uc-34- physics tid-4500 (i7th ed.) proton recoil energy

MASTER

1 * t <&> ORNL-3089

U C - 3 4 - Physics TID-4500 (I7th ed.)

PROTON RECOIL ENERGY LOSS DISTRIBUTION

IN PLANE GEOMETRY

H. B. Eldridge P. R. Flusser R. H. Ritchie

O A K R I D G E N A T I O N A L L A B O R A T O R Y operated by

UNION CARBIDE CORPORATION for the

U.S. ATOMIC ENERGY COMMISSION

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Printed in USA. Price $ 0 . 75 . Avai lable from the

Office of Technical Services U. S. Department of Commerce Washington 25, D. C.

— - ^——■ — LEGAL NOTICE - — —

This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, express or implied, with respect to the accuracy,

completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned r ights; or

B. Assumes any l iab i l i t ies with respect to the use of, or for damages result ing from the use of any information, apparatus, method, or process disclosed in this report.

As used in the above, "person acting on behalf of the Commission ' includes any employee or contractor of the Com miss ion to the extent that such emp loyee or contractor prepares, handle s or distr ibutes, or prov ides access to, any inf or mat ion pursuant to his emp loy ment or c ontract with the Commission.

ORNL-3089

Cont rac t No. W-7405-eng-26

HEALTH PHYSICS DIVISION

PROTON RECOIL ENERGY LOSS DISTRIBUTION IN PLANE GEOMETRY

H. B. E l d r i d g e , P. R. F l usse r , and R. H. R i t c h i e

Date Issued

Oak Ridge National Laboratory Oak Ridge, Tennessee

operated by Union Carbide Corporation

for the U. S. Atomic Energy Commission

TABLE OF CONTENTS

Abstract

I. Introduction

II. Method of Computation

References

»

X

4

4\

1

PROTON RECOIL ENERGY LOSS DISTRIBUTION IN PLANE GEOMETRY

Abstract

Computations of proton recoil energy losses from neutron irradiation

of hydrogenous systems possessing plane symmetry have been made for the

\ purpose of fast neutron counter design. A digital computer code has

been written to carry out the calculations for two irradiation geometries:

1) the neutron beam is assumed to be normally incident upon the system,

and 2) the system is exposed to an isotropic flux of neutrons. Numerical

results are presented for neutrons of various energies incident on plane

radiators of different thicknesses for these two irradiation geometries.

These results have been used in the conceptual design of fast'neutron

dosimeters employing a generalized dosimetry principle. The applications

are described more fully elsewhere.

I. Introduction

In the design of counters sensitive to proton recoils from fast

neutron irradiation, it is of some interest to consider systems possessing

plane symmetry. Figure 1 shows the geometry assumed for this problem.

Fast neutrons incident on the system, which is assumed to contain hydrogen

in the detector and/or wall materials, generate recoil protons throughout.

These protons deposit various amounts of their energy in the detector

volume, depending upon the distance of the point of their origin from

the wall surface F and upon the amounts of energy imparted to them by

incident neutrons.

2

The information required here is the integral recoil distribution,

i.e., the number of recoils depositing energy greater than e in the de

tector volume as a function of neutron energy E. Theoretical infor

mation on this function is of importance in adapting plane counting

systems for use as fast neutron dosimeters according to a generalized j • • • , 1 dosimetry principle.

In the past, computations of this quantity have been carried out for

certain plane geometries assuming irradiation by a normally incident 2 beam of fast neutrons in order to design a fast neutron counter with a

3 first collision dose response. It may be shown that the isotropic

irradiation of a composite plane slab is equivalent to plane irradiation

of a spherical shell of the same composition if the radius of the shell

is much greater than the maximum range of the most energetic protons.

Therefore, similar computations for isotropic irradiation have been made

in order to obtain a non-directional response. In addition, calcu

lations of the energy loss under the bias in dosimeters of the Hurst 4 5 integrating type have been made using the plane parallel model. '

The present report presents some results of calculations with a

digital computer code which has been written for the purpose of calcu

lating the integral recoil distribution function,

00

fde' n(e', E) e

for plane geometries in more detail than has been done previously. Here

n(€, E)d€ is defined to be the number of recoils which deposit energy

between e and e + de in the detector volume for a specified material

3

configuration by neutrons of energy E in a given irradiation geometry.

