NBS TECHN I \l

416

Study of a Halpern-Type 47T

Neutron Detector

H. M. Gerstenberg and E. G. Fuller

V*

*•" OF

Q

z\

£&

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
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NBS TECHNICAL NOTE 416

ISSUED JUNE 12, 1967

Study of a Halpern-Type 4 7T

Neutron Detector

H. M. Gerstenberg and E. G. Fuller

Radiation Physics Division

Institute for Basic Standards

National Bureau of Standards

• Washington, D.C., 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, Government Printing Office

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Contents

Page

1. Introduction 1

2. Experimental Detail 3

3. Neutron Sources 7

4. Counter Efficiencies 17

5. Attenuation and Moderation in Samples 29

6. Final Detector and Determination of Absolute Yields 32

Appendix 1. Determination of the Absolute Positron Efficiency 38

Appendix 2. Cryostat Geometry 42

References 44
Study of a Halpern-Type 4tt Neutron Detector

H. M. Gerstenberg and E. G. Fuller

The response to various neutron spectra of a 2-inch diameter BF proportional counter in a Halpern-type geometry has been studied as a function of moderator thickness. Neutron sources used were a calibrated

RaDBe(a,n) source and a series of photoneutron sources, using a number

of bremsstrahlung spectra. The reactions used were: 0(y,n) , P(y,n)

and d(y,n). For these sources absolute neutron yields were determined

either from the residual g+ activity or from the known cross section

and the absolute bremsstrahlung intensity. Using these empirical data

a final detector with 13 BF_ counters was constructed. Over the spectral

range covered by the above sources the measured efficiency for counting neutrons of the final detector was 9.6 percent with an estimated un- certainty of ±0.5 percent, independent of spectrum. The detector was used to measure the neutron yields from Pb, Au, Ta, Ho, Ag, Cu, Co, Ca,

P, Al, and C for a series of bremsstrahlung energies between 12.0 and

29.0 MeV. These yields were compared with those calculated from pre- viously published neutron yield cross sections. The data indicate that previously reported discrepancies in neutron yield data can probably be traced to the determination of neutron detector efficiencies.

Key Words: Detector, efficiency, four-pi, Halpern, neutron, photoneutron, response, yields.

1. Introduction

The study of photonuclear interactions by measurements of photoneutron cross sections has

been very fruitful. This is primarily because the photoneutron cross section represents a large

percentage of the total absorption cross section; the percentage ranges from about 50% for the

light elements to about 90% for the heavier elements such as lead. Of almost equal importance,

however, is the fact that neutrons weakly interact with matter. This allows the use of thick targets

and compensates for the relatively low photon yield available from accelerators such as the betatron.

Unfortunately, the magnitude of the photoneutron cross sections, as measured in different

laboratories, show differences of as much as 30%. The problem may be due, in part at least, to the

detectors used to measure the photoneutron yields. The most commonly used system is a relatively

simple 4 tt neutron detector which moderates and then captures the neutrons emitted from the target.

It is possible that variations in the designs of these detectors resulting in non-uniform responses

as a function of neutron energy may have caused the discrepancies in the measured neutron cross

sections

Halpern, Mann and Nathans [1] were the first to design a 4tt neutron detector for use with

photoneutron experiments. Their system was designed on the basis of data by Rossi and Staub [2]

1 Figures in brackets indicate the literature references at the end of this paper.
which showed that for a BF. counter placed in the center of a large paraffin cube, it was possible

to choose a moderator thickness between the counter and a source, such that the counting efficiency

would be reasonably insensitive to neutron energy. The basic design of the Halpern detector

consisted of a BF counter embedded in a 2 ft x 2 ft x 3 ft paraffin block. The photon beam from

the betatron passed through a one-inch diameter beam tube running through the center of the

block parallel to the long dimension. The sample to be irradiated was placed at the center of

the beam tube. The neutrons from the target were moderated by 3.8 inches of paraffin before

being detected by counters mounted parallel to the beam tube. The axial separation of the source

and counters used by Halpern, Mann and Nathans was the same as that recommended by Rossi and

Staub but the intervening paraffin thickness was not the same due to differences in the counter

diameters. Apparently, Halpern, Mann and Nathans felt that the distance between the source and

counters was more important than the moderator thickness. Fast et al. [3] used the same sourcecounter axial separation but since even smaller BF. counters were used the intervening paraffin

thickness was 4.1 inches. Other experimenters have used various moderator spacings between the

target and counters. Spicer et^ al^. [4] used 5.1 inches of moderator. In a later experiment by

Baglin, Thompson and Spicer [5], the distance was changed to 3.9 inches of moderator. In a yet

later experiment by Allum, Crawley and Spicer [6], a moderator distance of 2.76 inches was used. At

all these distances, the detector was thought to have a detection efficiency independent of the

initial energy of the emitted photoneutrons.

Attempts [7,8] have been made to determine the ideal moderator distance for a Halpern-type

detector by using calculated or measured slow neutron flux distributions in paraffin produced

by neutron sources having different energy spectra. Data of this type usually apply to an ideal

geometry situation, i.e., point detectors at some distance from a point source. They are difficult

to apply to the design of a Halpern-type detector which has one or more long cylindrical counters

at some distance from a finite-sized neutron source or target. In these detectors the moderator

thickness is usually considerably less than the dimensions of the sensitive volume of the BF.

counters used. While the calculation of the detector response for a single geometrical arrangement

of beam tube and counter undoubtedly could be carried out using Monte Carlo techniques, the problem

of optimizing the geometrical arrangement to give a high efficiency which at the same time was

independent of neutron energy appeared to be quite formidable. It was, therefore, decided to

determine empirically the parameters influencing the response of a Halpern-type detector. On

the basis of these empirically determined data, a detector was designed to have an efficiency

insensitive to neutron energy. After calibration of the detector, it was then used to determine

a number of bremsstrahlung-produced neutron yields.
2. Experimental Detail

An experimental arrangement was designed so that the response of a BF_ counter could be

studied as a function of the amount of moderator between the counter and a beam tube containing

a source of neutrons. Beam tubes of various diameters could be used and the counter position could be

adjusted to keep the moderator thickness constant. Fig. 1 shows this arrangement. It consisted

of a large aluminum container through which a beam tube passed parallel to the long dimension.

Mineral oil was chosen over paraffin as a moderator because it allowed parameters to be changed

with a minimum of trouble. The results for either moderator should be the same as the hydrogencarbon ratio is the same and the difference in density is less than 3%. The neutron background

* was reduced by a 0.25 inch boral shield placed on the inside of the container walls. In addition,

a minimum thickness of 10 inches of borax surrounded the outside of the container.

A total of 13 counters was used in the measurements. They all had very similar characteristics

as is shown in Table 1 which gives the relative counts observed in each of the counters when

exposed to RaDBe(a,n) source under identical conditions of geometry, anode voltage, amplifier

gain, and discriminator bias. The rms deviation of the counts listed in Table 1 is 0.65% or only

twice the deviation expected if the counters were identical.

FRONT VIEW

VARIABLES

D = 2.25 INCHES 3.00 INCHES 4.00 INCHES

H |»l" ALUMINUM TUB

UU- 1/4" BORAL SHIELD

+-

19"

£-

TARGET

-15.7'

L

LEVEL OF OIL MODERATOR

I

~jr

ACTIVE COUNTER LENGTH l|

I j

-37-

BEAM

DIRECTI0N

SIDE VIEW

d = I, 2, 3, 4, 6 INCHES

I, 2, 3, 4, 6 INCHES

I, 2, 3, 4, 6 INCHES

Fig. 1. The experimental arrangement used to study the response of the BF, counters. The counters, of which only one is shown, were placed at various distances d from a beam tube having a diameter D; mineral oil moderator was used to fill the aluminum tub.

* Aluminum with a uniform dispersion of boron carbide crystals.

3
Table 1. Comparison of BF3 counters. The statistical

uncertainty (l/n)?, for any given counter, is of the order of 0.4$.

Counter Number Relative Counts

1181 1,241 2001 1,251 1997 1,240

RH526 1,226

2002 1,249 2167 1,235

2000 1,243

1178 1,247

1177 1,256

1179 1,248

1180 1,253

1999 1,239

TB542 1,246

The counters used in the arrangement had an active length of 15.7 inches and a diameter

of two inches. The filling pressure for the boron trifluoride was 70 cm of mercury and the boron

was enriched to greater than 90% in B. The anode voltage applied to the counters was 3500

volts with measured plateaus approximately 400 volts long. Fig. 2 shows a typical voltage plateau.

With a given source and beam tube diameter, measurements were made simultaneously for counters

distributed about the beam tube with five different thicknesses of moderator (d = 1,2,3,4, and

6 inches) between the tube and counter.

2500 3000 3500

VOLTS

4000

Fig. 2. The plateau for a typical BF3 counter.

4
Three different beam tube diameters were used: D = 2.25, 3.0, and 4.0 inches. The counters

at each moderator thickness were connected to separate counting channels. Each channel had one

counter except the channels for d = 4 inches and 6 inches which contained 2 and 3 counters,

respectively.

