1.50+03 2.45-04 2.43-02 2.71-03 2.73-02

2.00+03 1.90-04 2.45-02 2.78-03 2.75-02

3.00+03 1.32-04 2.48-02 2.85-03 2.78-02

4.00+03 1.02-04 2.49-02 2.89-03 2.79-02

5.00+03 8.33-05 2.50-02 2.92-03 2.80-02

6.00+03 7.06-05 2.50-02 2.94-03 2.81-02

8.00+03 5.44-05 2.51-02 2.97-03 2.81-02

1.00+04 4.44-05 2.52-02 2.98-03 2.82-02

1.50+04 3.07-05 2.52-02 3.01-03 2.83-02

2.00+04 2.36-05 2.53-02 3.02-03 2.83-02

3.00+04 1.63-05 2.53-02 3.03-03 2.83-02

4.00+04 1.25-05 2.53-02 3.04-03 2.84-02

5.00+04 1.02-05 2.53-02 3.04-03 2.84-02

6.00+04 8.60-06 2.53-02 3.05-03 2.84-02

8.00+04 6.60-06 2.53-02 3.05-03 2.84-02

1.00+05 5.37-06 2.54-02 3.05-03 2.84—02

65
Table 3.-26. SODIUM IODIDE, Nal

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Withoutcoherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2lg cm2/g cm2/g cm2/g 1.00-02 2.53+60 1.65-01 1.36+02 1.39+02 1.36+02

1.50-02 1.69+00 1.62-01 4.57+01 4.74+01 4.59+01

2.00-02 1.23+00 1.59-01 2.11+01 2.23+01 2.12+01

3.00-62 7.48-01 1.54-01 6.70+00 7.45+00 6.86+00

3.32-02 6.60-01 1.52-01 5.03+00 5.69+00 5.19+00

*3.32-02 6.60-01 1.52-01 3.03+01 3.09+01 3.04+01

4.00-02 5.28-01 1.49-01 1.88+01 1.93+01 1.89+01

5.00-02 4.10-01 1.44-01 1.03+01 1.07+01 1.05+01

6.00-02 3.36-01 1.40-61 6.28+00 6.62+00 6.42+00

8.00-02 2.49-01 1.33-61 2.87+00 3.12+00 3.00+00

1.00-61 2.02-01 1.27-61 1.52+00 1.72+00 1.64+00

1.56-01 1.49-01 1.14-61 4.76-01 6.25-01 5.90-01

2.00-01 1.24-01 1.65-61 2.09-01 3.34-01 3.14-01

3.00-01 9.99-02 9.69-62 6.68-02 1.67-01 1.58-01

4.00-01 8.64-02 8.15-62 3.10-02 1.17-01 1.12-01

5.00-01 7.78-02 7.44-62 1.77-02 9.55-02 9.21-02

6.00-01 7.12-02 6.88-02 1.14-02 8.26-02 8.02-02

8.00-01 6.17-02 6.05-02 5.88-03 6.76-02 6.63-62

1.00+60 5.49-02 5.43-02 3.66-03 5.86-02 5.80-02

1.50460 4.45-02 4.42-02 1.66-03 7.36-04 4.69-02 4.66-02

2.00+60 3.78-02 3.77-02 1.02-03 2.49-03 4.13-02 4.12-02

3.00+00 2.97-02 2.97-02 5.46-04 6.40-03 1.63-65 3.66-02 3.66-02

4.00+00 2.48-02 2.47-02 3.61-04 9.89-03 4.25-65 3.51-02 3.50-02

5.00+00 2.14-02 2.70-04 1.29-02 8.35-65 3.46-02

6.00+00 1.89-02 2.11-04 1.55-02 1.28-64 3.47-02

8.00+00 1.54-02 1.47-04 1.97-02 2.26-04 3.55-02

1.00+01 1.32-02 1.13-04 2.32-02 3.00-04 3.68-02

1.50+01 9.73-03 7.08-05 2.99-02 4.68-04 4.02-02

2.00+01 7.81-03 5.14-05 3.49-02 5.97-04 4.33-02

3.00+01 5.69-03 3.31-05 4.18-02 7.82-04 4.84-02

4.00+01 4.52-03 2.45-05 4.65-02 9.13-04 5.20-02

5.00461 3.77-03 1.94-05 5.00-02 1.01-03 5.48-02

6.06461 3.25-03 1.60-05 5.28-02 1.09-03 5.71-02

8.06+61 2.56-03 1.19-05 5.67-02 1.22-03 6.05-02

1.06+62 2.13-03 9.52-06 5.95-02 1.31-03 6.29-02

1.56462 1.52-63 6.40-02 1.46-03 6.70-02

2.00+62 1.19-63 6.67-02 1.56-03 6.95-02

3.06+62 8.42-64 6.99-02 1.69-03 7.24-02

4.06+62 6.59-64 7.17-02 1.77-03 7.41-02

5.00+62 5.46-64 7.28-02 1.82-03 7.52-02

6.06+62 4.68-64 7.37-62 1.87-03 7.60-02

8.06+62 3.65-64 7.49-62 1.92-03 7.71-02

1.06463 3.06-64 7.55-62 1.96-03 7.78-02

1.56463 2.16-64 7.66-62 2.02-03 7.89-02

2.06463 1.62-04 7.72-62 2.06-03 7.94-02

3.66463 1.13-04 7.78-02 2.09-03 8.00-62

4.66463 8.71-65 7.81-02 2.11-03 8.03-02

5.66463 7.12-65 7.83-02 2.13-03 8.05-62

6.06+63 6.64-65 7.85-62 2.14-03 8.07-02

8.66+63 4.65-65 7.86-62 2.15-03 8.08-02

1.06+64 3.86-65 7.87-62 2.16-03 8.09-02

1.50+64 2.63-65 7.89-02 2.17-03 8.11-02

2.60+64 2.02-05 7.90-02 2.18-03 8.12-02

3.66464 1.39-05 7.91-02 2.18-03 8.13-02

4.66+64 1.07-65 7.91-02 2.19-03 8.13-62

5.66+64 8.76-06 7.92-02 2.19-03 8.14-02

6.06+64 7.36-66 7.92-62 2.19-03 8.14-02

8.66+64 5.64-66 7.93-62 2.19-03 8.15-02

1.66465 4.59-66 7.93-62 2.19-03 8.15-02

Iodine K-edge. 66
Table 3.-27. AIR, NBS Handbook 85(1964) Composition

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent

Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2 lg cm2/g cm2/g cm2lg cm2lg cm2/g 1.00-02 3.64-01 1.93-01 4.63+00 4.99+00 4.82+00

