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ClC-l 4 REPORT CtlLLECTION

REPRODUCTION

1

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COPY ..

.

26 December 1947 This docwwnt oontaina

.

\

Inelastio Scattering Cross Section8 of Is&d

tmd Uranium for 14 ?&m Neutrons

t

*

PUBLICLYRELEASABLE

. ,

work done by\ Report written by:

H. H. BarschalI H. T. Gittings

Arthur W remendinger

G. A. Jarvis

R. F. Tesohek

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Standard Distribution

Argonne National Laboratory

Atomio Energy Comics ion, Washington

Brookhaven I@tional Laboratory

Columbia University (Dunning)

(hnmral Eleotrie Company

Hanford Direoted Operations

Iowa State College

Los Alamou

Havml Radiation Laboratory

MEPA

Mew York Direeted Operations

Oak Ridge National Laboratory

Patent Ad~iaor, Washington

Teahuioal Infonnatlon Division, ORDO

UCLA Medioal Resezwoh Laboratory (Warren)

University of California Radiation Laboratory

,

Reproduced and distributed by

United St&tes Atomio Energy Commission

“ Teohniaal Information Division

Offioe of Oak Ridgo Direated Operations

Oak Ridge, Tennessee

Date Reaeivad May 20, 1948

“’”-’-~UNUN23 1943

~e Issues ‘ -

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Abstract

The ‘inelastioscattering cros6 sections

of lead ●nd uranium for 14 Yev neutrons have “

been rnea6uredby means of threshold detectors

wkone thre6kioldawere 12 h?ev●nd 3 Mav.

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~.

Inelastic Scattering CrBa8 Sections of Lead and Uranium

for 14 Mev Neutrons

Introduction

The purposo of this experiment was to measure the inelastic

scattering oross sectionof uranium for 14 Mev neutrons and to determine

the approximate”en6rgy 10S8 during an inelastic.collision. Duplicate .. . .

rune were made In every case, using lead in place of uraniumJ;a~ one ,.

would expeot similar results except for the offeota

The measurements were made with threshold

characteristicseere, ideally. zero deteoti.onorosu

,.

of fission..

detectors whose

seotton for neutrons

*

below threshold energy and an approximately constant oroas section abo~

thi8 energy. Aotually, however, instead of a critical energy there is

--

usually a transition zone one or two h’evwide. The true shape of this

,

curve was used in analyzing the data. (See Fig. 1. ) With deteotors

of this type the measured value of’the inelastic scattering cross

seotion is the sum of the cros6 sections for all processes in whioh the

neutron is either scattered out or degraded in energy below the threshold of the .detootor,the most probable proqesses being (a ) true inelastic scattering, (b ) n$2n, (u ) n,,fission.

Disk soatterin~

The ideal experimental setup should be one inwhioh the effects

af.elastic scattering ●re oancelled out. The firrntattempt at this was

thin disk scattering ●s suggested by John Manley. A thin uranium disk

---------.---”~.-----------------------------------------------------

,

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APPROVED FOR PUBLIC RELEASE
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● 0 ●bag.

. . ..-.

● * ●:0 ● *D ● OO ● 9* ● *

●

● :9 ●

●

:o.-~ :.. :: -o*” *:O :

:.O ●:a ● 00 . .

With both f’aceacovered with oopper foil detoators was plaaed normal to

tk beam of 14 Mev neutrons. The oopper foil on the side toward the neutron source 8hould see all th; primary neutrons plus all the olastica:ly

.

back-scattered neutbone.

,.;~

The foil on the face of the diek away from “::

the neutron source should see the primary neutrons minus tho8e elastically baok-scattered and-minus those inelastio’allyscattered in the

uranium. The effect of the primary neutrons alone was determined by \

s second run made with duplicnte copper disks and without the uranium

disk. For a primary

souroe is IT and the

—

Then

IT = 10 (1

1A = l..(l

Adding give8

‘Uin = 2 -

beam of l., the intensity on the 8ide toward tha

—

intenuiky away ie 1A .

—

+ I’Jcrelastic ) \

- TTuelastia - % ~elaatio)

-.