A block diagram of the electronics involved is shown in Fig. 3. A signal from a BF

3 counter,

in one of the five channels, was fed into a preamplifier and then into an amplifier and a discriminator.

The output pulse of the discriminator passed through a cathode follower to the experiment room.

If the pulse passed through the gate, it was recorded on the scalars as a count in one of the

BF counters at a given position of d. An oscilloscope was used to display the relative time

positions of the photon yield pulse, gate opening and closing, and the discriminator pulses due

to neutrons.

For all measurements a gate width of 700 jisec was used to decrease the background counts. With

the gate opening 10 |!sec before the yield pulse, 98% of the neutrons detected were counted.

AMPLIFIERS AND CATHODE

Dr 3 PREAMPLIFIERS DISCRIMINATORS FOLLOWERS COUNTERS

^}

COUNTER

ANODE VOLTAGE

A, I D,

A2 jD2

A,.D,

a4 ;d4

a. 1d f

BETATRON

EJECTION PULSE PHOTON YIELD PULSE

GATES SCALERS

GATE WIDTH CONTROL

DELAY |

MIXER

SCOPE

TRIGGER —^"NSCO

(Jdisf

PE PLAY

EXPERIMENT ROOM CONTROL ROOM

Fig. 3. Block diagram of the electronics. A total of five separate counting

channels was used.
This procedure was preferable to having the gate open after the yield pulse since in the latter

case uncertainties in the gate factor could be as high as 5%. This point is further discussed

in Section IV. Each counter close to the beam tube had its own counting system. This was done

to minimize yield pulse pile-up which could register as a false neutron count. In addition, care

was used to insure that the peak of the photon yield burst was always less than the discriminator bias at the highest yield rate used.

The amplifiers were a non-overloading type with a maximum possible gain of 9,000. Delay

line clipping was used at the input of the amplifier in order to obtain a well-shaped output

pulse. The discriminator bias was set by measuring integral discriminator curves and biasing

in a region of the counting plateau. Fig. 4 shows a typical integral discriminator curve.

400

300

200

(S>

8 100

i r

Q

i—r~r~i nn r

HIGH VOLTAGE: 3500 VOLTS

-O—Q—o—o—Q Q Q_

I I I 1

I I I

1

I I I I I I I I L 20 40 60 80

DISCRIMINATOR SETTING IN VOLTS

100

Fig. U. A typical integral discriminator curve for a BF3 counter.
The experimental arrangement is shown in Fig. 5. A photon beam, produced by a betatron, was

collimated by a brass plug in a lead and nickel shielding wall. The beam then passed through

the two lead collimators, a transmission monitor, and a final clean-up collimator, before striking

a target located in the beam tube of the neutron detector.

The transmission monitor was a thin-wall, multi-plate, air ionization chamber with a total

2 thickness of 5.66 g/cm of aluminum. The charge created in the chamber was collected on capacitor

plates. The voltage across the plates was measured with a vibrating reed electrometer. An absolute

determination of the beam intensity was made by measuring the ionization charge collected from

the transmission monitor and comparing it with the ionization charge collected from a standard NBS

chamber [9] . The standard chamber is calibrated so that a measurement of the ionization charge

collected during an x-ray exposure determined the total beam energy incident on the front face

of the chamber.

CONCRETE

, BORAX

Ni WALL

BETATRON

TARGET

Fig. 5. The experimental arrangement. For all measurements the photon beam

from the betatron was one inch in diameter at the sample position.

I

BEAM

DEFINING

APERTURE

The counter efficiencies were determined for the detection of neutrons from a calibrated

RaDBe(a,n) source and from three photoneutron sources made with bremsstrahlung . For the latter

sources the neutron spectra were changed by varying the peak energy in the bremsstrahlung spectrum.

The reactions used were: D(y,n)p, 0(y,n) 0, and P(Y» n) p > 210 210 210 Since in the decay of RaD(RaD -. Bi- Po) alpha particles are not emitted until Po is

reached, the (a,n) source was considered to have the same neutron energy spectrum as a PoBe(a,n) source.

7
Representative spectra [10] measured for PoBe(u,n) sources are shown in Fig. 6. The different

spectral shapes possibly result from variations in the geometry and construction techniques used

prepare the different sources.

>

<v \

cr3

1 1 1 1 1

1 -

-

II ^is —J

"'" —

Vv.

^§v S7^ — -

—

1 1 1 1 1 1

>fe —

5 ( c 12 NEUTRON ENERGY. MeV

Fig. 6. Measured neutron energy spectra of various PoBe(a,n) sources are obtained

from Ref. 10. The differences in the curves are assumed to be due to the methods

of measurement and variations in the construction of the sources. It is assumed

that the RaDBe(a,n) source used in this work has the same spectrum.

The energy spectrum for a photoneutron source depends on the photon (in this case bremsstrahlung)

spectrum, the photonuclear cross section, and the level scheme of the daughter nucleus. Fig. 7 shows

a typical bremsstrahlung spectrum as well as the cross section for the D(y,n)p reaction. The spectrum,

obtained from the Penf old-Leiss Tables [11] , is corrected for attenuation by both the betatron

doughnut wall and the transmission monitor. The cross section, obtained from a review article by

Fuller and Hayward [12], is that calculated by Hulthen and Nagel [13] at the low energies and de Swart

and Marshak [14] for energies above 10 MeV. In this particular case, where the reaction is strictly

a two-body breakup and the residual nucleus has no level structure, there is a one-to-one relationship

in the center-of-mass system between photon energy and neutron energy. For a thin deuterium target
Ld

COz

o

a.to

hi

rr

rrpo.20

3\ 0.10

COz

o1-o

I

0.

^CROSS SECTION for \ d ( y, n ) p

PEAK

PHOTON

ENERGY

30

2Qr-*0

10

CO

CO

COo

rro

8 12 16 PHOTON ENERGY, Me V

Fig. 7. The deuterium photodisintegration cross section and the incident

photon spectrum. These curves were folded together to give the neutron

spectrum from deuterium when operating the betatron at a peak bremsstrahlung energy of 19 MeV.

and a bremsstrahlung spectrum given by I(E,E )/E, the number of disintegrations by photons of

energy E in the photon interval dE is proportional to d,(E) I(E,E )dE/E where E is the peak bremsd o o strahlung energy and cSj(E) is the cross section for the D(y,n)p reaction. If the momentum transferred

by the photon is neglected, the normalized neutron energy spectrum is then given by:

2d,(E)l(E,E )dE

N(E ,E )dE = %

' ° "

E

J VE)-E^

(1)

dE

where the neutron energy is given by E = (E-2.22)/2. The calculated energy spectrum of the neutrons

for various peak bremsstrahlung energies is shown in Fig. 8. The spectrum of the RaDBe(a,n) source

is also shown for comparison.

The (Y,n) reaction in was picked as a photoneutron source to use both because the cross

section has a number of sharp peaks [15,16] .which would result in well-defined neutron energy

groups as well as because the daughter nucleus 0, had a convenient half-life so that the induced

radioactivity could be used to determine the absolute yield of neutrons. In this case, the (y ,n)

reaction also proceeds by a two-body breakup. However, only for photons having energies below the

threshold for the production of neutrons leaving in its first excited state is there a simple oneto-one relationship of photon energy to neutron energy.
Fig. 9 gives the total neutron yield cross section measured by Caldwell et al, [16]. Also

shown is the cross section for leaving in its ground state. This latter cross section, taken

from the work of Firk [17] , has been normalized to the total neutron yield cross section over

the photon energy range 20.5 - 21.5 MeV, i.e. near the threshold for transition to the 5.2 MeV

states in 0. (See energy level diagram at top of Fig. 9). Neutron counter efficiencies were

determined for the neutron spectra produced by 18.0, 19.0, 20.0, 21. A, 22.4 and 24.5 MeV bremsstrahlung

spectra. These peak energies are indicated by the arrows in Fig. 9.

>l.60

\

3.0 MeV

Ih

o

(X

hUJ

1.20

6.0 MeV

RaDBe SOURCE

4 6 8

NEUTRON ENERGY, MeV

Fig. 8. Neutron energy spectra from a thin deuterium target. These curves were

calculated for peak bremsstrahlung energies of 3.0, 6.0, 10.0, and 19.0 MeV. Also shown is the neutron spectrum from a RaDBe(a,n) source which was obtained

by drawing a smooth curve through the data shown in Fig. 6.

Representative spectra of the photoneutrons from the oxygen source are given in Figs. 10,

11 and 12. The spectra in Figs. 10 and 11, where the peak bremsstrahlung energy is effectively

2.5 below the threshold for the emission of neutrons leaving in the 5.2 MeV states, were calculated

in the same way as those for the deuterium source. The spectrum produced by 27 MeV bremsstrahlung

given in Fig. 12 is that measured by Firk [17].

31 30 The reaction P(y,n) P was chosen as a photoneutron source primarily because of its convenient

half-life which made the determination of an absolute efficiency possible. In addition, it had been

used for some of the original checks on the response of the Halpern-type detector. Neither detailed

cross section nor neutron spectral data are available for energies up to the (y, 2n) threshold. As a

10
30 result of the relatively high level density of P, it can probably be assumed that the spectrum

is considerably softer than that of 0.