1.50-02 2.85-01 1.89-01 1.27+00 1.55+00 1.45+00

2.00-02 2.47-01 1.86-01 5.05-01 7.52-01 6.91-01

3.00-02 2.11-01 1.80-01 1.39-01 3.49-01 3.18-01

4.00-02 1.93-01 1.74-01 5.53-02 2.48-01 2.29-01

5.00-02 1.81-01 1.69-01 2.70-02 2.08-01 1.96-01

6.00-02 1.73-01 1.64-01 1.52-02 1.88-01 1.79-01

8.00-02 1.61-01 1.56-01 6.06-03 1.67-01 1.62-01

1.00-01 1.51-01 1.48-01 2.94-03 1.54-01 1.51-01

1.50-01 1.35-01 1.33-01 8.05-04 1.36-01 1.34-01

2.00-01 1.23-01 1.22-01 3.24-04 1.23-01 1.23-01

3.00-01 1.07-01 1.06-01 9.30-05 1.07-01 1.06-01

4.00-01 9.53-02 9.52-02 3.99-05 9.54-02 9.53-02

5.00-01 8.70-02 8.70-02 2.15-05 8.70-02 8.70-02

6.00-01 8.05-02 8.04-02 1.34-05 8.05-02 8.05-02

8.00-01 7.07-02 6.79-06 7.07-02

1.00+00 6.36-02 4.20-06 6.36-02

1.50+00 5.17-02 1.96-06 9.89-05 5.18-02

2.00+00 4.41-02 1.25-06 3.94-04 4.45-02

3.00+00 3.47-02 6.97-07 1.13-03 1.21-05 3.58-02

4.00+00 2.89-02 4.73-07 1.83-03 4.97-05 3.08-02

5.00+00 2.50-02 3.61-07 2.46-03 9.76-05 2.75-02

6.00+00 2.21-02 2.88-07 3.01-03 1.50-04 2.52-02

8.00+00 1.81-02 2.06-07 3.94-03 2.57-04 2.23-02

1.00+01 1.54-02 1.61-07 4.70-03 3.51-04 2.04—02

1.50+01 1.14-02 6.14-03 5.47-04 1.81-02

2.00+01 9.14-03 7.18-03 7.02-04 1.70-02

3.00+01 6.65-03 8.65-03 9.35-04 1.62-02

4.00+01 5.28-03 9.67-03 1.11-03 1.61-02

5.00+01 4.41-03 1.04-02 1.24-03 1.61-02

6.00+01 3.80-03 1.11-02 1.36-03 1.62-02

8.00+01 3.00-03 1.20-02 1.53-03 1.65-02

1.00+02 2.55-03 1.26-02 1.65-03 1.68-02

1.50+02 1.77-03 1.38-02 1.87-03 1.74-02

2.00+02 1.39-03 1.45-02 2.02-03 1.79-02

3.00+02 9.85-04 1.53-02 2.22-03 1.85-02

4.00+02 7.71-04 1.58-02 2.34-03 1.89-02

5.00+02 6.38-04 1.61-02 2.43-03 1.92-02

6.00+02 5.47-04 1.63-02 2.50-03 1.94-02

8.00+02 4.27-04 1.67-02 2.60-03 1.97-02

1.00+03 3.51-04 1.69-02 2.67-03 1.99-02

1.50+03 2.45-04 1.72-02 2.79-03 2.02-02

2.00+03 1.90-04 1.73-02 2.86-03 2.04-02

3.00+03 1.32-04 1.75-02 2.95-03 2.06-02

4.00+03 1.02-04 1.76-02 2.99-03 2.07-02

5.00+03 8.33-05 1.77-02 3.02-03 2.08-02

6.00+03 7.07-05 1.77-02 3.05-03 2.08-02

8.00+03 5.44-05 1.78-02 3.08-03 2.09-02

1.00+04 4.44-05 1.78-02 3.10-03 2.09-02

1.50+04 3.07-05 1.78-02 3.12-03 2.10-02

2.00+04 2.36-05 1.79-02 3.14-03 2.10-02

3.00+04 1.63-05 1.79-02 3.15-03 2.11-02

4.00+04 1.25-05 1.79-02 3.16-03 2.11-02

5.00+04 1.02-05 1.79-02 3.17-03 2.11-02

6.00+04 8.60-06 1.79-02 3.17-03 2.11-02

8.00+04 6.60-06 1.79-02 3.18-03 2.11-02

1.00+05 5.37-06 1.79-02 3.18-03 2.11-02

67
Table 3.-28. CONCRETE, Grodstein — McGinnies Composition

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2lg cm2lg cm2lg cm2lg 1.00-02 6.00-01 1.93-01 2.63+01 2.69+01 2.65+01