10

“a

in =

2 10 - IT - 1A ,

. r?Io

where N is the number of uranium atoms per cm~ and the I~a are obtaimd

from the Geiger counting rate of the foils after irradiation. This is

of cour8e a crude pioture but the method will not be di60u68ed in more

detail since it was not satjsfaotory; a oorrectfon faotor in the foil

sensitivity wa8 larger than the main effeat and very diffiuult to

>

.aompute. . . .$

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●

●

:0 :0

.:. moe

- 50-””” “ ●:0 :.0●::.

..

This correction, called the obliquity fnctor, oomes about .

in the following way. If the detector foil is in a uniform neutron

flux, the 8ize, shape, or orientation is of no importance, only the

totel number of atoms in the flux, provided of ccurse the patktlengths

.

.

,.

in the detector are vary small compared to a mean free path. ~~e ~ r

in a non-uniform flux this is not the case. Let ~, the neutrons per

see, be expressed as a func%ion of a parameter, 13. Let dA be that —

differential area of the foil which sees a constant value of neutrok .

2

cm

.,..

“r.

flux and.let it be expressed as function of e . Let P, the associated -.

path length in the foil, be expressed as a function of 0. Tha rate of

u! v

formation of radioactive atoms in the detector foil, ~, is then givan by

R.~an(e) -#atorn<oc .p(g)=dA (e) +x ~1)

e

If ~.is a constant, this results in ?

R. . on .#atomu/cc J Pd A = u<~toms/ae x volume

which ia customarily used. 4“

..-‘----

A more convenient form of equation (1 \ in the cnae of a point

source of nautrons in

F? . a#atoms/om3

J

n neuts/unit solid angle x F x dfL(3 )

f?.

As an example of-this obliquity correction oonsider a point source Q

neutrons per second and a cimular disk deteotor.

d~=2rsint9dt3

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
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.. .

%

if ~ were small enough ;o.tlpt the flux could be considered parallel,

the expeated reaction rate would

Ro=&G Ax fix

be Ro.

b;fi= a2

—-r% A . # Atoms/oc

r=

R. = aQAb ●; a2

4 7

The obliquity factor -.& .

0 W-

, which increases to 1

as air gets 8ma11. Now in the case of disk scattering the obliquity

faotor would have to be obtained by considering each point of the

uranium disk in the above manner and integrating over the volume, a

uomplioated procedure when 8uch other factors as secondary elastic

or inelautio scattering in the uranium associated with the different

path lengths are considered.

%

Method

The method finaIly used for the experiment was spw+o~at%er~

ing. Lead and uranium spheres of radius about one-half mean free path

...

..

‘. .

. .

“,,

for energy loss were made with a small central oavity in whickthe

detector foils were placed. In suoh a spherical geometry the effects

of elastio 8cattering do not enter into the cnloulations since >ust as

meny neutrons are elastically scattered out as are elastically scattered

into the detector. The foils were made in long thin strips which were -

rolled up tight to approximate a p8eudosphere when placed in the cevity

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(x

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and which aould be unrolled and wrapped around a Geiger counter for good

counting geometry.

Several sizes of uranium spheres were tried with copper

detectors. Radii.of 3, 4, and 5 cm all gave the same value of inelastia

scattering cross section within the experimental error. -; )1; “.,..+

The experimental procedure (Fig. 2 ) consisted of placing the

+

,.

sphere with the internal detector in tb neutron beam for about 3flY.

minutes (approximate-lyone half-life) and then counting the induced

foil activity. A second run was then made with a duplicate detiaotor

but without the sphere. The ratio.of the two foil activities was then

a maasure of what we have called inelastic scattering. 10 minute runs

were chosen as a compromise sinoe the foils would be up to about half of

saturated activity and a number of runs could be made in a reasonable

time.

,

\

Of oour6e S was necessary to normalize the neutron flux during

the two run8. This was done by using a mohitor foil of the same material

as the detector foil, placed in the beam in a standard geometry far enough

from the s“phereto minimize any back-scattering effects from the spbre.

After irradiationwith the sphere in, the detector and monitor

foils were counted simultaneously in two ~eig.ercounteru for about ~0

minutes. The ratio of the total ccunts in ouch a case is the same as

,

the ratio of the two foil activities at the end of irradiation. The

same retio was determined for the sphere-out run.

,

Commutation

The

by

transmission T of a neutron beam through a mdium is given

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
“3

3 -

.

.

.

where Y is the number of

and a is the total cross

in our case.