The code is designed so that one may obtain an arbitrary moment^

Im(e, E) = / (€')m n(e', E)d€'

of the distribution function.

The method of computation and the input data are given below and a

number of graphical representations of

. E

e

are presented for various geometrical configurations. .,.,

II. Method of Computation

In Fig'. 1 the breadth of the beam and the lateral extension of the

slab are both supposed to be much greater than the range of the most .

energetic proton which may be generated by an (n-p) reaction in the

system. Attenuation of the neutron beam in the system was .neglected

in the present study. Recoils other than those from the H(n,p)

scattering process are also neglected.

One assumes here that if one expresses R(E ) , the range of a recoil

proton of energy E , in units of gm/cm , it will be independent of

position in the system. This assumption is not very restrictive in a

practical sense. It is well known that the stopping power of a given

atom, expressed in terms of energy loss per gm/cm , is a slowly varyin

function of the atomic number Z of that atom. Hence, if one wishes to

design a plane system having a given response function for neutrons of

a given energy, one may use alternate layers of hydrogenous and non-

hydrogenous material in order to obtain the desired response. It is

easy to find low Z substances not containing hydrogen which have nearly 2 the same R(E ) relation as most hydrogenous substances.

In all of the computations described below, it has been assumed that

R(E ) is given by the range-energy relation of protons in a hydrocarbon

having the composition (CH?) .

If unit flux of neutrons having energy E is incident normally upon

the slab under consideration, there will be generated in an incremental

thickness dx a number of proton recoils d N lying in the interval be

tween p. and |i + du. given by

d2N = 2 AN cru(E) udu dx p o Hx '

where u, is the cosine of the angle at. which a recoil proton emerges

from an n-p collision relative to the initial neutron direction, A is

the area of the system normal to the beam direction, N is the number of o

hydrogen atoms per unit volume at x and cru(E) is the n-p cross section n

at energy E.

The number of these recoils which deposit energy in d€ at e in the

detector region is a function of E, x, u., and the thickness of the

detector. This leads to the expression E M-2(e,E) x2(e,E,u.)

Im(e, E) = j T u ' ) m np(e', E)de' = 2ANQcrH(E) ' J'u du J [e' (x,u) f € u-jfe.E) x^e.E.u.)

5

where the limits on the u. and x integrations depend upon the range

energy relations of recoil protons in the materials of the system and

where the dependence on the detector thickness is not indicated in order

to simplify notation. If, however, unit flux of neutrons having energy

E is incident isotropically upon a slab, there will be generated in a 3

layer of thickness dx a number of proton recoils d N_ lying in the

interval between \i and u + du, e and e + d€ given by:

d3NT = N Aou(E)dx du ^ I o H

v E

where the symbols have the same meaning as in the normal irradiation

case. In this case,

T p N A(ru(

E)

■I / ,N / / 14m . . _. , . o H

*2(e) ^.(e)' E

Im(e,E) = J (€')'" n^e'.Ejde1 = * ^ J dx J du J de'(€') e x^e) Uj(€) e

The integral energy distribution,

m

Io(€,E) = / n(€',E)de'

was evaluated for a variety of detector and radiator thicknesses (here

after called gas and wall, respectively) for both normal and isotropic

irradiation, utilizing a digital computer. The indicated integrations

were carried out using rather standard numerical methods. The inte

gration meshes were chosen as small as possible, commensurate with

reasonable computation times. The curves drawn in Figs. 2 through 18

6

are b e l i e v e d to be accu ra te t o b e t t e r than + 3$> in most cases.