1.50-02 4.21-01 1.89-01 7.82+00 8.24+00 8.01+00

2.00-02 3.34—01 1.86-01 3.26+00 3.59+00 3.45+00

3.00-02 2.56-01 1.80-01 9.38-01 1.19+00 1.12+00

4.00-02 2.20-01 1.74—01 3.84-01 6.05-01 5.59-01

5.00-02 2.00-01 1.69-01 1.92-01 3.92-01 3.61-01

6.00-02 1.86-01 1 .64—01 1.09-01 2.95-01 2.73-01

8.00-02 1.69-01 1.56-01 4.45-02 2.13-01 2.00-01

1.00-01 1.57-01 1.48-01 2.19-02 1.79-01 1.70-01

1.50-01 1.37-01 1.34—01 6.20-03 1.44-01 1.40-01

2.00-01 1.25-01 1.22-01 2.56-03 1.27-01 1.25-01

3.00-01 1.07-01 1.07-01 7.52-04 1.08-01 1.07-01

4.00-01 9.60-02 9.54-02 3.27-04 9.63-02 9.58-02

5.00-01 8.75-02 8.72-02 1.77-04 8.77-02 8.73-02

6.00-01 8.09-02 8.06-02 1.11-04 8.10-02 8.07-02

8.00-01 7.09-02 7.08-02 5.64—05 7.09-02 7.09-02

1.00+00 6.37-02 3.50-05 6.37-02

1.50+00 5.18-02 1.63-05 1.58-04 5.19-02

2.00+00 4.42-02 1.03-05 6.22-04 4.48-02

3.00+00 3.47-02 5.67-06 1.77-03 1.21-05 3.65-02

4.00+00 2.90-02 3.84-06 2.87-03 4.98-05 3.19-02

5.00+00 2.50-02 2.86-06 3.84-03 9.78-05 2.90-02

6.00+00 2.21-02 2.32-06 4.70-03 1.50-04 2.70-02

8.00+00 1.81-02 . 1.65-06 6.13-03 2.57-04 2.45-02

1.00+01 1.54-02 1.29-06 7.31-03 3.52-04 2.31-02

1.50+01 1.14-02 9.21-08 9.52-03 5.48-04 2.15-02

2.00+01 9.15-03 6.58-08 1.11-02 7.03-04 2.10-02

3.00+01 6.67-03 1.34-02 9.37-04 2.10-02

4.00+01 5.30-03 1.49-02 1.11-03 2.13-02

5.00+01 4.42-03 1.61-02 1.24-03 2.18-02

6.00+01 3.81-03 1.70-02 1.35-03 2.22-02

8.00+01 3.00-03 1.84-02 1.51-03 2.29-02

1.00+02 2.49—03 1.94-02 1.64-03 2.35-02

1.50+02 1.78-03 2.11-02 1.85-03 2.47-02

2.00+02 1.39-03 2.20-02 1.99-03 2.54--02

3.00+02 9.87-04 2.32-02 2.18-03 2.64-02

4.00+02 7.73-04 2.39-02 2.30-03 2.69-02

5.00+02 6.40-04 2.43-02 2.38-03 2.73-02

6.00+02 5.48-04 2.47-02 2.44-03 2.76-02

8.00+02 4.28-04 2.51-02 2.54-03 2.81-02

1.00+03 3.52-04 2.54-02 2.60-03 2.83-02

1.50+03 2.46-04 2.58-02 2.71-03 2.87-02

2.00+03 1.90-04 2.60-02 2.77-03 2.90-02

3.00+03 1.32-04 2.63-02 2.85-03 2.92-02

4.00+03 1.02-04 2.64-02 2.89-03 2.94—02

5.00+03 8.35-05 2.65-02 2.92-03 2.95-02

6.00+03 7.08-05 2.65-02 2.93-03 2.95-02

8.00+03 5.45-05 2.66-02 2.96-03 2.96-02

1.00+04 4.45-05 2.67-02 2.97-03 2.97-02

1.50+04 3.08-05 2.67-02 3.00-03 2.98-02

2.00+04 2.37-05 2.68-02 3.01-03 2.98-02

3.00+04 1.63-05 2.68-02 3.02-03 2.98-02

4.00+04 1.25-05 2.68-02 3.03-03 2.99-02

5.00+04 1.02-05 2.68-02 3.03-03 2.99-02

6.00+04 8.62-06 2.68-02 3.04-03 2.99-02

8.00+04 6.61-06 2.68-02 3.04-03 2.99-02

1.00+05 5.38-06 2.69-02 3.04-03 2.99-02

68
Table 3.-29. 0.8N H2 S04 SOLUTION

Photon

energy

Scattering Photoelectric

Pair pr< duction Total

With

coherent

Without

coherent Nuclearfield

Electron

field With

coherent Withoutcoherent

MeV cm2/g cm2lg cm2lg cm2 lg cm2lg cm2lg cm2\g 1.00-02 4.03-01 2.13-01 5.36+00 5.76+00 5.57+00

1.50-02 3.13-01 2.10-01 1.45+00 1.76+00 1.66+00

2.00-02 2.72-01 2.06-01 5.78-01 8.49-01 7.84—01

3.00-02 2.32-01 1.99-01 1.59-01 3.91-01 3.58-01

4.00-02 2.13-01 1.93-01 6.32-02 2.76-91 2.56-01

5.00-02 2.00-01 1.87-01 3.10-02 2.31-01 2.18-01

6.00-02 1.91-01 1.82-01 1.74-02 2.08-01 1.99-01

8.00-02 1.78-01 1.72-01 6.92-03 1.85-01 1.79-01

1.00-01 1.68-01 1.64-01 3.33-03 1.71-01 1.68-01

1.50-01 1.49-01 1.48-01 9.11-04 1.50-01 1.49-01

2.00-01 1.36-01 1.35-01 3.67-04 1.37-01 1.36-01

3.00-01 1.18-01 1.18-01 1.05-04 1.18-01 1.18-91

4.00-01 1.06-01 1.06-01 4.49-05 1.06-01 1.06-01

5.00-01 9.65-02 9.64—02 2.43-05 9.65-02 9.64-02

6.00-01 8.93-02 8.92-02 1.52-05 8.93-02 8.92-02

8.00-01 7.83-02 7.64-06 7.83-02

1.00+00 7.04-02 4.73-06 7.04-02

1.50+00 5.72-02 2.22-06 1.00-04 5.73-02

2.00+00 4.88-02 1.41-06 3.99-04 4.92-02

3.00+00 3.84-02 7.85-07 1.15-03 1.34-05 3.96-02

4.00+00 3.21-02 5.35-07 1.86-93 5.51-05 3.40-02

5.00+00 2.77-02 4.08-07 2.49-03 1.08-04 3.03-02

6.00+00 2.45-92 3.25-07 3.05-03 1.66-04 2.77-02

8.00+00 2.00-02 2.33-07 3.99-03 2.85-04 2.43-02

1.00491 1.70-02 1.82-07 4.76-03 3.89-04 2.22-02

1.50+01 1.26-02 6.21-03 6.06-04 1.94-92

2.00+01 1.01-02 7.27-03 7.78-04 1.82-92

3.00+01 7.37-03 8.77-03 1.04-03 1.72-02

4.00+01 5.86-03 9.78-03 1.23-03 1.69-02

5.00+01 4.89-03 1.06-02 1.38-03 1.68-02

6.00+01 4.21-93 1.12-02 1.50-03 1.69-02

8.00+01 3.32-03 1.21-02 1.69-03 1.71-02

1.00+02 2.76-03 1.28-02 1.83-03 1.74-02

1.50+02 1.96-03 1.39-02 2.08-03 1.80-02

2.00+02 1.54-03 1.46-02 2.25-03 1.84r-02

3.00+02 1.09-03 1.55-02 2.47-03 1.90-02

4.00+02 1 8.55-04 1.60-02 2.61-03 1.94-02

5.00+02 7.08-04 1.63-02 2.72-03 1.97-02

6.00+02 6.06-04 1.65-02 2.79-93 1.99-02

8.00+02 1 4.73-04 1.68-02 2.91-93 2.02-02

1.00+03

1 3.89-04 1.70-02 2.98-03 2.04-02

1.50+03 2.72-04 1.73-02 3.11-03 2.07-02

2.00+03 2.10-04 1.75-02 3.19-03 2.09-02

3.00+03 1.46-04 1.77-02 3.28-03 2.11-02

4.00+03 1.13-94 1.78-02 3.33-03 2.12-02

5.00+03 9.23-95 1.78-02 3.37-03 2.13-02

6.00+03 7.83-05 1.79-02 3.39-03 2.13-02

8.00+03 6.03-05 1.79-02 3.42-03 2.14-02

1.00+04 4.92-05 1.79-02 3.44-03 2. 14—02

1.50+04 3.40-05 1.80-02 3.47-03 2.15-02

2.00+94 2.62-05 1.80-02 3.49-03 2.15-02

3.00+04 1.80-05 1.81-02 3.50-03 2.16-02

4.00+04 1.39-05 1.81-02 3.51-03 2.16-92

5.00+04 1.13-05 1.81-02 3.52-03 2.16-02

6.00+04 9.54-96 1.81-02 3.52-03 2.16-02

8.00+04 7.31-96 1.81-02 3.52-03 2.16-02

1.00+05 5.95-06 1.81-02 3.53-03 2.16-92

69
Table 3. — 30. COMPACT BONE, NBS Handbook 85(1964) Composition

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent

Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2lg cm2lg cm2lg cm2lg 1.00-02 4.90-91 2.05-01 1.98+01 2.03+01 2.00+01