The neutron emission rate of the RaDBe(a ,n) source was determined in the NBS graphite pile

by comparison with a secondary standard PuBe(a ,n) source. The PuBe(a,n) source had been calibrated

by comparison with the primary standard RaDBe(y,n) source, NBS-1, in the NBS manganese sulfate bath.

The size and description of the various sources used are given in Table 2.

15

( 3 5 i> 10 ENERGY LEVEL DIAGRAM FOR

NORMALIZED

GROUND STATE CR0SS_

SECTION OF FIRK MEASURED TOTAL NEUTRON

CROSS SECTION OF CALDWELL

et ol, SHIFTED 150 kV INDICATES PEAK BREMSSTRAHLUNG I ENERGIES USED IN THIS EXPERIMENT T

18 20

PHOTON ENERGY,

22

M eV

24 26

Fig. 9. Total neutron production cross section of 16 and the cross section for

the production of neutrons leaving 15 in its ground state. The difference

between the two gives the cross section for leaving 16 in one of the excited

states.

11
.0 2.0 3.0

NEUTRON ENERGY, M e V

Fig. 10. Calculated neutron energy spectrum from 16 for a peak bremsstrahlung

energy of 18.0 MeV. This was obtained by folding the cross section for leaving the 15 nucleus in the ground state with the filtered bremsstrahlung

spectrum having a peak energy of 18.0 MeV.

An absolute detector efficiency, using the d(y,n)p source, was obtained from the ratio of

the measured neutron yield to the yield calculated from the known photodisintegration cross section,

bremsstrahlung spectrum and an absolute measurement of the intensity of the bremsstrahlung beam.

The efficiency of the neutron counters is then given by:

Y(E

o

) f°x( E , Eo )dE

:(E ) r o

ntp

J d d

(j l(E,E

r r—

lit

(2)

dE

where I(E,E )/E, ,(E) , E and E are the same as defined earlier; Y(E ) is the measured neutron

o a o o

2 yield in terms of the total energy in the beam; n is the number of target nuclei/cm ; [1-exp (-|it) ] /|it

12
2 4

NEUTRON ENERGY, M eV

Fig. 11. Calculated neutron energy spectrum from 16 for a peak bremsstrahlung

energy of 21.4- MeV. See caption of Fig. 10 for details.

is the correction factor used to obtain the effective target thickness; ^ is the photon attenuation

2 2 coefficient in cm /g ; t is the target thickness in g/cm ; and m is the gate factor or the ratio

of neutrons counted with a gate to neutrons counted without a gate. It was realized that the counter

efficiency also depended on the extent of neutron moderation and absorption occurring in the

targets themselves. This is discussed further in Section V.

The detector efficiency for the and P sources was determined from the ratio of the neutron

counting rate to the neutron production rate resulting from a constant betatron output.

13
4 6 8

NEUTRON ENERGY, M e

V

10 12

Fig. 12. The measured photoneutron spectrum from 1 6 produced by 27 MeV bremsst rah lung. Due to uncertainties in the response function of the detector used in these measurements

the spectrum shape below about 2 MeV is in some doubt.

The absolute neutron production rate for each run was determined from a measurement of the absolute

positron disintegration rate of the sample bombarded. Each run was monitored in terms of the

equilibrium voltage developed across a "leaky" capacitor that was charged by the ionization current

from the transmission monitor. The plates of the capacitor were shorted through a resistor whose

value was chosen such that the RC time constant of the monitoring circuit was equal to the mean

life for decay of the positron activity induced in the samples by the (y,n) reaction.

A schematic diagram of the time sequence used for absolute calibration of the and P

sources is shown in Fig. 13. The beam was turned on at t and the sample irradiated until an

equilibrium decay rate I was reached at t.. A total neutron count, N, was then recorded in the

period from t. to t_ . The irradiation was stopped at t~ and the sample placed in a Nal(Tl) well

crystal calibrated for absolute positron counting. Between t, and t,- a total positron count, 7],

was measured. This positron count is given by:

14
u e(p+)l (E ) _ , 4 - e-^sl

(3)

where g (j3+) is the positron detection efficiency of the Nal crystal and X is the positron decay

constant of the target. The total number of neutrons detected by the neutron counters in the

time interval t„ - t

1 is:

N(E

q

) = cpe (E

o

)l

c (t

s

- t

x (4)

where e (E ) is the efficiency of the neutron counters and cp is the gate factor. Using Equation 3 in

Equation 4, e(E ) is given by:

s(3+)N(E

o

) -\t4 e -\t

«<V = M(Eo

) L t

3

- t, J

(5)

Typical values for the parameters and constants are shown in Table 3.

NEUTRON

COUNTERS

ON

t3 BEAM

NEUTRON 0FF

COUNTERS

OFF

POSITRON

COUNTER

ON

t 5

POSITRON

COUNTER

OFF

Fig. 13. Schematic of the time sequence used for the calibration of the 3l P and 1S sources. N is the total neutron counts recorded by the scalers in the time interval

t

p

- 1, and 1\ is the total positron counts recorded by the positron counter in the

15
Table 2. Size and description of sources used for calibration of the neutron detector

Source

Absolute Calibration

Diameter Length Description

(inches) (inches)

Relative Calibration

Diameter Length Description

(inches) (inches)

d(y,n)p 2.0 2.75, 2.00,

1.00, 0.50, & 0.20

Ds contained

in thin-wall

aluminum cylinders

2.0 2.75 D

a contained

in a thin- wall aluminum cylinder

160( Y

,n) 15 0.58 0.88 H

s contained

in a thin-wall

plastic cylinder

0.65 2.75 HO contained

in a thin-wall

plastic cylinder

31 P( Y,n)

3 °P 0*58 0.88 Red phosphorous

contained in a thin-wall plastic cylinder

0.65 2.75 Red phosphorous contained

in a thin-wall

plastic cylinder

RaDBe(a,n) 0.35 0.35 RaDBe(a,n)

sealed in a metal cylinder

The peak photon energy produced by the betatron was controlled by a system [18] based on the determination of the average magnetic field In the vicinity of the electron orbit at the instant of x-ray

production. The field was sampled by a search coil whose signal was proportional to the time rate

of change of field. The signal was integrated and the integrator output was a voltage analog of the

field, i.e., proportional to the electron's momentum. A discriminator was set to fire when this

Table 3. Typical values for the constants and parameters

used to obtain the neutron counter efficiencies.

Parameter or Constant Value

\( 1S source) 5.634 x 10" (sec) "i h - \ . 10.0 min

£ (6+

) 0.83

C

B

" t 4 260 sec

t

4

- h 20 sec

V 0.98

16
voltage reached a predetermined value. The ejection pulse to the expander coils of the betatron was

timed manually such that the betatron yield pulse and discriminator pulse from the integrator were

coincident in time; this condition insured that x-ray production occurred at the predetermined

magnetic field value.

The energy calibration of the betatron was based on (y,n) reaction thresholds and positions of

peaks in the 0(y,n) cross section. An analysis of the calibration indicated that the standard

deviation for the peak bremsstrahlung energy was less than 1% for all energies above 8 MeV. From the

reproducibility of the counting rate it has been estimated that the betatron energy can be reset and

maintained within 60 keV at 20 MeV [19].

4. Counter Efficiencies

The sources described in the previous section were used to determine the efficiency of a BF,

counter placed in various geometries in the moderator container shown in Fig. 1. Measurements were

made with a moderator thickness (d) of 1, 2, 3, 4, and 6 inches and with beam tube diameters (D) of

2.25, 3.00, and 4.0 inches. In the following section only the results obtained with D = 2.25 inches

will be described in detail. A brief description is also given of the effects of neighboring counters

and voids in the moderating bath.

The efficiency per counter for detecting the spectrum of neutrons resulting from the d(y,n)p

reaction is given in Fig. 14 and Table 4 as a function of both the counter position in the moderating

bath and the peak bremsstrahlung energy. While the two highest energy points plotted in Fig. 14 are

above the 0(y,n) threshold the magnitude of the bremsstrahlung weighted yield from this reaction

is negligible compared with that from the deuteron reaction at these energies. The bar on each

of the d(y,n)p points is the expected rms deviation due to uncertainties in the gate factor, the

2 number of nuclei/cm , the calibration of the betatron energy, the absolute calibration of the

photon beam intensity, the shape of the photon spectra, and the number of counts observed. There is

an additional factor of ± 10% in all of these efficiencies arising from the uncertainty in the

magnitude of the d(y,n)p cross section. These data have been corrected for the finite thickness

of the D„0 target by assuming that only a part of the Compton cross section was effective in removing

photons from the bremsstrahlung beam. (See discussion on thick target effects in Section V).

The efficiencies indicated by the black dots to the right of Fig. 14 were determined with the

RaDBe(a,n) source. These cannot be compared directly with the data obtained with the D.O source since

no corrections have been made for the absorption of neutrons in the large volume of the D.O source.