The range energy r e l a t i o n o f protons in (CH?) was taken from the

numer ica l work o f He rsch fe lde r and Magee. A t a b l e o f 59 values of

range vs energy was s to red i n the f a s t memory, and l i n e a r i n t e r p o l a t i o n

was used f o r immediate va lues (see Tab le I ) . In the c a l c u l a t i o n s which

have been c a r r i e d o u t , the th ickness of w a l l and d e t e c t o r and the range 2

o f p ro tons o f va r i ous energ ies have a l l been expressed i n mg/cm of

m a t e r i a l . For the purposes o f t h i s computa t ion , the hydrogen cross 7

s e c t i o n was represented by the t h e o r e t i c a l equa t ion

or (E) = =• 1.206 E + (0 .422 - 0.1447 E)

3TT

+ (1.206 E + 5.383) [0.6506 + 0.007225 (1.206 E + 5 .383 ) ]

where cr is in u n i t s of barns and E is i n u n i t s o f Mev. H

The r e s u l t s a re presented f o r the case of normal i r r a d i a t i o n in

F i g s . 2 through 8 where each curve is labe led w i t h the i n c i d e n t neutron

energy , and the th i ckness of gas or w a l l is expressed i n terms o f the

energy of a p ro ton whose r e s i d u a l range is equal to t h a t t h i c kness . A

w a l l th i ckness des igna ted as i n f i n i t e corresponds to a th ickness g rea te r

than the range of the most e n e r g e t i c r e c o i l p ro ton from an n-p r e a c t i o n

f o r a g i ven neutron energy. The u n i t s of the i n t e g r a l d i s t r i b u t i o n s ,

E

fde1 n(€',E)

for all curves shown are (barn) • (mg)/cm . In order to obtain the number

7

Table I . Range-Energy Re la t i on in P a r a f f i n [(CH?) ] Taken from Ref. 6

2 2 E(Mev) R(mg/cm ) E(Mev) R(mg/cm )

0.0 0.0 2.0 6.268 0.002 0.014 2 .1 6.817 0.005 0.02322 2.2 7.385 0.010 0.03197 2.3 7 .974 0.015 0.03732 2 .4 8.583

0.02 0.04143 2 .5 9.212 0.03 0.04824 2 .6 9.861 0.04 0.05462 2 .7 10.529 0.05 0.06096 2.8 11.217 0.07 0.07350 2 .9 11.925

0.10 0.09613 3.0 12.652 0.15 0.1386 3.5 16.571 0.20 0.1891 4 .0 20.960 0.30 0.3137 4 .5 25.811 0.40 0.4683 5.0 3 1 . 118

0.50 0.6512 5.5 36.87 0.6 0.8610 6.0 43.07 0.7 1.0968 6.5 49.70 0.8 1.3576 7.0 56.77 0 .9 1.6429 7.5 64.26

1.0 1.9520 8.0 72. 18 1.1 2.2845 8 .5 80.52 1.2 2.6398 9.0 89-28 1.3 3.0176 10.0 108.02 1.4 3.4175 11.0 128.40

1.5 3.8393 12.0 150.40 1.6 4.2827 13.0 174.00 1.7 4.7476 14.0 199-17 1.8 5.2336 15.0 225.91 1.9 5.7406

o f r e c o i l s d e p o s i t i n g energy > € i n the d e t e c t o r f o r u n i t f l u x i n c i d e n t

on a system of area A, a tomic hydrogen d e n s i t y N and dens i t y p, one

-24 /

needs on ly to m u l t i p l y the o r d i n a t e s of a l l curves by 10 AN / p . In

o rder to conver t the w a l l t h i ckness expressed in un i t s of energy to

u n i t s of l e n g t h , one must f i r s t determine the corresponding range f rom

the range-energy t a b l e used and then d i v i d e by the d e n s i t y o f t h e

m a t e r i a l . F igures 9 through 18 show s i m i l a r r e s u l t s f o r the case of

i s o t r o p i c i r r a d i a t i o n . In a l l cases considered here i t has been assumed

t h a t the d e n s i t y of hydrogen, and hence the d e n s i t y o f r e c o i l s genera ted,

is un i fo rm throughout the system. However, the code is designed so t ha t

one may vary the hydrogen ic d e n s i t y i f d e s i r e d .

A few c a l c u l a t i o n s were made o f I . ( e , E ) and I _ ( e , E ) , the f i r s t and

second moment d i s t r i b u t i o n s , r e s p e c t i v e l y , of the depos i ted energy.

These have been desc r ibed i n re fe rence 1 and w i l l not be g iven here .