1.50-02 3.67-01 2.01-01 5.95+00 6.32+00 6.15+00

2.00-02 3.05-01 1.97-01 2.49+00 2.79+00 2.68+00

3.00-02 2.46-01 1.91-01 7.16-01 9.62-01 9.07-01

4.00-02 2.18-01 1.85-01 2.93-01 5.12-01 4.78-01

5.00-02 2.02-01 1.79-01 1.47-01 3.49-01 3.27-01

6.00-02 1.90-01 1.74—01 8.39-02 2.74-01 2.58-01

8.00-02 1.75-01 1.65-01 3.45-02 2.09-01 2.00-01

1.00-01 1.63-01 1.57-01 1.70-02 1.80-01 1.74-01

1.50-01 1.45-01 1.42-01 4.86-03 1.49-01 1.47-01

2.00-01 1.31-01 1.30-01 2.01-03 1.33-01 1.32-01

3.00-01 1.14-01 1.13-01 5.93-04 1.14-01 1.14-01

4.00-01 1.02-01 1.01-01 2.59-04 1.02-01 1.01-01

5.00-01 9.26-02 9.24-02 1.40-04 9.27-02 9.25-02

6.00-01 8.56-02 8.55-02 8.79-05 8.57-02 8.56-02

8.00-01 7.52-02 7.51-02 4.46-05 7.52-02 7.51-02

1.00+00 6.75-02 6.75-02 2.77-05 6.76-02 6.75-92

1.50+00 5.49-02 1.29-05 1.27-04 5.50-02

2.00+00 4.68-02 8.15-06 5.01-04 4.73-02

3.00+00 3.68-02 4.48-06 1.43-03 1.29-05 3.83-92

4.00+00 3.07-02 3.02-06 2.31-03 5.28-05 3.31-92

5.00+00 2.65-02 2.30-06 3.10-03 1.04—04 2.97-92

6.00+00 2.35-02 1.83-06 3.79-03 1.59-04 2.74-92

8.00+00 1.92-02 1.30-06 4.95-03 2.73-04 2.44-92

1.00+01 1.63-02 1.02-06 5.90-03 3.73-04 2.26-02

1.50+01 1.21-02 7.69-03 5.81-04 2.04-02

2.00+01 9.71-03 8.99-03 7.45-04 1.94-02

3.00+01 7.07-03 1.08-02 9.93-04 1.89-02

4.00+01 5.62-03 1.21-02 1.18-03 1.89-02

5.00+01 4.69-03 1.30-02 1.32-03 1.90-02

6.00+01 4.04-03 1.38-02 1.44—03 1.93-02

8.00+01 3.18-03 1.49-02 1.61-03 1.97-02

1.00+02 2.65-03 1.57-02 1.75-03 2.01-02

1.50+02 1.88-03 1.71-02 1.98-03 2.10-02

2.00+02 1.48-03 1.79-02 2.14-03 2.15-02

3.00+02 1.05-03 1.89-02 2.35-03 2.23-02

4.00+02 8.19-04 1.95-02 2.48-03 2.28-92

5.00+02 6.78-04 1.98-02 2.57-03 2.31-92

6.00+02 5.81-04 2.01-02 2.65-03 2.33-02

8.00+02 4.54-04 2.05-02 2.75-03 2.37-02

1.00+03 3.73-04 2.07-02 2.83-03 2.39-02

1.50+03 2.61-04 2.11-02 2.95-03 2.43-02

2.00+03 2.02-04 2.13-02 3.02-03 2.45-02

3.00+03 1.40-04 2.15-02 3.10-03 2.47-02

4.00+03 1.08-04 2.16-02 3.15-03 2.49-02

5.00+03 8.85-95 2.17-92 3.18-03 2.49-02

6.00+03 7.51-05 2.17-02 3.20-03 2.50-02

8.00+03 5.78-05 2.18-02 3.23-03 2.51-02

1.00+04 4.72-05 2.18-02 3.25-03 2.51-02

1.50+04 3.26-05 2.19-02 3.28-03 2.52-92

2.00+04 2.51-05 2.19-02 3.29-03 2.52-92

3.00+04 1.73-05 2.19-02 3.31-03 2.53-02

4.00+04 1.33-05 2.20-02 3.32-03 2.53-02

5.00+04 1.08-05 2.20-02 3.32-03 2.53-02

6.00+04 9.14-06 2.20-02 3.33-03 2.53-02

8.00+94 7.01-06 2.20-02 3.33-03 2.53-92

1.00+05 5.70-06 2.20-02 3.33-03 2.53-92

70
Table 3.-31. MUSCLE, Striated, NBS Handbook 85(1964) Composition

Photon

energy

Scattering Photoelectric

Pair prt duction To al

With

coherent Withoutcoherent * Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2lg cm2tg cm2/g cm2 lg cm'2 /g cm2/g cm2/g 1.00-02 3.89-01 2.12-01 4.88+00 5.27+00 5.09+00