As an indication of the magnitude of this ef feet , when the RaDBe(a,n) source was mounted in the

center of the DO container the counting rate observed when the container was full of D_0 or H.O

was 0.93 times that observed when the container was empty. This measurement was made with 4 inches

of moderator separating the counter from the beam hole. Note that with this sort of correction

17
applied to the data in Fig. 14, the efficiency of the counter with 4 inches of moderator is roughly

insensitive to the spectrum emitted by the source. It should also be noted that the ratio of the

efficiencies determined with the D„0 and RaDBe(a,n) neutron sources is by no means independent of

moderator thickness. This ratio gives, for a given moderator thickness, the magnitude of the factor

by which photoneutron cross sections could be in error if the photoneutron spectra being detected

differed markedly from the spectrum of the source used to calibrate the detector.

10

Ld

o

o

orLd>

o

z:

Ldo

U_

L.Ld

Ld

O

(/) CD<

.0

0.

1 1 i

1

1 1 1 Id

i i i 1

i 2.25 INCHES

: f.

o d( y, n)p SOURCE

• Ra DBe(a,n)S0URCE — o o —

K>

o o o o

d.-r —

o

o o

o o o

d = 2"

<

" \° o o o o o

° d = 3"

n

- T o o

o o o d = 4" n : }

f

o —

— —ii —

o

o o

d = 6" o —

o

o

i

( f ,

1 1 1

1 1 1

| 8 16 24

PEAK PHOTON ENERGY, M e V

Fig. U. Measured neutron counter efficiencies for the d(y,n)p source as the peak photon energy is varied. Except where bars are shown, the uncertainties in the measurements

are equal to or less than the size of the circles. The measurements were made with a beam tube diameter of 2.25 inches. These data have been corrected for the finite thick- ness of the D

? target by assuming that only a part of the Compton cross section was effective in removing photons from the bremsst rah lung beam.

18
Table 4. Neutron counter efficiencies for the d(y,n)p source. The efficiencies as measured with

the RaDBe(a,n) source are also shown. No correction has been made for the finite thickness of

the target. The statistical uncertainties (N"p) only are indicated for each measurement.

Bea

Dia

(

u Tube Peak

meter, D. Photon

i u \ Energy, inches) „ ' MeV

Counter Efficiency, o/o

Moderator Thickness, d

1.0 inches 2.0 inches 3.0 inches 4.0 inches 6.0 inches

2 .25 (RaDBe) 2.59±0.01 1.84±0.07 1.25±0.05 0.84±0.04 0.39±0.02

19 4.. 14- 0.02 2.35 0.02 1.45 0.01 0.77 0.01 0.25 0.002

16 4.24 0.03 2.45 0.02 1.47 0.01 0.75 0.01 0.23 0.002

13 4.35 0.04 2.54 0.03 1.48 0.01 0.76 0.01 0.22 0.003

' 10 4.45 0.04 2.84 0.03 1.45 0.01 0.73 0.01 0.21 0.002

8 4.91 0.05 2.74 0.03 1.52 0.02 0.72 0.01 0.19 0.003

6 5.35 0.10 2.89 0.06 1.53 0.03 0.68 0.01 0.16 0.004

4 6.24 0.23 3.30 0.13 1.59 0.06 0.67 0.03 0.11 0.007

3 7.22 0.59 3.61 0.30 1.53 0.14 0.66 0.06 0.10 0.03

3 .0 (RaDBe) 2.19±0.09 1.67±0.07 1.12±0.05 0.76±0.03 0.35±0.014

19 3.50 0.06 2.19 0.04 1.28 0.02 0.69 0.01 0.23 0.004

16 3.51 0.06 2.20 0.04 1.27 0.02 0.67 0.01 0.22 0.004

13 3.61 0.06 2.27 0.04 1.30 0.02 0.67 0.01 0.21 0.004

10 3.70 0.06 2.30 0.04 1.28 0.02 0.64 0.01 0.19 0.004

8 4.07 0.07 2.45 0.04 1.33 0.03 0.65 0.01 0.17 0.003

6 4.38 0.10 2.56 0.06 1.31 0.03 0.59 0.01 0.14 0.003

4 5.17 0.20 2.86 0.10 1.35 0.05 0.58 0.02 0.11 0.008

3 5.58 0.78 3.17 0.44 1.31 0.20 0.53 0.08 0.0960.031

4 .0 (RaDBe) 1.75±0.07 1.41±0.06 0.99±0.04 0.68±0.03 0.31±0.012

19 2.95 0.03 1.85 0.03 1.11 0.02 0.61 0.01 0.21 0.006

16 3.02 0.05 1.86 0.04 1.12 0.02 0.60 0.01 0.20 0.004

13 2.95 0.06 1.93 0.04 1.13 0.02 0.61 0.01 0.18 0.004

10 2.97 0.05 1.97 0.03 1.12 0.02 0.58 0.01 0.16 0.003

8 3.21 0.07 2.10 0.04 1.16 0.02 0.58 0.01 0.15 0.003

6 3.68 0.09 2.15 0.05 1.14 0.03 0.53 0.01 0.12 0.003

4 4.36 0.17 2.53 0.10 1.21 0.05 0.51 0.02 0.092 0.005

3 4.65 0.65 2.69 1.08 0.15 0.15 0.48 0.07 0.051 0.008

The neutron counter efficiencies for the 0(y,n) source are plotted as a function of peak

bremsstrahlung energy in Fig. 15. The bar shown on each point for the 0(y,n) source represents

the rms deviation expected as a result of the number of counts observed. The relative data plotted

in Fig. 15 were all obtained with the large size water sample listed in Table 2. The points taken

with the RaDBe(a,n) source have been normalized to the data taken with the oxygen sample for a

moderator thickness of 4 inches. Note that in this case, in contrast with Fig. 14, the ratio of the

efficiency determined at the higher bremsstrahlung energies to that determined with the RaDBe(a.n)

source is independent of the amount of moderator between the beam tube and the counter. This is to

be expected since the neutron energy spectra of the two sources are similar.

31 30 The relative neutron counter efficiencies for the P(y,n) P source are plotted versus peak

bremsstrahlung energy in Fig. 16. The bar, as shown on each point, is the standard deviation due

to uncertainties in the counting statistics as only a relative comparison is made. The general shape

of the plots are more like those measured for the d(y,n)p source but show less change in the

19
efficiency as the bremsstrahlung energy is varied. This indicates that the spectra are reasonably

soft and do not change their average energy as the peak bremsstrahlung energy is changed. Note that

again the ratio of the efficiency determined with the phosphorous source to that determined with

the RaDBe(a,n) source is strongly dependent on moderator thickness.

The general features indicated in Figs. 14-16 for the dependance of counter efficiency on neutron

spectral shape and moderator thickness were the same when measurements were carried out with beam

tube dimensions of 3.0 and 4.0 inches. IU

1 r 1 1 1 1 D= 2.25 INCHES

o

,60(y,n)l5 SOURCE —

• RaDBe (a,n) SOURCE — i __ 5

n 1

§

w

5

° Q d=l" 1

1

>- 5

w o

2 t Q

° d = 2" -11 o §

U- i o d=3" » Ld

cc 1.0 Ld ir

§ 5 5

O ° Q d=4" t 1-

-z. | z> — o

o —

Ld — >

I 5 I a

q d=6"

< Y

_l

Ld 1 $

cr c>

—

0.1 ,

,

, 20 24 28

PEAK PHOTON ENERGY, M e V

32

Fig. 15. Relative counter efficiencies for the 160(Y

,n)is source as the peak photon energy is varied. The solid points are the measured counter efficiencies for the RaDBe(a,n) source. The two sets of data have been normalized together for a modera- tor thickness of 4. inches.

20
Neutron time distributions from lead and D_0 targets were measured to determine if the gate

factor (ratio of neutrons counted with a gate to neutrons counted without a gate) could in any

way be influenced by the neutron spectra being measured. A beam tube diameter of 3.0 inches was

used for the measurements made with the lead target at a peak bremsstrahlung energy of 18.0 MeV

as well as for the D„0 target at peak bremsstrahlung energies of 19.0 and 8.0 MeV. A beam tube

diameter of 4.0 inches was also used with the D.O target at a peak bremsstrahlung energy of 19.0

MeV. These data were consistent with those obtained with the smaller beam tube.

>-O

-z. UJO

Z)O

o

UJ>

or

10

i

5

}

§

D= 2.25 INCHES

31 P SOURCE

RaDBe (a.n)SOURCE

ad = i

O d=2

O d=3

Qd= 4

i

14 16 18 PEAK PHOTON ENERGY, MeV

o d = 6"

20

Fig. 16. Measured relative neutron counter efficiencies for the 31 p(v n) 3 °P source as the peak photon energy is varied. Data obtained with the RaDBe(a,n) source (indicated by solid circles) are normalized to the phos- phorous data for a moderator thickness of 4 inches.

21
10 LEAD TARGET ' E = I 8 M e V

D = 3.0 INCHES.

200 400 600

TIME AFTER EJECTION, ft sec

Fig. 17

10

if) \-

-z. 3

O

o

o

tr

IDUJ

<

I-O

li. o

o

<

tr 0.