These r e s u l t s have been used in the conceptual design of a f a s t neut ron

dos imeter which is assumed to respond t o the second moment I ? ( e , E ) o f

the p ro ton d i s t r i b u t i o n . Reference 1 a l s o descr ibes the use of these

d a t a , shown in F i g s . 1 through 18, in the design of an e l e c t r o n i c system

which operates on the p ro ton r e c o i l d i s t r i b u t i o n from a s imple s lab

r a d i a t o r i n order to p rov ide a d o s e - l i k e response w i t h respect to the

neut ron energy.

9

UNCLASSIFIED ORNL-LR-DWG-64841

INCIDENT NEUTRON FLUX OF ENERGY E

Radiator Region

Detector Region

N

Fig. 1. Schematic Representation of Proton Recoil Counter System.

10

100

90

80

UNCLASSIFIED ORNL-LR-DWG 64609

CM E

70

E Z cr 6 0 < m

" * l > 5 0 ■o

vy 4 0

W c

AH 3 0

20

10 -

0 2 0.4 0.6 0.8 1.0

C MEV

I 2 1.4 1.6 1.8 2.0

F i g . 2. Integral Response of Plane Detector, Normal I r rad iat ion. (3.0 Mev gas, °° wal l )

I 10

100

90

80

70

60

UNCLASSIFIED ORNL-LR-OWG 64610

w 5 0 •o

Ul 4 0

Au 30

20

10

0 2 0.4 0.6 0.8 1.0

€ MEV

1.2 1.4 1.6 1.8 2.0

Fig. 3. Integral Response of Plane Detector, Normal Irradiation. (3.0 Mev gas, 3.0 Mev wall)


100

90

80

6 70 9 £ z or < CD

60

50

Vu 40

8"—-sy 30

20

10

0.2 0.4 0.6 0.8 1.0

€ MEV

1.2 1.4

tSJ

1.6 1.8 2.0

F ig . 4 . Integral Response of Plane Detector, Normal I r rad iat ion. (3.0 Mev gas, 0 Mev wa l l )

13

3 5

3 0

25

ME 20

< m

15

UJ

8^—^

10

0 I

UNCLASSIFIED ORNL-LR-DWG 6 4 6 1 2

0 2 0 3 04

€ MEV

0 5 0 6 0 7

F i g . 5. Integral Response of Plane Detector, Normal I r rad ia t ion. (0.5 Mev gas, ■*> wal l )


8^-*

€ MEV

F i g . 6. Integral Response of Plane Detector, Normal I r rad iat ion. (0.5 Mev gas, 3.0 Mev wal l )

CM

E u

E

or < CD

10 -

* ->vu

UNCLASSIFIED 0RNL-LR-DWG.646 I4

U i

0.1 0.2 0.3 0.4 0.5 0.6 0.7

€ MEV

F ig . 7. Integral Response of Plane Detector, Normal I r radiat ion. (0.5 Mev gas, 1.0 Mev wa l l )

' . ' t .- ' f .-

o: < CD

vy ■o

Ui

6.0

5.0

4.0

3.0 -

2.0 -

-AV

1.0

0.1 0.2 0.3 0.4 0.5

€MEV


0.6 0.7

o

F i g . 8. Integral Response of Plane Detector, Normal I r rad iat ion. (0.5 Mev gas, 0 Mev wal l )

<» i

17

UNCLASSIFIED ORNL-LR-OWG 64616

Fig. 9. Integral Response of Plane Detector, Isotropic Irradiation. (3 Mev gas, 10 Mev wall)

18

8 0 0 UNCLASSIFIED ORNL-LR-DWG 64617

0 5 5 20 25 ENERGY €-Mev


5 0 0

E u

E .

or < 03

UJ

C

4 0 0

3 0 0

»vu 200

100


vO


20

1700 UNCLASSIFIED

ORNL-LR-DWC, K4f i l3

1600

1500

E

f 1

1200

1100

1000

9 0 0

8 0 0

7 0 0

5 0 0

2 0 0

100



800

700

600

500

400

300

200

100

ro

55 60 65 70 75

e-Mev

F i g . 13. Integral Response of Plane Detector, Isotropic I r rad iat ion. (2 Mev gas, 5 Mev wa l l )