1.50-02 3.05-01 2.08-01 1.32+00 1.63+00 1.53+00

2.00-02 2.66-01 2.05-01 5.26-01 7.93-01 7.31-01

3.00—02 2.29-01 1.98-01 1.44-01 3.73-01 3.42-01

4.00-02 2.10-01 1.92-01 5.73-02 2.68-01 2.49-01

5.00-02 1.98-01 1.86-01 2.81-02 2.27-01 2. 14—01

6.00-02 1.90-01 1.81-01 1.58-02 2.05-01 1.97-01

8.00-02 1.76-01 1.71-01 6.31-03 1.83-01 1.78-01

1.00-01 1.67-01 1.63-01 3.04—03 1.70-01 1.66-01

1.50-01 1.49-01 1.47-01 8.32-04 1.49-01 1.48-01

2.00-01 1.35-01 1.35-01 3.35-04 1.36-01 1.35-01

3.00-01 1.18-01 1.17-01 9.59-05 1.18-01 1.17-01

4.00-01 1.05-01 1.05-01 4.11-05 1.05-01 1.05-01

5.00-01 9.59-02 9.58-02 2.22-05 9.60-02 9.59-02

6.00-01 8.88-02 8.87-02 1.39-05 8.88-02 8.87-02

8.00-01 7.79-02 6.99-06 7.79-02

1.00+00 7.00-02 4.33-06 7.00-02

1.56+00 5.69-02 2.03-06 9.69-05 5.70-02

2.00+00 4.86-02 1.29-06 3.86-04 4.89-02

3.00+00 3.82-02 7.18-07 1.11-03 1.33-05 3.93-02

4.06+00 3.19-02 4.89-07 1.80-03 5.47-05 3.37-02

5.06+00 2.75-02 3.73-07 2.41-03 1.08-04 3.00-02

6.00+00 2.43-02 2.97-07 2.95-03 1.65-04 2.74—02

8.06+00 1.99-02 2.13-07 3.86-03 2.83-04 2.40-02

1.00+01 1.69-02 1.66-07 4.60-03 3.87-04 2.19-02

1.50+01 1.25-02 6.00-03 6.03-04 1.92-02

2.00+01 1.01-02 7.03-03 7.73-04 1.79-02

3.00+01 7.33-03 8.47-03 1.03-03 1.68-02

4.00+01 5.82-03 9.46-03 1.22-03 1.65-02

5.00+01 4.86-03 1.02-02 1.37-03 1.64-02

6.00+01 4.19-03 1.08-02 1.49-03 1.65-02

8.00+01 3.30-03 1.17-02 1.68-03 1.67-02

1.00+02 2.75-03 1.24-02 1.82-03 1.70-02

1.56+02 1.95-03 1.35-02 2.07-03 1.75-02

2.00+02 1.53-03 1.42-02 2.24-03 1.79-02

3.00+02 1.09-03 1.50-02 2.46-03 1.85-02

4.00+02 8.50-04 1.54-02 2.60-03 1.89-02

5.06+02 7.04—04 1.58-02 2.70-03 1.92-02

6.00+02 6.02-04 1.60-02 2.78-03 1.94-02

8.00+02 4.70-04 1.63-02 2.89-03 1.97-02

1.06+03 3.87-04 1.65-02 2.97-03 1.99-02

1.50+03 2.70-04 1.68-02 3.10-03 2.02-02

2.00+03 2.09-04 1.69-02 3.18-03 2.03-02

3.00+03 1.46-04 1.71-02 3.27-03 2.05-02

4.00+03 1.12-04 1.72-02 3.32-03 2.06-02

5.00+03 9.18-05 1.73-02 3.36-03 2.07-02

6.00+03 7.79-05 1.73-02 3.38-03 2.08-02

8.06+03 6.00-05 1.74-02 3.41-03 2.08-02

1.00+04 4.90-05 1.74-02 3.43-03 2.09-02

1.50+04 3.38-05 1.74—02 3.46-03 2.09-02

2.00+04 2.60-05 1.75-02 3.48-03 2.10-02

3.00+04 1.79-05 1.75-02 3.49-03 2.10-02

4.00+04 1.38-05 1.75-02 3.50-03 2.10-02

5.00+04 1.12-05 1.75-02 3.51-03 2.10-02

6.00+04 9.48-06 1.75-02 3.51-03 2.10-02

8.00+04 7.27-06 1.75-02 3.52-03 2.10-02

1.00+05 5.91-06 1.75-02 3.52-03 2.11-02

71
Table 3.-32. POLYSTYRENE, (C8H8 02 )„

Photon

Scattering Photoelectric

Pair production Total

energy With

coherent Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2lg cm2/g cm2tg cm2/g 1.00-02 3.13-01 2.08-01 1.82+00 2.13+00 2.03+60

1.50-02 2.64-01 2.04-01 4.91-01 7.55-01 6.95-01

2.00-02 2.39-01 2.00-01 1. 86-01 4.24-01 3.86-01

3.00-02 2.13-01 1.94-01 4.63-02 2.59-01 2.40-01

4.00-02 1.99-01 1.88-01 1.76-02 2.17-01 2.05-01

5.00-02 1.90-01 1.82-01 8.95-03 1.99-01 1.91-01

6.00-02 1.83-01 1.77-01 5.33-03 1.88-01 1.82-01

8.00-02 1.71-01 1.68-01 2.09-03 1.73-01 1.70-01

1.00-01 1.62-01 1.60-01 1.00-03 1.63-01 1.61-61

1.50-01 1.45-01 1.44-01 2.67-04 1.45-61 1.44-01

2.00-01 1.32-01 1.06-04 1.32-01

3.00-01 1.15-01 2.99-05 1.15-01

4.00-01 1.03-01 1.28-05 1.03-01

5.00-01 9.38-02 6.91-06 9.38-02

6.00-01 8.68-02 4.30-06 8.68-02

8.00-01 7.63-02 2.17-06 7.63-02

1.00+00 6.85-02 1.34-06 6.85-02

1.50+00 5.57-02 6.26-07 7.64-05 5.58-02

2.00+00 4.75-02 3.99-07 3.05-04 4.78-02

3.00+00 3.74-02 2.23-07 8.76-04 1.30-05 3.83-02

4.00+00 3.12-02 1.53-07 1.42-03 5.36-05 3.27-02

5.00+00 2.69-02 1.17-07 1.91-03 1.05-04 2.90-02

6.00+00 2.38-02 9.32-08 2.34-63 1.62-04 2.63-02

8.00+00 1.95-02 6.68-08 3.06-03 2.77-04 2.28-02

1.00+01 1.66-02 5.19-08 3.65-03 3.79-04 2.06-02

1.50+01 1.23-02 4.77-03 5.90-04 1.76-02

2.00+01 9.86-03 5.59-03 7.57-04 1.62-02

3.00+01 7.17-03 6.74-03 1.01-03 1.49-02

4.00+01 5.70-03 7.54-03 1.19-03 1.44-02

5.00+01 4.76-03 8.14-03 1.34-03 1.42-02

6.00+01 4.10-03 8.62-03 1.46-03 1.42-02

8.00+01 3.23-03 9.34-63 1.65-03 1.42-02

1.00+02 2.69-03 9.87-03 1.79-03 1.44-02

1.50+02 1.91-03 1.08-02 2.04-03 1.47-02

2.00+02 1.50-03 1.13-02 2.20-03 1.50-02

3.00+02 1.06-03 1.20-02 2.42-03 1.55-02

4.00+02 8.32-04 1.24-02 2.57-03 1.58-02

5.00+02 6.89-04 1.27-02 2.67-03 1.60-02

6.00+02 5.90-04 1.29-02 2.75-03 1.62-02

8.00+02 4.61-04 1.31-02 2.86-03 1.65-02

1.00+03 3.79-04 1.33-02 2.94-03 1.66-02

1.50+03 2.65-04 1.36-02 3.07-03 1.69-02

2.00+03 2.05-04 1.37-02 3.15-03 1.71-02

3.00+03 1.43-04 1.39-02 3.25-03 1.73-02

4.00+03 1.10-04 1.39-02 3.31-03 1.74-02

5.00+03 8.99-05 1.40-02 3.34-03 1.74-02

6.00+03 7.62-05 1.40-02 3.37-03 1.75-62

8.00+03 5.87-05 1.41-02 3.40-03 1.75-62

1.00+04 4.79-05 1.41-02 3.42-03 1.76-62

1.50+04 3.31-05 1.42-02 3.45-03 1.76-62

2.00+04 2.55-05 1.42-02 3.47-03 1.77-62

3.00+04 1.76-05 1.42-02 3.49-03 1.77-62

4.00+04 1.35-05 1.42-02 3.50-03 1.77-62

5.00+04 1.10-05 1.42-02 3.51-03 1.77-62

6.00+04 9.28-06 1.42-02 3.51-03 1.77-62

8.00+04 7.12-06 1.42-02 3.52-03 1.78-62

1.00+05 5.79-06 1.42-02 3.52-03 1.78-62

72
Table 3.-33. POLYMETHYL METHACRYLATE (Lucite), (C5H8 02) n

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Withoutcoherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2/g cm2/g cm2lg cm2lg 1.00-02 3.42-01 2.08-01 2.90+00 3.25+00 3.11+00