-Ill I 1 1 —

D 2 TARGET —

1 Eo = 19 MeV —

D = 3.0 INCHES —

—

— ^^d =6 —

—

>v

d=^\V —

d = \

/CENTER OF YIELD PULSE

|

| 200 400 600

TIME AFTER EJECTION, ^sec

Fig. 18

Figs. 17 & 18. Neutron time distribution. See discussion in text.

22
Measurements were made by opening a gate, of a given width, at time intervals determined by

a time marker generator triggered at zero time by the betatron ejection pulse. A gate with a width

of approximately 10 U sec was positioned every 10 ^isec for the first 100 |j.sec after the ejection

pulse, a gate having a width of approximately 20 ^tsec was positioned every 20 \isec for the next

100 Usee, and a gate having a width of 100 p.sec was positioned every 100 (isec for the time interval between 200 to 700 (isec. The data were recorded in counts per unit monitor response for a given

gate width. The ungated counts per unit monitor response was then measured to obtain the fraction

of total neutrons counted for a given gate width. The gate widths were determined by measuring at a

known gate repetition rate the ratio of gated to ungated neutron counts from a RaDBe source. Using

the measured gate widths, the fraction of total neutrons counted per [isec was then determined.

The data obtained from the measurements, in units of fraction of total neutrons counted per (isec,

are plotted in Figs. 17-22. The beam pulse for these measurements had a rounded top and was about

15 M-sec wide at the base. Figs. 17-19 are semilog plots giving the entire time distribution from zero

to 700 Usee. Figs. 20-22 are linear plots showing the initial rise of the neutron counting rate.

For clarity the individual data points are not given in these graphs. The smooth curves represent

"best fits by eye" to the actual points. Statistical uncertainties (N *) were of the order of 2% for

each point.

Although interpretation of the curves is made difficult because of poor geometry in the experiment, some general observations pertaining to their applications with the neutron detector can be

made. The data in Figs. 17-19 which show the logarithmic decay of neutrons with time, can be fitted

with essentially a straight line although the plots in general are convex downwards for a moderator

thickness less than 4 inches and convex upwards for a moderator thickness greater than 4 inches.

This effect has been observed before [20] . From these plots the half-life for the absorption of

neutrons with time is found to be approximately 137 p.sec for the counters with a moderator thickness of

A inches. The counters with less moderator have a slightly shorter half-life for absorption while

those counters with more moderator have a slightly longer half-life.

The time distribution of neutrons in Figs. 20-22 vary in both shape and magnitude depending upon

the target, the peak bremsstrahlung energy and the moderator thickness d. A neutron counting system

using a long gate (approximately 700 pisec) , opening 20 (isec after the yield pulse, will be sensitive

to these variations in the time distributions. As much as a 5% difference in the gate factor is

obtained between the counters with one and 6 inches of moderator using a D„0 target and a peak

bremsstrahlung energy of 8.0 MeV; similar variations in the gate factor are found as the targets and

peak bremsstrahlung energies are changed. This is understood by considering the time distributions

in Figs. 20-22; the number of neutrons not counted by the gate is essentially the area under the

curves from zero time to the time of the opening of the gate. Changes in these areas are reflected

23
10 'O D2 TARGET

E = 8.0 MeV

D = 3.0 INCHES

200 400

TIME AFTER EJECTION, ^sec

Fig. 19. Neutron time distribution. See discussion in text.

as changes in the gate factor. When gating after the yield pulse, the gating factor is particularly

sensitive to small shifts in the gate opening since the fractional number of neutrons per |isec

after the yield pulse is a maximum.

The influence of one counter on another counter in the oil bath was studied, using a RaDBe(a,n)

source, in the geometry shown in Fig. 23. The neutron source was placed half-way down the beam

tube but slightly below the beam tube axis. A counter, designated as A and shown in Fig. 24, was

placed in a stationary position parallel to the beam tube such that there were 6 inches of oil

moderator between it and the source. The neutron counting rate was recorded in A as a second counter

designated as B, was paraded in a plane parallel to the tub wall on either side of A. The result

of these measurements are given in Fig. 24; the value given at A was the counting rate of A when

B was out of the moderator and the values given at various positions of B were the counting rates

of A when B was in one of the given positions. The counting rate of A increased when B was between

the source and A because B replaced mineral oil which would normally absorb neutrons. The counting

rate of A was found to decrease for measurements made with B between A and the tub wall because the

presence of B now meant the removal of oil which would normally scatter neutrons back to the counter.

24
'O6.0

o

4)

</»

(/) h-4.5 Z

3

O

o

o

criUJz

4.(

<

I-O

1.5 O

<

cr

LEAD TARGET

E = 18 MeV

D=3.0 INCHES

50 100 150 TIME AFTER EJECTION, ^sec

Fig. 20.

•O

x 6.0

in

Z> 4.5J O

o

cr

<

o

LlO

o

<

d=l

D 2 TARGET

E = 19 MeV

D =3.0 INCHES

50 100 150 TIME AFTER EJECTION, ^sec

Fig. 21. Figs. 20 & 21. Neutron time distribution on a linear scale.

See discussion in text.

25
D 2 TARGET

E = 8 MeV

D = 3.0 INCHES

50 100 TIME AFTER EJECTION, ^sec50

Fig. 22. Linear plot of the time distribution shown in Fig. 19. See discussion in text.

These effects were the greatest when B was in the plane determined by A and the source. These data

indicate that counters of these dimensions (2-inch diameter, 15.7-inch active length) can be considered

to respond independently of each other if there is at least 1 inch of moderator between adjacent

counters arranged such that one is above or below the other (See Fig. 24). Further data, shown

in Fig. 25, indicate a similar response if there are at least 2 inches of moderator between adjacent

counters arranged such that one is in the shadow of the other.

The spacial distributions of neutrons within the moderator bath were measured by counting

neutrons with a BF. counter at various positions in the tub. The experimental geometry and the

position of the RaDBe(a,n) source was the same as that shown in Fig. 23. Although the geometry

was far from ideal for this type of experiment, some indication of the counting rate decrease with

moderator thickness was obtained and is shown in Fig. 26 where the numerical values given are the

counting rates recorded by the counter at the given positions. A plot of the data taken in the

horizontal plane through the axis of the beam tube decreased approximately exponentially. (See

Fig. 27.)

26
3 INCH

DIAM. TUBE

BEAM

FRONT SECTION SIDE SECTION

Fig. 23. Geometry used to study the influence of one counter on another counter.

24

20 'source r

COUNTER A

I _ V

218 o

214 o

21 I o 205 o

1204 o

>202°

21 I o 214 o

N ,-COUNTER B r

o 219 o 214 o 218 o 219 •

o 219 o 220

216 o - V J

POSITIONS OF COUNTER B

I

O 4 R I?

BORAL-^y ALUMINUM ^TUB

V

V

8 INCHES

Fig. 24. Fig. 25.

Figs. 24 & 25. Influence of neighboring counters on the response of a fixed counter.

27
24

20

COUNTS/UNIT TIME

413 183 J 501 219 84 33 13

(/) J^w-T SOURCE x ?' O 16

o

UJa

o

5

O

I

hQ.UJa 4 B0RAL7^,\

*?.

°k < ««^k\'«,< ,' < si8vw- a\ v ^^ INCHES

SS^J

'ALUMINUM TUB

20

UJ

1- 10 <

(T 8 O

?

b

h-^

n>Oo 4

1.0 4.0 8D MODERATOR THICKNESS, INCHES

Fig. 26. The spacial distribution of neutrons

from a RaDBe(a,n) source.

Fig. 27. Neutron counting rate versus modera- tor thickness as measured with the RaDBe(a,n)

source. The data are from Fig. 26 taken in

a horizontal plane through the axis of the beam tube.

Shielding of the neutron counters against neutrons produced by cosmic rays, an adjacent

synchrotron, and the betatron itself was accomplished, as mentioned in Section II, by using both

boral and borax shielding. The mineral oil itself also acted as a very good shield. Fig. 28

shows that for a BF, counter placed below 4 inches of oil, the background counting rate was reduced

a factor of 10 of that with the counter at the surface of the oil. A combination of boral, borated

paraffin, and paraffin placed around the aluminum moderator container was found to reduce the

background anywhere from a factor of 2 to 5, depending on the depth of the counters in the mineral

oil moderator.

28
1 !

1 1 1

10 E" "IE

V —

1.0 —

=

OIL LEVEL AT COUNTER CENTER. —

___J^o_____ p'si T

0.1 cr_ r-^r_

" Z-Z 1 ~ — ""— —~-— =:

~~ ~z ~ — ^ ^- - —

—

OIL LEVEL BELOW COUNTER OIL LEVEL ABOVE COUNTER CENTER CENTER

.01 1

1 1

1

1 -12 -8 -4 4 8 12 16 OIL LEVEL RELATIVE TO BF 3 COUNTER CENTER, INCHES

Fig. 28. Background counting rate versus oil moderator level,

5. Attenuation and Moderation in Samples

In order to determine the absolute yield per nucleus from measurements made of the neutron

yield from samples of finite dimensions, it was necessary to make corrections for the effects that

can take place in the samples themselves. The most important of these were: (1) the attenuation

of the bremsstrahlung beam as it passes through the sample and (2) the moderation and absorption

of the photoneutrons in the sample. These effects can be particularly important when the yields

are measured for thick samples of low atomic weight materials.