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s*~& :

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atoms per cc, r is the distance in centimeters

8ection in general, but is only the inelastic

“in = -

lo~ T

TTSi~, detedor foils of equal mass, the transmission i8 the ratio of foil

activities, Ad, with the spkare in and out, normalized to the same neutron —

flux by means of the monitor foil activities, @ ..

T= Ad in x Am out

Ad out ~ Am in

This ratio is evaluated from the counting date, using equal monitor masses. “.

‘....

T= {Ad/Am~ in “(.

(Ad/Am I out

“Nhencomputed in this fashion the irradiation tiun and the counting tinm

do not enter into the calculations, and so do not need to be known.

I?esultswith 14 !:evNeutron8

The results to date are shown in the tabls below. The errors

given are the mean deviations from the average. The geometrical cross

sections are included for comparison. ‘i’~lecross seotions are in barns.

Cu detector

u

run8 ~ in geomet- fi~sion tr~e

rical inelastic

11 2.29 + 0.12. 2.5

2.25 + 0.15

15 2.50~ 0.08 2.7 9.85

,. 1*83 + 0.10

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w

co

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.

—

In the table we see that the inelnstic cross sect<.on of lead is

essentially the same when measured by the copper and aluminum detectors.

I

This suggests that tk,einelastically scattered neutrons which are degraded .

I

in energy below the csopperthreshold are also degraded below the aluminum

I

threshold, or, a 14 WV neutron loses over 11 Yev ir,its first inelastic

I

collision in lead. 7

I

In the cese of ‘~raniumthere i8 a signif.icsntdifference in th

I

results of the measm-enmnta with the two detectors. This difference might

I

be due to an average energy loss between the two thresholds but more probably is due to activation of the aluminum detector by-the faster of the

I

28 fission neutrons. If this is so, then,kke results of the experiment

t .+ I

are that the true inelastic scattering cr~ss section (measured-minus

\

I

f,i8sionj of Ilraniumis twice as Freat as the fission cross section and

I

-.

the average energy loss due to an inelmst:~-cqllision of a i+, l!evneutron

.

,:y”{ -

~a ,..

in l~raniunis over 11 ~~ev. ‘, ,

4

“.

... .!

/“ . ,-.

. . .

+

Correction of measurements with aluminum detector.

?valuettcn of the expected ccintri$utlonfrom fission neutrors to

. -a

, the aluminum foil activation is givem below.

b

/.

.,

\ The ratio c of detector ~ctivption R from fissicn neutrons to

4

. ‘

‘the detector activation ~ from primar$ bdnrr!xlewtronsis

.- * C=R/l?

c’ -

i.’

I?.i8 computed @n the basis of the value c$finelestic scattering cross

— 4

section; u determined with

●*8

●

●

.:4

be

the

●

.

copper

● *a

●

● 00

detector,

,0 “ : ::

9* 20 ● , :0 ● ●

● ** ‘e ● *

● * ● oo ● ** “000 :fe ● *

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● 0 ●:0 :00 ●:= :.. :00

●

● ● 000 -+).;.i“ ● :9* :● *O :80 :

R. . no neutrons/ orn2 see x .-Nur X ~Al x#Al 8tOm8/co

where .41refers to al~xr.inum.

—

R is the produot of three oomputed functions.

where

d

b)

c)

x ‘Jolum Al,

The average number of fiseiona/cm3 seo = F.

The average number of neutron8/fiseiondetectable with

●luminum =

The number

inte~rated

[;.

of ●luminum reactiona/ detectable neutron

over the uranium sphere = R2 .

R=FxGxR2 .

Gt . 2.5 neuton8/fiesiorix 0.218 detectable netirons/

fissicm neutron

G - 0.55 tiekeotableneutrons/ fission.

:-~ + $](’-’”’’%)’2d~

(’.. R/R FGR2/Ro 0=

[

377wfp Za - ~(i-e-zAwa

c=

)] f f(b)db● 0.55

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~e-Awra3A02

C = 0.064E ~“6.45~

.

P . 0.6 cm

v x 0.95 Oc

r = 3.34 cm

.

.a . 3.97 cm

---------- --:..”-------------------------------------------------------------c-

.

.

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
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(s

-24

. 2e5@ x l@ ~mz

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-24

‘f = 0.86 x 10 omz

A = 0.464 x 1023 atoms/cm3 ~,

A

..,’

. 9.2 cm for 3 Y%v neutrtmzh.i

~f(b) =0.7~.m3

The average value of the trmsmission as measured was 0.731.