1.50-02 2.79-01 2.04—01 7.78-01 1.06+00 9.82-01

2.00-02 2.48-01 2.01-01 3.03-01 5.51-01 5.03-01

3.00-02 2.18-01 1.94—01 7.98-02 2.98-01 2.74-01

4.00-02 2.03-01 1.88-01 3.12-02 2.34-01 2.19-01

5.00-02 1.92-01 1.83-01 1.54-02 2.08-01 1.98-01

6.00-02 1.84-01 1.77-01 8.86-03 1.93-01 1.86-01

8.00-02 1.72-01 1.68-01 3.50-03 1.76-01 1.72-01

1.00-01 1.63-01 1.60-01 1.68-03 1.64-01 1.62-01

1.50-01 1.46-01 1.44-01 4.52-04 1.46-01 1.45-01

2.00-01 1.33-01 1.32-01 1.81-04 1.33-01 1.32-01

3.00-01 1.15-01 1.15-01 5.14-05 1.15-01 1.15-01

4.00-01 1.03-01 1.03-01 2.19-05 1.03-01 1.03-01

5.00-01 9.41-02 9.41-02 1.18-05 9.41-02 9.41-02

6.00-01 8.71-02 8.70-02 7.39-06 8.71-02 8.70-02

8.00-01 7.65-02 3.72-06 7.65-02

1.00+00 6.87-02 2.30-06 6.87-02

1.50+00 5.59-02 1.08-06 8.49-05 5.59-02

2.00+00 4.77-02 6.85-07 3.38-04 4.80-02

3.00+00 3.75-02 3.83-07 9.72-04 1.31-05 3.85-02

4.00+00 3.13-02 2.62-07 1.58-03 5.37-05 3.29-02

5.00+00 2.70-02 2.00-07 2.12-03 1.06-04 2.92-02

6.00+00 2.39-02 1.59-07 2.59-03 1.62-04 2.66-02

8.00+00 1.95-02 1.14-07 3.39-03 2.78-04 2.32-02

1.00+01 1.66-02 8.92-08 4.05-03 3.80-04 2.11-02

1.50+01 1.23-02 5.29-03 5.91-04 1.82-02

2.00+01 9.88-03 6.19-03 7.59-04 1.68-02

3.00+01 7.19-03 7.46-03 1.01-03 1.57-02

4.00+01 5.72-03 8.34-03 1.20-03 1.53-02

5.00+01 4.77-03 9.00-03 1.35-03 1.51-02

6.00+01 4.11-03 9.54-03 1.47-03 1.51-02

8.00+01 3.24-03 1.03-02 1.65-03 1.52-02

1.00+02 2.69-03 1.09-02 1.79-03 1.54-02

1.50+02 1.92-03 1.19-02 2.04-03 1.59-02

2.00+02 1.50-03 1.25-02 2.20-03 1.62-02

3.00+02 1.06-03 1.32-02 2.42-03 1.67-02

4.00+02 8.34-04 1.37-02 2.56-03 1.71-02

5.00+02 6.90-04 1.40-02 2.67-03 1.73-02

6.00+02 5.91-04 1.42-02 2.74-03 1.75-02

8.00+02 4.62-04 1.45-02 2.86-03 1.78-02

1.00+03 3.80-04 1.46-02 2.94-03 1.80-02

1.50+03 2.65-04 1.49-02 3.06-03 1.82-02

2.00+03 2.05-04 1.51-02 3.14-03 1.84-02

3.00+03 1.43-04 1.52-02 3.24-03 1.86-02

4.00+03 1.10-04 1.53-02 3.29-03 1.87-02

5.00+03 9.01-05 1.54-02 3.33-03 1.88-02

6.00+03 7.64-05 1.54-02 3.35-03 1.88-02

8.00+03 5.89-05 1.55-02 3.38-03 1.89-02

1.00+04 4.81-05 1.55-02 3.40-03 1.89-02

1.50+04 3.32-05 1.55-02 3.43-03 1.90-02

2.00+04 2.55-05 1.56-02 3.45-03 1.90-02

3.00+04 1.76-05 1.56-02 3.47-03 1.91-02

4.00+04 1.35-05 1.56-02 3.48-03 1.91-02

5.00+04 1.10-05 1.56-02 3.48-03 1.91-02

6.00+04 9.31-06 1.56-02 3.49-03 1.91-02

8.00+04 7.14-06 1.56-02 3.49-03 1.91-02

1.00+05 5.80-06 1.56-02 3.50-03 1.91-02

73
Table 3.-34. POLYETHYLENE, (CH2 )«

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2lg cm2 lg cm2/g cm2lg cm2/g 1.00-02 3.18-01 2.20-01 1.69+00 2.01+00 1.91+00