2 For a bremsstrahlung spectrum given by I(E,E )dE/E, the number of neutrons counted per nucleus/cm

in the photon beam is given by:

<£ 0. I(E,E ) Y(E

o

) = « M(E

o

,t)

J ° ^-

2_ T(E>t)dE

(6)

1 - e U.(E)f

T(E,t)

(i(E)t

29
where o = d(y,n) + d(y,+n) + 2d(y,2n) + is the neutron production cross

section, T(E,t) is a correction for the attenuation of the photon beam in the sample of thickness

t, |i(E) is the photon attenuation coefficient, e is the mean neutron detection efficiency and M(E ,t)

is a function to correct e for the moderation and absorption of the neutrons in the sample. For

reasonably thin samples and for the heavier nuclei the function T(E,t) is essentially independent

of the photon energy E. It can be removed from under the integral sign and evaluated at the mean

photon energy absorbed by the nucleus. In the case of the calculated deuterium yields the dependence

of T(E) on E was explicitly taken into account. For all other samples the dependence of T on the

photon energy was negligible (less than 3% between the (y,n) thresholds and the peak bremsstrahlung

energies used)

.

(a) D 2

1.10

1.00

9

0.90 — B E =l8.3MeV 80 1 1 "

1.20

1. 10

1.00

0.90

(c) CARBON

D E n

= 21.2 MeV

1

' ' ' ' ' I > > ' ' Z E =26.2 MeV

2.0 3.0 4.0 5£> THICKNESS, grams/cm 2 6P 7.0 8.0

Fig. 29. Comparison of calculated and measured neutron yields per unit target thickness versus

target thickness. The data have been arbitrarily normalized such that the extrapolated yield

at zero target thickness is approximately equal to one. The two curves indicated in each sub- figure represent the calculated yields using the total attenuation coefficient in Eq. 6 (lower

curve) and that obtained calculated assuming that the Compton cross section did not contribute

to the photon attenuation coefficient (upper curve). The diameter of the Dp and H

g targets

was 2.0 inches while that of the carbon target was 1.75 inches.

For most of the nuclei studied the (y,n) thresholds are high and the total photon attenuation

coefficient (Compton scattering plus pair production cross sections) is the proper quantity to use

for U(E) . This is not the case for the D.O samples where Compton scattering is the dominant factor

in the attenuation coefficient. Since this cross section is strongly peaked in the forward direction

and since many of the scattered photons have energies above the (y,n) threshold in deuterium, only

30
a fraction of the total attenuation coefficient is effective in removing photons from the incident

beam (for 10 MeV photons only about 50% of the scattered photons have energies below 2.2 MeV)

.

For the light nuclei the absolute neutron yield (neutrons per MeV of beam energy per nucleus

2 per cm ) was determined from an extrapolation to zero target thickness of the measured yields per

unit thickness. The results of these measurements for targets of DO, H„0, and carbon, using various

bremsstrahlung energies, are shown in Fig. 29. In all cases, the data have been arbitrarily normalized

such that the extrapolated yield at zero target thickness is approximately equal to one. The two

curves indicated in each subfigure represent the calculated yields using the total attenuation coefficient in Eq. 6 (lower curve) and that obtained assuming that the Compton cross section did not

contribute to the photon attenuation coefficient (upper curve)

.

If neutron moderation and absorption effects were not occurring the experimental points for

the DO data should fall somewhere between the two solid lines in Fig. 29-a. The point calculated

2 for a target 7.76 g/cm thick is 0.92 if only that part of the Compton cross section that results in

scattered photons with energies below 2.2 MeV is used in |J.(E) . The difference between the experimental value and the expected value represents the effects of moderation and absorption occurring in

the DO target.

Both the direction and magnitude of this moderation effect are consistent with results obtained

when the RaDBe(u,n) source was placed in a cell containing either D.O and H_0. For the H„0 data,

shown in Fig. 29-b, the experimental points should be compared with the lower curve since even the

highest energy photon used when scattered through an angle greater than 10 degrees loses enough

energy to be below the (y,n) threshold in 0. The data obtained with the lower energy bremsstrahlung

spectra indicate that the moderation effect is strongly dependent on the neutron spectrum. This

correction would probably not affect the shape of the curve in Fig. 15 appreciably since the H„0

source used was relatively thin in. a direction perpendicular to the bremsstrahlung beam. On the

other hand, the correction could effect the data for low energies plotted in Fig. 14 appreciably

since the diameter of the D„0 sample was the same as that used for these measurements. The shapes

of curve indicated by the data points in Fig. 14 should therefore only be considered to give a qualitative indication of how the efficiency varies with neutron spectrum shape.

The measurements using a carbon target are shown in Fig. 29-c. As in the case of the

measurements, the experimental points should be compared with the lower curve as almost all the

photons that Compton scatter will have their energy reduced below the (y» n ) threshold. The data

taken at 21.2 MeV are above this curve and are inconsistent with the measurements made with other

samples. The cause of this discrepancy is not understood. It may be connected with the low (y,n)

13 and (n,2n) thresholds In C. At E = 21.2 MeV, a large fraction of the neutrons from a carbon sample

13 are due to the C(y,n) reaction. In any event, the effect points out the need for caution in

31
analyzing data obtained using thick targets in a Halpern-type detector.

Similar measurements were made with aluminum, silver, and gold targets. As was expected, the

measured yield curves agreed with those calculated using the total photon attenuation coefficient.

6. Final Detector and Determination of Absolute Yields

Based on the previous measurements, a final detector was constructed in order to determine

a number of absolute neutron yields. This detector had a moderator thickness (d) of 4 inches between

the counters and a beam tube diameter (D) of 3 inches. Thirteen BF_ counters were arranged on

the circumference of a circle around the beam tube center such that there was a spacing of one

inch between adjacent counters. The electronic and counting arrangements were essentially the

same as that described in Section II.

The absolute efficiency of this detector was determined as a function of neutron source. The

d(y,n)p, 0(y,n) 0, P(y,n) P, and RaDBe(a,n) sources were used to make the measurements;

these sources are described in Section III and their dimensions are given in Table 2. Except for

target thickness corrections, the measurements were carried out as previously described. Because

of its small dimensions, it was not felt necessary to make any corrections for finite sample

size in the measurements made to determine the neutron detection efficiency with the 0(y,n)

reaction. It was necessary to make these corrections in the latter measurements made with the

larger samples to determine the absolute photoneutron yield. The uncertainties in the measurements

are listed in Table 5.

Table 5. Uncertainty in the factors used to obtain

the neutron detector efficiency.

Target

RAr.TDR 31p D

s°

is 16 RaDBe(a,n)

E

o

17.4. MeV

18.3 MeV21.4 MeV

24.5 MeV Counting statistics 1.1$ 0.3$ 2.8$ 2.2$ 0.4$

Gate 0.6$ 0.6$ 0.6$ 0.6$ - Target purity - 0.5$ - - - Extrapolation for zero thick target yield - 2.0$ . - - Monitor calibration - 1.1$ - - - Calibration of betatron

energy scale - 0.32$ - - Photon spectrum shape - 1$ - - - Cross section - 10$ - - - Well crystal efficiency 3.2$ - 3.2$ 3.2$ - Decay constants 0.5$ - 0.3$ 0.3$ - Source strength - - - - 3.75$

Final estimated uncertainty 3.5$ 10.3$ 4.3$ 3.9$ 3.8$

32
The uncertainty in the extrapolation to obtain the absolute neutron yield at zero target

thickness was obtained from estimating the highest and lowest yield value obtained with different

extrapolations consistent with the measured points. Uncertainties in the calibration of the

well crystal are described in a later section. The influence of uncertainties in the photon spectral

shape on the determination of the D_0 efficiency were estimated by calculating the efficiency

using the spectrum for zero angle [22] and comparing it with the result obtained with the integrated

over the angle spectrum [11]. The difference in efficiency, which probably represents an extreme,

was found to be less than 1% at 16.0 MeV. The final results of the detector calibration are

shown in Fig. 30. The sources used in the final calibration can be divided into two groups: High

energy RaDBe( a,n) and 0(y,n) (E = 24.5 MeV), having a mean energy of about 4 MeV and low

energy, d(y,n)p (E = 18.3 MeV),

16 0(Y,n)15

(E = 21.4 MeV),

31P(y,n)

3 °P (E = 17.4 MeV) having

a mean energy of 2.0 MeV or less. The data of Fig. 30 indicate that the efficiency of the detector

for these two groups of sources might be slightly different, 9.1% for the former and 10.1% for

the latter. It should be pointed out that the usual photonuclear spectrum is probably much closer

to that of the low energy sources used here. Only from some of the light nuclei would spectra

similar to the high energy sources be obtained. For a photoneutron source of unknown spectral

composition, the efficiency of the final detector is assumed to be (9.6±0.5)%. The uncertainty

quoted is assigned because of the possible variation of efficiency with spectral shape.