If w aonsider tbwrtthe value wo should use is 0.731 ( 1 - o) we get

y

= 0.6W. Putting this in the cross aect$on formula gives

loge T

‘in = - —— = o.3t?o = 2.44 barns.

N r 1.56 x 1024

The mean deviation will be about the same, so

b

in = 2.44 + 0.21 barns,

.

which is in agreenent with the value obtained with’copper

.

u. = 2.50 4 0.08 barns. In

Therefore the results of’the experiment are probably correct as stated.

,.

,

,,

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1,

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Fig. 1

fiasion neutron.spatrum,

LA 140 arid!3.E. Watts

,

.!

E

The detection efficiency is the

product of these two functions,

percent detectable neutrons per

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normalized, integrated “

whioh is equal to 21.8

fission neutron.

:;

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ExperitrmntalSet-up

..

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APPROVED FOR PUBLIC RELEASE
--—

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Appendix A

Oetector Reaction T~reshold Half-life Cross Section Size

— - ————

CU63 n-2n’ - 12 N*V 10.4 min g.25 barna 12” x 1/4”

x 0.003”

. .

Al *-P -

3 bf~v 10.2 min 00032 bqrns 12” x 1/2”

X 0.@08n

●

✎

. . .

.“

r.

k

.

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.“e ● 00 ● *

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● m** **m ● *

● **m ● *

● * ● ** ● 9* ● 00 :00 ● O

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● *.. ● ● 0

● :“ ● O::.::

● ● ●

:0 :

9*

● ,* :09 . .

Appendix B

‘- To e valuate the fetal number of fissions in a uranium sphe~$

in a uniform flux of neutrons,

.

First assumption

Any effects of elastic scattering cancel out due to the

spherical

flux is a

geometry.

The locus of differential volumes which see

ring of volume dv . 2r(y dy dx. The number

dv/sec . df.

df=ofnx #

GC dv ,

th same neutron

of fissions in

.

t

..

The neutron flux n falls off due

n=noe

-Aat

●

to inelastic scattering ●nd fission as

where t is the thickness of material.

To obtain the averageoOqun@$ oP:f&i6?w per seoond cm3 we take

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● : 8*

● 0 ●:0 :** ● 00 :00 ● O

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● *9 ●** ●

● ** ●

● 0,00 : i$;i:A d ●.000.:

● 9 990 9 9 9*

- . . * --- - ---

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APPROVED FOR PUBLIC RELEASE
c%)

●

.

.-

● ✎ ✎

:00 ● 9**

● *...

● ***

L“O&”-””o

● ☛ ● ☛✎ ● ☛✎

●

●

●

✚ ● ✎

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9 ●:0 :

●:0 :0. ..

●0:: :

● : :: ● @* ● .0 . .

.’. “., ,

.

. .

.

‘ ‘-7&7-

which is given as equation (a ) . As e check on the validity of tlw

equation, we can see if it reduces to the simple form of

F.nu A

o of

which we know holds true for small values of a. The procedure is to —

take Iim F, the necessity being that F is indeterminate for small a.

a+ o

Xrrite

F=Fox. 3

za3A20-zIDifferentiatin$ three tires to get rid of the a3 in the —

we Fet

.

. .

,

Iim F= F.

a-+o “

4A30-3-

6A3C2-3

● 9* ● ● 00 ● 99 ● m ●** ● ● ● *

● : :0

● :00000 ::

● ● *

● a ●:0 :00 ●:0 :00 ● *

denominator

.-

● b ● *a 9** ● ●

● *9 ●** ● ● ● ●’*

● *Oe *O* ● *

● ● -*

:O*da‘I:*”:’ O_ @%oJ w:.

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
. . . . . .. --— ----- . .. . . - 4--------- . . . . . —.. , . . . . . .

.

.

- ;;i :: i:: ;e*:::

.;:; .

● *●:0 ● ** ● 00 ● *e . .

●

90:. ::0

:: ● :

● .

:

● ● ** :

● : :: ● ** ● .* ● *

Appendix C

To determine the rate of formation of radio-aIuminum atoms

due to the presenoe of’fission neutrons of Q per cc with energy above

3 Wev, c onaider firat a point source of neutrons, N neutrons per unit ,..,

solid angle, at a distsnce b from the center of tl-iialuminum detector ‘

rediua a.