1.50-02 2.72-01 2.16-01 4.56-01 7.28-01 6.72-01

2.00-02 2.48-01 2.13-01 1.73-01 4.20-01 3.85-01

3.00-02 2.23-01 2.06-01 4.30-02 2.66-01 2.49-01

4.00-02 2.10-01 1.99-01 1.63-02 2.26-01 2.15-01

5.00-02 2.00-01 1.93-01 8.30-03 2.09-01 2.01-01

6.00-02 1.93-01 1.88-01 4.95-03 1.98-01 1.93-01

8.00-02 1.81-01 1.78-01 1.94—03 1.83-01 1.80-01

1.00-01 1.71-01 1.69-01 9.29-04 1.72-01 1.70-01

1.50-01 1.54—01 1.53-01 2.47-04 1.54—01 1.53-01

2.00-01 1.40-01 9.85-05 1.40-01

3.00-01 1.22-01 2.78-05 1.22-01

4.00-01 1.09-01 1.19-05 1.09-01

5.00-01 9.95-02 6.41-06 9.95-02

6.00-01 9.21-02 3.99-06 9.21-02

8.00-01 8.09-02 2.01-06 8.09-02

1.00400 7.27-02 1.24-06 7.27-02

1.50+00 5.91-02 5.81-07 7.28-05 5.92-02

2.00+00 5.04-02 3.70-07 2.91-04 5.07-02

3.00+00 3.96-02 2.07-07 8.35-04 1.38-05 4.05-02

4.00+00 3.31-02 1.42-07 1.35-03 5.68-05 3.45-02

5.00+00 2.86-02 1.08-07 1.82-03 1.12-04 3.05-02

6.00+00 2.53-02 8.65-08 2.23-03 1.72-04 2.77-02

8.00+00 2.07-02 6.20-08 2.92-03 2.94—04 2.39-02

1.00+01 1.76-02 4.82-08 3.48-03 4.02-04 2.15-02

1.50401 1.30-02 4.55-03 6.26-04 1.82-02

2.00+01 1.05-02 5.33-03 8.03-04 1.66-02

3.00+01 7.61-03 6.42-03 1.07-03 1.51-02

4.00+01 6.05-03 7.19-03 1.27-03 1.45-02

5.00+01 5.05-03 7.76-03 1.42-03 1.42-02

6.00+01 4.35-03 8.22-03 1.55-03 1.41-02

8.00401 3.43-03 8.91-03 1.75-03 1.41-02

1.00+02 2.85-03 9.42-03 1.90-03 1.42-02

1.50+02 2.03-03 1.03-02 2.17-03 1.45-02

2.00+02 1.59-03 1.08-02 2.34-03 1.47-02

3.00+02 1.13-03 1.15-02 2.58-03 1.52-02

4.00+02 8.82-04 1.19-02 2.73-03 1.55-02

5.00+02 7.30-04 1.21-02 2.85-03 1.57-02

6.00402 6.25-04 1.23-02 2.93-03 1.59-02

8.00+02 4.88-04 1.26-02 3.05-03 1.61-02

1.00+03

1 4.02-04 1.27-02 3.14—03 1.63-02

1.50+03 2.81-04 1.39-02 3.28-03 1.65-02

2.00+03 2.17-04 1.31-02 3.36-03 1.67-02

3.00+03 1.51-04 1 .33-02 3.46-03 1.69-02

4.00+03 1.17-04 1.33-02 3.52-03 1.70-02

5.00+03 9.53-05 1.34-02 3.56-03 1.70-02

6.00+03 8.08-05 1.34—02 3.59-03 1.71-02

8.00+03 6.23-05 1.35-02 3.62-03 1.72-02

1.00+04 5.08-05 1.35-02 3.64—03 1.72-02

1.50+04 3.51-05 1.35-02 3.68-03 1.73-02

2.00+04 2.70-05 1.36-02 3.70-03 1.73-02

3.00+04 1.86-05 1.36-02 3.72-03 1.73-02

4.00+04 1.43-05 1.36-02 3.73-03 1.73-02

5.00+04 1.16-05 1.36-02 3.73-03 1.73-02

6.00+04 9.84-06 1.36-02 3.74-03 1.74-02

8.00+04 7.55-06 1.36-02 3.74-03 1.74-02

1.00+05 6.14-06 1.36-02 3.75-03 1.74-02

74
Table 3 .- 35 . BAKELITE (Typical), ( C^I^Oy),,

Photon

energy

Scattering

Phot.,- electric

Pair production To al

With

coherent

Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

MeV cm2/g cm2lg cm2/g cm2lg cm2lg cm2lg cm2/g

1 . 00-02 3 . 27-01 2 . 04-01 2 . 43+00 2 . 76+00 2 . 64+00

1 . 50-02 2 . 69-01 2 . 00-01 6 . 53-01 9 . 23-01 8 . 54-01

2 . 00-02 2 . 41-01 1 . 97-01 2 . 52-01 4. 92-01 4 . 48-01

3 . 00-02 2 . 12-01 1 . 90-01 6 . 50-02 2 . 77-01 2 . 55-01

4. 00-02 1 . 98-01 1 . 84—01 2 . 51-02 2 . 23-01 2 . 09-01

5 . 00-02 1 . 88-01 1 . 79-01 1 . 26-02 2 . 00-01 1 . 91-01

6 . 00-02 1 . 80-01 1 . 74-01 7 . 31-03 1 . 87-61 1 . 81-01

8 . 00-02 1 . 68-01 1 . 65-01 2 . 88-03 1 . 71-01 1 . 68-01

1 . 00-01 1 . 59-01 1 . 57-01 1 . 38-03 1 . 61-01 1 . 58-01

1 . 50-01 1 . 42-01 1 . 41-01 3 . 70-04 1 . 43-01 1 . 42-01

2 . 00-01 1 . 30-01 1 . 29-01 1 . 48-04 1 . 30-01 1 . 30-01

3 . 00-01 1 . 13-01 4 . 19-05 1 . 13-01

4 . 00-01 1 . 01-01 1 . 79-05 1 . 01-01

5 . 00-01 9 . 21-02 9 . 66-06 9 . 21-02

6 . 00-01 8 . 52-02 6 . 02-06 8 . 52-02

8 . 00-01 7 . 49-02 3 . 04—06 7 . 49-02

1 . 00+00 6 . 73-02 1 . 88-06 6 . 73-02

1 . 50+00 5 . 47-02 8 . 78-07 8 . 20-05 5 . 48-02

2 . 00+00 4 . 67-02 5 . 59-07 3 . 27-04 4 . 70-02

3 . 00+00 3 . 67-02 3 . 13-07 9 . 40-04 1 . 28-05 3 . 77-02

4. 00+00 3 . 06-02 2 . 13-07 1 . 53-03 5 . 26-05 3 . 22-02

5 . 00+00 2 . 64—02 1 . 63-07 2 . 05-03 1 . 03-04 2 . 86-02

6 . 00+00 • 2 . 34-02 1 . 30-07 2 . 50-03 1 . 59-04 2 . 60-02

8. 00+00 1 . 91-02 9 . 32-08 3 . 28-03 2 . 72-04 2 . 27-02

1 . 00+01 1 . 63-02 7 . 27-08 3 . 91-03 3 . 72-04 2 . 06-02

1 . 50+01 1 . 21-02 5 . 12-03 5 . 79-04 1 . 78-02

2 . 00+01 9 . 67-03 5 . 99-03 7 . 43-04 1 . 64-02

3 . 00+01 7 . 04-03 7 . 22-03 9 . 90-04 1 . 53-02

4 . 00+01 5 . 60-03 8 . 07-03 1 . 17-03 1 . 48-02

5 . 00+01 4 . 67-03 8 . 72-03 1 . 32-03 1 . 47-02

6 . 00+01 4 . 02-03 9 . 23-03 1 . 44-03 1 . 47-02

8 . 00+01 3 . 17-03 1 . 00-02 1 . 62-03 1 . 48-02

1 . 00+02 2 . 64-03 1 . 06-02 1 . 76-03 1 . 50-02

1 . 50+02 1 . 88-03 1 . 15-02 2 . 00-03 1 . 54-02