700 UNCLASSIFIED ORNL-LR-DWG 64621



a. < CO

8 ^ * ,

55 60 65 70 75

F i g . 15. Integral Response of Plane Detector, Isotropic I r rad iat ion. (2 Mev gas, 3 Mev wal l )

E o

E

or < CD

T3

c

UNCLASSIFIED c r\r\ ORNL-LR-DWG 64623 <J\J\J

-,E=IOMev

4 0 0

^3Mev \

3 0 0

^ 2 Mev

\ ' \

2 0 0 \

\ \ \

100 v j Mev

\ o 5Mev

v j Mev

\ o 5Mev

— • - " '< • i — i — ■ — ■ — i —

0.5 1.0 15 2.0

€ - Mev

2 5 3.0 3.5


25

UNCLASSIFIED ORNL-LR-DWG 6 4 6 2 4

8 0 0 —

F i g . 17. Integral Response of Plane Detector, Isotropic I r rad ia t ion. (1 Mev gas, 5 Mev wa l l )

CM

£ u

£

DC < CD

c 8^"°

^W

UNCLASSIFIED

500 ORNL-LR-DWG 64625 500 ^^E=5Mev

400

—-̂ 3Mev

300

-~^2Mev V

200 - \V

100 >\IMev

\^5Mev

\v ^ V 3 ^ \ ^ - ^ ^ - ^ $ 2 ^

0.5 1.0 1.5 2.0 2.5

ENERGY £ -Mev

3.0 3.5


27

References

1. G. S. Hurst and R. H. Ritchie, Health Phys. 8, 117 (1962).

2. G. S. Hurst, R. H. Ritchie, and H. N. Wilson, Rev. Sci. Instr. 22, 981 (1951).

3. B. J. Moyer, Nucleonics _10, No. 5, 14 (1952); R. Skjoldebrand, J. Nuclear Energy J., 299 (1955).

4. I. I. Petrov, Atomnya Energiya 3, 326 (1959).

5. R. H. Ritchie, Health Phys. 2, 73 (1958).

6. J. L. Hershfelder and J. L. Magee, Phys. Rev. 73, 207 (1948).

7. J. M. Blatt and V. F. Weisskopf, THEORETICAL NUCLEAR PHYSICS (John Wiley and Sons, New York, 1952) p 66.

THIS PAGE ,

WAS INTENTIONALLY

LEFT BLANK

29

INTERNAL DISTRIBUTION

ORNL-3089 UC-34 — Physics

TID-4500 (17th ed.)

1 . B io logy L i b r a r y 2 - 3 . C e n t r a l Research L i b r a r y

4 . Reactor D i v i s i o n L i b r a r y 5. Laboratory S h i f t Superv isor 6. ORNL - Y-12 Techn ica l L i b r a r y

Document Reference Sec t ion Laboratory Records Department Laboratory Records, ORNL R.C.

Alsmi H e r B i r k h o f f Har t Hurst Jenkb Jordan (Y-12) Jordan

7 -56 . Labo 57. Labo 58. R. G 59. R. D 60. J . C 6 1 . G. S 62, G. M 63. R. G 64. W. H

65. C. E. 66. K. Z. 67. J . P.

68-92. R. H. 93. M. J . 94. J . A. 95. D. K. 96. A. M. 97. C. D. 98. G. M. 99. J . C.

100. W. H. 101. E. P. 102. R. L. 103. L. S.

Larson Morgan Murray (K-25) R i t c h i e Skinner Swartout Trubey Wei nberg Zerby Fai r ( consu l t an t ) Frye ( consu l t an t ) Lanqham (consu l t an t ) Odum ( consu l t an t ) Platzman ( consu l t an t ) Tay lo r ( consu l t an t )

EXTERNAL DISTRIBUTION

104-108. H. B. E l d r i d g e , Aerospace C o r p o r a t i o n , 2400 El Segundo B l v d . , El Segundo, C a l i f o r n i a

109-113. P. R. F lusse r , 616 S. Sycamore S t . , Ottawa, Kansas 114. D i v i s i o n o f Research and Development, AEC, ORO

115-746. Given d i s t r i b u t i o n as shown in TID-4500 (17th ed.) under Physics category (75 copies - 0TS)

uc-34- physics tid-4500 (i7th ed.) proton recoil energy

Documents