N b

For different angles ~ the flux inoident on the sphere is different by

l/r2 and the path length P is different in the sphere and hence the

reaction probability is ‘alsodifferent. Let the number of reactiona

per seoond in the differential solid angle dJl be dR1 ●

.- (3RI = CJA1 X N d.Ax# Al/cc P.

First to express P as a funokion of 9.

where k . b/p ●

,

.

.-L. 4.4

y .xten O

2

xmbcos e~PcOse 1 - k2 Sixz ~

y= b8int3C06 (3+_p slna

-/

1- k2 sin2 0

in2

- Y2

.—

e

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APPROVED FOR PUBLIC RELEASE
&*!

.

“

● ☛ ● D* ●...*.: 99* ●

● ****

:“ IJNMKSSIFih ● * :

:.03!)00: ● .

:0: 000: ●

“;~.”;, –-

●

● *●:0●O*● *O● **● * ●

● ,**

● :. ● *

● ● 00 : ● ** :.0 . .

To get d ~ as a function of 8,

d~= dA .!2nYt rde

T r2

but yl/r = sin 8.

dfl.2nsinf3d6)

.

—

~ is determined by setting 4/3n~3 = volume

volume = mass = 2.S6 O*95 cc

density —=

2.’7

.

P“ 0.61 cm

This will hold for small b but for large b it doe6 not take into

account the inelastic scattering in the uranium. However for these large

b the ohange in flux duu to the factor e-rh is Small .Comparddt@ the”

chnge due to 1/2r , and so this form is

is the contribution of a point souroe.

Fiwn b is 11x 4nb2 d b.

still e fair approximation. This

The total source strength for

[

I - b2-/a2Iog b+~

1

tl‘b

2 bp b -p

● ● **● 990● **● *

● :0 ● ● 9

: :@ ● *

● ::90 :0:: ..—

9* ●

● *•~m● .0● o*● *m ● a

- .—

——

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APPROVED FOR PUBLIC RELEASE
c%

w

● O ● ea

● oo ●°0 :

9*

● 000. 9**.

● 0,

● 9

● *D :e: u?iCIASSIFIlkI :s: coo:

● o 4639 e ● 0, ● ● ●

● O ●:0 :.@ ●:0 *CO . .

~.. ..

●

● ●

●

● *

● m

● O :: ● :

:0 ● *

● ●:0 : ● ● 9

:* :00 . .

.

.

*

We must put in the exponential decay factor now since we have varying b.

This is e‘b~ where A is the mean free path for energy 10SS, since

.

again we assume e~astt~tiscattering cancels out. For our range of

values of ~we oan act this to (1 - 0.84 bfi)s . N . ~4n., ..

c1

R;=8 Z’p ql N #Al

[[P ‘-s++w””’’+)

R:z2n-p51Q#Al f f (b)db

.

Thi8 integral

integrand and

*.

2 Pp q, #A1/’f (b)dk)

is too messy to evaluate analytically. so we plot the

measure the area, giving s

a

f

f(b) db=O.76cm3.

p“

.

.

-------------------------- --------- ----------------- -------- -------------

x ‘This is the best ~ittin~ straight line for: O<b< ~/3.

● ✘☛ ● ● 00 99* ● * ●** ● ● ● 9*

● 9 :0

● : ● * ● :-

●

: :

c ● *

be ●:O ● ** ●:* ● *9 ● *

.,,.

.

f

APPROVED FOR PUBLIC RELEASE

APPROVED FOR PUBLIC RELEASE
u~~ASSIFIED

~

‘“?.<. . . .

.,

-#

● ☛

●

●

●

● O

●

: ●°0

●

:

:00

● O* ●

● 9*

●:

:

● 00

●5✚ ●

●

●

☛

a☛

● 0

● 0 ●0: .:. *.. .:. ● .

● 0 ●

● ebem ●:

● e ●

●

:

● . ● : : :0

● O ● *O ● ** ● ●:0 ●

IDOCUMENTROOMI

1

.- ● m. . . .

: . . .

:: :: ● :00

:: 9* ● ●: 4

● O ●e: ●:0 ●0: ●:.

:.

. . ● I

● ● . . . . b. ● ●

● 9**

● .*. .*: .=:

● ●

:

● e. ● :: ● *: 9**.

●0... ● 0.

● 9* .*

4 

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