2 . 00+02 1 . 47-03 1 . 21-02 2 . 16-03 1 . 57-02

3 . 00+02 1 . 04-03 1 . 28-62 2 . 37-03 1 . 62-02

4 . 00+02 8 . 17-04 1 . 33-62 2 . 51-03 1 . 66-02

5 . 00+02 6 . 76-04 1 . 35-02 2 . 61-03 1 . 68-02

6. 00+02 5 . 79-04 1 . 37-02 2 . 69-03 1 . 70-02

8 . 00+02 4 . 52-04 1 . 40-02 2 . 80-03 1 . 73-02

1 . 00+03 3 . 72-04 1 . 42-02 2 . 88-03 1 . 74-02

1 . 50+03 2 . 60-04 1 . 45-02 3 . 00-03 1 . 77-02

2 . 00+03 2 . 01-04 1 . 46-02 3 . 08-03 1 . 79-62

3 . 00+03 1 . 40-04 1 . 48-02 3 . 17-03 1 . 81-02

4 . 00+03 1 . 08-04 1 . 49-02 3 . 23-03 1 . 82-02

5 . 00+03 8 . 82-05 1 . 49-02 3 . 26-03 1 . 83-62

6 . 00+03 7 . 48-05 1 . 50-02 3 . 29-03 1 . 83-02

8 . 00+03 5 . 76-05 1 . 50-62 3 . 32-63 1 . 84-02

1 . 00+04 4 . 71-05 1 . 50-62 3 . 34-63 1 . 84-02

1 . 50+04 3 . 25-05 1 . 51-62 3 . 37-03 1 . 85-02

2 . 00+04 2 . 50-65 1 . 51-62 3 . 39-63 1 . 85-02

3 . 00+04 1 . 72-05 1 . 51-62 3 . 41-63 1 . 85-02

4 . 00+04 1 . 32-05 1 . 51-62 3 . 42-63 1 . 86-02

5 . 00+04 1 . 08-05 1 . 51-62 3 . 42-63 1 . 86-02

6 . 00+04 9 . 11-06 1 . 52-02 3 . 43-63 1 . 86-02

8 . 00+04 6 . 99-06 1 . 52-02 3 . 43-63 1 . 86-02

1 . 00+05 5 . 68-06 1 . 52-02 3 . 44-63 1 . 86-02

75
Table 3.-36. PYREX GLASS, (Corning 7740)

Photon

energy

Scattering Photoelectric

Pair production Total

With

coherent Without

coherent Nuclear

field

Electron

field With

coherent Without

coherent

Met' cm2/g cm2/g cm2/g cm2lg cm2lg cm2lg cm2/g 1.00-02 5.36-01 1.92-01 1.65+01 1.71+01 1.67+01

1.50-02 3.79-01 1.88-01 4.76+00 5.14+00 4.95+00

2.00-02 3.06-01 1.85-01 1.94+00 2.25+00 2.13+00

3.00-02 2.40-01 1.79-01 5.46-01 7.86-01 7.24-01

4.00-02 2.10-01 1.73-01 2.21-01 4.31-01 3.94-01

5.00-02 1.93-01 1.68-01 1.09-01 3.02-01 2.77-01

6.00-02 1.81-01 1.63-01 6 . 1 5

K32 2.42-01 2.25-01

8.00-02 1.65-01 1.55-01 2.47-02 1.90-01 1.80-01

1.00-01 1 .54—01 1.47-01 1.21-02 1.66-01 1.60-01

1.50-01 1.36-01 1.33-01 3.34-03 1.39-01 1.36-01

2.00-01 1.23-01 1.22-01 1.36-03 1.25-01 1.23-01

3.00-01 1.07-01 1.06-01 3.95-04 1.07-01 1.06-01

4.00-01 9.53-02 9.48-02 1.71-04 9.54-02 9.50-02

5.00-01 8.69-02 8.66-02 9.23-05 8.70-02 8.67-02

6.00-01 8.03-02 8.01-02 5.77-05 8.04-02 8.02-02

8.00-01 7.04-02 2.91-05 7.04-02

1.00+00 6.33-02 1.80-05 6.33-02

1.50+00 5.14-02 8.43-06 1.40-04 5.16-02

2.00+00 4.39-02 5.35-06 5.53-04 4.44-02

3.00+00 3.45-02 2.96-06 1.58-03 1.20—05 3.61-02

4.00+00 2.88-02 2.01-06 2.56-03 4.95-05 3.14-02

5.00+00 2.49-02 1.46-06 3.43-03 9.72-05 2.84-02

6.00+00 2.20-02 1.22-06 4.20-03 1.49-04 2.63-02

8.00+00 1.80-02 8.71-07 5.49-03 2.56-04 2.37-02

1.00+01 1.53-02 6.82-07 6.54-03 3.50-04 2.22-02

1.50+01 1.13-02 8.52-03 5.44-04 2.04-02

2.00+01 9.10-03 9.96-03 6.99-04 1.98-02

3.00+01 6.62-03 1.20-02 9.31-04 1.95-02

4.00+01 5.26-03 1.34-02 1.10-03 1.98-02

5.00+01 4.39-03 1.45-02 1.24-03 2.01-02

6.00+01 3.78-03 1.53-02 1.34-03 2.04-02

8.00+01 2.98-03 1.65-02 1.51-03 2.10-02

1.00+02 2.48-03 1.74-02 1.63-03 2.15-02

1.50+02 1.76-03 1.89-02 1.84-03 2.25-02

2.00+02 1.38-03 1.98-02 1.99-03 2.32-02

3.00+02 9.80-04 2.09-02 2.17-03 2.40-02

4.00+02 7.68-04 2.15-02 2.29-03 2.45-02

5.00+02 6.36-04 2.19-02 2.38-03 2.49-02

6.00+02 5.44-04 2.22-02 2.44-03 2.52-02

8.00+02 4.25-04 2.26-02 2.54-03 2.56-02

1.00+03 3.50-04 2.29-02 2.60-03 2.58-02

1.50+03 2.44-04 2.32-02 2.71-03 2.62-02

2.00+03 1.89-04 2.34-02 2.78-03 2.64-02

3.00+03 1.31-04 2.37-02 2.85-03 2.67-02

4.00+03 1.01-04 2.38-02 2.90-03 2.68-02

5.00+03 8.29-05 2.39-02 2.92-03 2.69-02

6.00+03 7.03-05 2.39-02 2.94-03 2.69-02

8.00+03 5.42-05 2.40-02 2.97-03 2.70-02

1.00+04 4.42-05 2.40-02 2.98-03 2.71-02

1.50+04 3.06-05 2.41-02 3.01-03 2.71-02

2.00+04 2.35-05 2.41-02 3.02-03 2.72-02

3.00+04 1.62-05 2.42-02 3.04-03 2.72-02

4.00+04 1.24-05 2.42-02 3.04-03 2.72-02

5.00+04 1.01-05 2.42-02 3.05-03 2.72-02

6.001+04 8.57-06 2.42-02 3.05-03 2.73-02

8.00+04 6.57-06 2.42-02 3.06-03 2.73-02

1.00+05 5.34-06 2.42-02 3.06-03 2.73-02

76
The author is particularly indebted to M. J. Berger and U. Fano for suggestions and comments

on the manuscript, and to E. G. Fuller for supplying material presented in section 2.6. Helpful in- formation and corrections were also received from

a number of other including F. Biggs, A. B. Chilton,

J. W. Cooper, R. D. Deslattes, R. D. Evans, S. Meshkov, and R. H. Pratt. The author also thanks

S. Seltzer for computational assistance.

77
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