NEUTRON

SOURCE

3l

p

D2

,6

I6

RaDBe

E , MeV

17.4

18.3

21.4

24.5

DETECTOR EFFICIENCY, %

10.1 ± 0.4

9.8 ± 1.0

10.2+0.4

9.2 ±0.4

9.1 ±0.3

8 9 10 II

Fig. 30. Efficiency of the final detector as a function of neutron source. (Beam tube diameter 3.00 inches, moderator thickness 4.00 inches.) Esti- mated uncertainties are indicated.

33
The efficiencies determined with the water samples shed some light on the magnitude of the

0(y,np) N cross section. If this reaction was occurring neutron emission would take place without

the subsequent positron decay of the daughter nucleus. Since the detector efficiency was based

on the ratio of neutron to positron counts, the efficiency would show an increase when measured

above the (y,pn) threshold of 0(23.0 MeV) . The fact that no such increase is indicated in

Figs. 15 or 30 can be taken as evidence that for an energy up to 28.9 MeV the integrated (y,np)

cross section is small compared with the integrated (y ,n) cross section.

The neutron yield from twelve elements throughout the periodic table was measured at peak

bremsstrahlung energies ranging from 12 to 29 MeV. The experimental arrangement was the same

as that described in Section II and shown in Fig. 5. The background was determined by measuring the

neutron yield per unit monitor response with the target out of the detector. A comparison of

the charge collected from the monitor chamber and the standard NBS ionization chamber, which was

calibrated in terms of the photon beam energy incident on the front face, then gave the number

of MeV of beam energy incident on the front face of the target. The absolute neutron yield, Y(E ),

2 in units of neutrons per MeV per nucleus per cm , was then given by:

y(E ) Y(E ) = ° . (7) o cpenT(E ,tj

2 where y(E ) is the measured neutron yield per MeV of bremsstrahlung from n nuclei/cm , cp is the gate

factor, g is the neutron detection efficiency and T(E ,t) is the correction for the finite thickness

of the target. For all samples the neutron detection efficiency was taken to be (9.6± 0.5)%. The

gate factor cp, or the ratio of the number of neutrons counted with a gate to those counted without

a gate, was found to be 0.98 ± 0.005 for the 700|Jisec gate opening 10 \x sec before the yield pulse.

2 The target thicknesses in g/cm , as given in Table 6, were determined by measuring the mass

2 and area for all targets except holmium and oxygen. Because of its irregular shape, the g/cm for

2 holmium was obtained by measuring the mass, volume, and average thickness. The g/cm for oxygen

was determined from the target thickness and the known density of water. Within the uncertainties

of the measurements the measured densities were consistent with handbook values [23].

The results of the neutron yield measurements are shown in Table 7 where the absolute neutron

yield Y(E ) is given at peak bremsstrahlung energies of 27.0 and 22.0 MeV. The target out neutron

yield was, in each case, less than 10% of the target in neutron yield. Fig. 31 shows how the absolute

neutron yield varies as a function of Z at a peak bremsstrahlung energy of 27.0 MeV. For any given

element the estimated uncertainty of the absolute yield points is of the order of 6% and is due to

uncertainties in the counting statistics (0.5%), monitor comparison and absolute calibration (1.1%),

34
Table 6. Target properties.

Target Target Thickness Effective Nuclei/cm8 Target Thickness

t(g/cm2

)

Correction Factor 6T(E

Q

,t)

N tT(E ,t) , 3 ° ° x 10 A

Carbon 4.76 0.91(E =26.2 MeV) 2.I7(E =26.2 MeV)

o Oxygen 6.99 0.87(Ev =26.2 MeV)

o 2.03(E =26.2 MeV)

Aluminum 4.60 0.97 0.99

Phosphorous 6.25 0.95 1.15 Calcium 1.83 0.98 0.269

Cobalt 3.39 0.96 0.332

Copper 1.54 0.98 0.143

Silver 2.15 0.96 0.115

Holmium 5.66 0.87 0.180

Tantalum 1.69 0.95 0.0535

Gold 2.17 0.94 0.0623

Lead 2.04 0.95 0.0562

Table 7. Comparison of neutron yields. Yields are given in units of (neutron cm3 /MeV nucleus) xlO 28 , The estimated uncertainties in Y and Y are of the order of 6% and 10%, respectively.

Element E Y(E

q

) UCRL £ aclay Va. >IBS(Old) UCRL Saclay Va. NBS(Old) Ref

.

Exp Exp Exp Exp

Y

c v*

Pb 27

22

103 HI86

92 116 0.830.83 1.05 26,30

Au 27

22

8992

9798 88 115 1.09

1.07 0.96 1.25 24,30, 38

Ta 27

22

8185 82

79 77

80 113 1.01 0.93

0.95

0.94 1.33 27,30, 38

Ho 27

22

67

69

7577 82 103 1.12

1.12 1.19 1.49 27,31,

39

Ag 2722 3634.8

Cu 2722 14.4

12.6

13.2

11.5 12.4 0.92

0.91 0.98

28,30

Co 27

22 12.7 10.6

12.1 9.9 13.5 0.95 0.94 1.27 29,34

Ca 27 1.69 1.13 1.01 0.67 0.60 32,35

P 27 2.35 1.76 0.75 36

Al 27 1.92 1.62 1.38 0.84 0.72 25,37

16

C

27

27

0.54

0.50

0.42

0.35

0.48

0.33

0.42

0.46

0.78

0.70

0.89

0.66

16,32, 3725,32,

33

35
gate factor (0.6%), number of target nuclei (1%), correction for the finite thickness of the

target (2%), detector efficiency (5.0%), and the estimate of the betatron's peak bremsstrahlung

energy. The uncertainty of the peak energy was determined to be less than 220 keV which, in the

worst case, changed the absolute neutron yield by only 2%.

Fig. 31. Absolute neutron yield as a function of atomic number. The neutron yield from calcium

(Z = 20) is particularly low in comparison with the other elements because its (y> n ) threshold

is high compared to the mean energy of the giant resonance.

The neutron yield from the high Z elements changed slowly with peak bremsstrahlung energy

when operating at 22 MeV or higher. The yield at these energies was thus (1) insensitive to any

reasonable variation in energy that might have occurred with the betatron and (2) not strongly

dependent on the accurate knowledge of the betatron energy calibration. For these reasons it

was meaningful to compare absolute yields for the high Z elements not only at 27 MeV but also at

22 MeV.

The neutron yields calculated from the cross sections measured at the Lawrence Radiation Laboratory, Saclay, University of Virginia, and the National Bureau of Standards, are compared with the

present measurements in Table 7. The uncertainty in the calculated neutron yields resulting from the

estimated uncertainties in the cross section is ± 10%. In order to facilitate a comparison the final

36
part of this table gives the ratios of the calculated yields to those measured in this work.

For the high Z elements, the calculated yields determined from the cross sections measured

by the Lawrence Radiation Laboratory showed good agreement with the yields measured here except

for lead which differed by 17%. A similar comparison, using the cross sections measured by the

group at Saclay, showed excellent agreement for all elements except for holmium which differed

by 19%. The only "heavy" element for which a comparison can be made with the Virginia group is

cobalt. Here the yield calculated from their cross section data is 27% higher than the present

measurements. The yields calculated from the previous NBS measurements are all high by factors

that are quite consistent with the results of the present study. These early measurements were

all made with a detector which had only three inches of paraffin moderator between the beam tube

and the BF- counters. For such a detector the detector efficiency is about 20% lower for the

RaDBe(a,n) spectrum used for calibration than for a "typical" photoneutron spectrum. (See Fig. 14

and discussion). In addition, the published holmium and lead cross sections [39,40] should be

further reduced by 10% to correct for an erroneous gate factor that was used at the time the original

data were analyzed [41]

.

For the low Z elements (calcium, phosphorous, aluminum, oxygen and carbon) the yields calculated

from the published cross sections measured at other laboratories are all lower than these present

measurements.

Although not shown in Table 7 , a comparison was made of the experimental yield from carbon

and the calculated yield from the data of Cook [42] who used a Halpern-type neutron detector with

a moderator thickness of 10.3 cm. The agreement was excellent. A similar comparison was made

using the recently measured 0(y,n) cross section of Cook et_ al. [43] . Good agreement was obtained. This measurement was obtained by detecting the residual activity.

In summary, the results of the experimental and calculated yields agree reasonably well for

the high Z elements. For the low Z elements, where the neutron spectra change rapidly with energy,

the agreement of experimental and calculated yields is, in general, very poor. This disagreement

of cross section magnitudes for the light elements may be mainly a problem of the energy response

of the neutron detectors used to measure the cross sections.

37
Appendix 1. Determination of the Absolute Positron Efficiency

A schematic diagram of the detector and electronics used in the positron calibration of the

Nal(Tl) crystal is shown in Fig. 32. The crystal was a 3x3 inch cylindrical well crystal having

a well diameter of 0.75 inches and a well depth of 2.0 inches. The crystal was shielded in a lead

hut having a minimum thickness of 4.0 inches; the inside surface of the hut was covered with 0.04

inches of cadmium, followed by 0.013 inches of brass in an attempt to reduce fluorescent radiation

from the lead shield [44] . The signal from the cathode of the phototube went to a cathode follower

and was then amplified and fed to a standard 256 channel pulse height analyzer.

22 A calibrated Na source was used to determine the efficiency of the crystal for detecting

positrons because it had a reasonably simple decay scheme and was readily available as an accurately

calibrated sourcej . The source was obtained as a liquid solution sealed in a cylindrical glass

vial. The liquid in the vial had a diameter of 0.62 inches and a height of 0.91 inches. In order

to minimize the effects due to geometry, these dimensions were very nearly the same (±5%) as those

of the water and phosphorous targets used during the absolute calibration of the neutron detector.

HIGH VOLTAGE POWER SUPPLY

FOR PMT

IXX^I {

AMPLIFIER

PULSE HEIGHT ANALYSER

LEAD SHIELD

-CADMIUM SHIELD

-BRASS SHIELD

Fig. 32. A schematic diagram of the detector and electronics used for the positron calibration

of the Nal(Tjfc) crystal. The cylindrical well crystal was shielded with a minimum thickness of

4-.0 inches of Pb; the cadmium and brass shields were used to reduce fluorescent radiation from

the lead shield.

'Supplied by the Radioactivity Section of the National Bureau of Standards.

38
22 The decay scheme of Na, which is shown in Fig. 33, is such that it decays to the 1.274 MeV

22 excited state of Ne by positron emission 89.8% of the time and by orbital electron capture 10.2%

of the time. The Nal(Tl) crystal detected not only the positron annihilation radiation (0.511 MeV

photons) but also the 1.274 MeV photons. Since the source to be counted with the crystal emitted

22 positrons only, it was necessary to correct the counting rate observed with the Na source for

the additional counts resulting from the presence of this line. The pulse height spectrum obtained

22 when counting the Na source in the well crystal is shown in Fig. 34. The five major peaks were

due to the 0.511 MeV positron annihilation photons and the 1.274 MeV photons interacting in the

crystal either separately or in coincidence. The expression for the number of interactions that

occurred in the crystal can be written as:

Q = f(p+)N

d {

e(p+) [l - e(l.27)] + e(l.27) [l - e(p+)]

+ e(l.27) e(e+)} + Nd

e (l.27)[l - f(p+)]

22 where Q is the observed counting rate in the crystal, Nd is the disintegration rate of Na, f(g+)

22 is that fractional number of Na disintegrations which decay by positron emissions [45] , e(P+)

is the probability that the crystal detects a positron, and e(l-27) is the probability that the

crystal detects a 1.27 MeV photon. The first term in eq. 8 expresses the interactions in the crystal

for the decay scheme which takes place by positron emission followed by photon emission and the

second term expresses the interactions in the crystal for the decay scheme which takes place by

internal conversion followed by photon emission.

Eq. 8 can be solved for e(B+):

Q - Nd e(l.27)

e(p+) =

F n (9) f(p+) Nd^l - e(l.27)

J

where the only unknown is e(1.27).

The efficiency for detecting the 1.27 MeV photons, e(l>27), was obtained by first determining

the crystal efficiency for detecting the 1.11 MeV photon from a calibrated Zn source. For extrapolation purposes, the measured efficiency of the crystal can be expressed in terms of the photon

attenuation coefficient and a mean crystal thickness defined by:

6(E) = 1 - e"^ (10)

39
where e(E) is the crystal efficiency for detecting photons of energy E, |i(E) is the photon attenuation

2 coefficient at photon energy E, and t is a mean crystal thickness in g/cm . From this equation,

the effective (it for 1.27 MeV photons was estimated from the expression:

U(1.27)

Ht(l.27) = ^d.n) Ut(l.ll) (ID

where |j.(1.27) and |i(l.ll) are the published mass absorption coefficients for 1.27 and 1.11 MeV

photons. Using eqs. 9 and 10, e(1.27) can be expressed as:

-ii(l.27)/|!(l.ll)

(1.27) = 1 - [l - e(l.ll)J (12)

The uncertainty in e(g+) , the positron efficiency of the crystal, was estimated to be ±3.2%

and was primarily due to uncertainties in the source calibration (1%) , the extrapolation of the

22 pulse height distribution (1%) and the branching ratio (1%) for the disintegration of Na source.

Another possible uncertainty could have been caused by the fact that the response of the well crystal

varied somewhat with the depth of the source in the well and the activity of the target could

vary along the long axis of target due to attenuation of the bremsstrahlung beam. This effect

was probably negligible for the water target as mixing (due to handling) occurred which distributed

22 the activity evenly similar to that of the liquid Na ccalibration source. With the solid phosphorous target, however, no mixing could occur. It was estimated that this caused an error of no

more than 0.2% in the absolute efficiency of the neutron detector. The efficiency of the crystal was

determined 5 times over a period of 7 months. The rms deviation of these determinations was 1%

indicating that the reproducibility of the measurement was considerably better than the estimated

3.2% uncertainty given above.

The crystal efficiency for detecting positrons, e(g+), was also determined, as a check on

the measured value, by calculating e(0.511) in a way similar to that used to obtain e(1.27). This

was then used to obtain e(|3+) from the following relationship:

e(p+) = 2«(0.5H)[l - e(0.5H)] + e3 (0.51l)

(13)

The difference between the two determinations of e((3+) was less than 1.25%, well within the estimated

uncertainties in the measurements.

40
22

2.6 YEARS

No

544 MeV

(89.8% £

+

, 10.2% ELECTRON CAPTURE )

.274 MeV PHOTON

STABLE 22 Ne

Fig. 33. The decay scheme of 22 Na. Decay modes less than 0. are not shown.

16,000

1

i

1 0.511 MeV

1 1 1 1

UJ 12,000 s

1- —

hz.

Z>

<£ 8,000

UJ — 1.022 MeV

Q.

1-

C/) _

z

Z)o° 4,000 / 1 1.274 MeV

-A, 1.785 MeV _ xJ 2.296 MeV

i I 1 1 1 1 ^T^.

20 40 60 80 CHANNEL NUMBER

100 120

Fig. 34. The pulse height spectrum obtained when counting the 23 Na source in the Nal(Tjj) well crystal. The five major peaks indicated are due to the positron annihilation

radiation and the 1.274 MeV photons interacting in the crystal either separately or in coincidence.

41
CRYOSTAT

SHELL

3.0

DIAMVI. \

COUNTERS

ALUMINUM CONTAINER

WITH MINERAL OIL

AS A MODERATOR

i

3 C

+ -BEAM

FRONT SECTION SIDE SECTION

Fig. 35. Cryostat neutron detector.

Appendix 2. Cryostat Geometry

3 Fig. 35 shows the geometry that was used for an experiment in which a He refrigerator was

used to cool a sample so that the neutron yield could be studied as a function of the orientation

of the nucleus with respect to the photon beam direction [46] . The arrangement of the detectors

in this case was determined primarily by the size and shape of the cryostat and the need for high

detection efficiency. In order to obtain a detection efficiency that was uniform for a heavy nucleus

photoneutron spectrum, an attempt was made to keep a minimum of approximately three inches of

moderator between the neutron source and the midpart of any counter. Twelve BF_ counters were

arranged parallel to the beam tube below and to the side of the target . The moderator thickness

between the target and the counter was 3 inches for the counters to the side of the target and

1 to 3 inches (the distance varied due to the smaller hole below the beam tube) for the counters

below the target. A moderator thickness of 0.5 inches was used between any two adjacent walls.

Fig. 36 gives the efficiency for the crystal detector obtained using the d(y,n) source and

the RaDBe(a,n) source. As was done for the data plotted in Fig. 14, the data taken with the D„0

source were corrected for the finite thickness of the target by assuming that only half of the

Compton cross section was effective in removing photons from the bremsstrahlung beam. Also shown

in Fig. 36 are the data from Table 4 for a beam tube diameter of D = 3.0 inches. The two sets

of data have been normalized to have the same efficiency for the RaDBe(a,n) source. On the basis

42
of this comparison, the cryostat detector would seem to have a detection efficiency that depends upon

neutron energy very similar to that of a single counter having three inches of moderator between it

and the source. (See Figs. 14, 15, 16 and the discussion in Section IV.) On the basis of the results

given in Sections IV and VI, the true efficiency for detecting a photoneutron spectrum from a heavy

nucleus with this detector was about 20% larger than the figure of 7.8% quoted in ref [46].

10

>-o

z —

LlI o

LlU_

LlI

a: 1.0 O

h-o

Ld

1-

UJQ

1-<

1-

(/) o

> —

cro

0.1

i—

r

o

u ®

o o — o

J L

o o

o o

Jo o

d= 2

® ® © ®

o o

d = 3 —

d= 4 9

8 16 PEAK PHOTON ENERGY, M e V

24

Fig. 36. Efficiency of the cryostat detector. The points along the right ordinate scale were determined with the RaDBe(a,n) source. Points indicated by solid circles were measured for the cryostat detector shown in Fig. 35. Points indicated by open circles are from Table 4. (D-3.0 inches). The two sets of data are normalized at the RaDBe(a,n) points.

43
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44
[30

[31

[32

[33

[34

[35

[36

[37

[38

[39

[40

[41

[42

[43

[44

[45

[46

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U.S. GOVERNMENT PRINTING OFFICE: 1967 — 251-027/120

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