The transmission of neutrons and gamma-rays through air slots

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Title:
The transmission of neutrons and gamma-rays through air slots
Series Title:
BNL ;
Physical Description:
v. : ill. ; 27 cm.
Language:
English
Creator:
Schamberger, Robert D
Shore, Ferdinand J
Sleeper, Harvey P
Brookhaven National Laboratory
U.S. Atomic Energy Commission
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United States Atomic Energy Commission, Technical Information Service
Place of Publication:
Oak Ridge Tenn
Publication Date:

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Subjects / Keywords:
Nuclear physics   ( lcsh )
Neutrons -- Diffraction   ( lcsh )
Gamma rays   ( lcsh )
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federal government publication   ( marcgt )
non-fiction   ( marcgt )

Notes

Statement of Responsibility:
by Robert D. Schamberger, Ferdinand J. Shore, Harvey P. Sleeper, Jr.
General Note:
Cover title.
General Note:
Originally published 1954.
General Note:
"September 1, 1954."
General Note:
"Subject category: Physics."
General Note:
"Brookhaven National Laboratory, Upton, New York."
General Note:
"Date Declassified: November 21, 1955."--P. 2 of cover.

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University of Florida
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uNCLA- 2 2 SSI
uNCLASSIFIED


UNCLASSIFIED


BNL-2022

Subject Category: PHYSICS



UNITED STATES ATOMIC ENERGY COMMISSION



THE TRANSMISSION OF NEUTRONS AND
GAMMA-RAYS THROUGH AIR SLOTS.
PART IV. THE EFFECT OF AN OFFSET ON
THE TRANSMISSION OF NEUTRONS THROUGH
AN AIR SLOT IN WATER


By
Robert D. Schamberger
Ferdinand J. Shore
Harvey P. Sleeper, Jr.


ICA56
*,. .- "=.
/


September 1, 1954

Brookhaven National Laboratory
Upton, New York


Technical Information Service, Oak Ridge, Tennessee
























Date Declassified: November 21, 1955.


This report has been reproduced directly from the best
available copy.

Issuance of this document does not constitute authority
for declassification of classified material of the same or
similar content and title by the same authors.

Printed in USA, Price 20 cents. Available from the
Office of Technical Services, Department of Commerce, Wash-
ington 25, D. C.
GPO 9880


This report was prepared asa scientific account of Govern-
ment-sponsored work. Neither the United States, nor the Com-
mission, nor any person acting on behalf of the Commission
makes any warranty or representation, express or implied, with
respect to the accuracy, completeness, or usefulness of the in-
formation contained in this report, or that the use of any infor-
mation, apparatus, method, or process disclosed in this report
maynot infringe privatelyowned rights. The Commission assumes
no liability with respect to the use of,or from damages resulting
from the use of, any information, apparatus, method, or process
disclosed in this report.








BNL-2022









THE TRANSMISSION OF NEUTRONS AND GAMMA-RAYS THROUGH AIR SLOTS


Part IV

The Effect of an Offset on the Transmission
of Neutrons Through an Air Slot in Water


Robert D. Schamberger
Ferdinand J. Shore
Harvey P. Sleeper, Jr.




1 September 1954












REACTOR DEPARTMENT

BROOKHAVEN NATIONAL LABORATORY
Associated Universities, Inc.

under contract with the
United States Atomic Energy Commission

Work performed under Contract No. AT-30-2-Gen-16






Part IV

The Effect of an Offset on the Transmission
of Neutrons Through an Air Slot in Water


As an aid in shielding against the passage of neutrons in air
slots, the expedient often employed is to put a step or offset in the slot
to impede the direct travel of radiation. As part of our investigation of
neutron transmission through slots we studied the effect of a single such
offset for slots of thickness 0.5 and 1.5 inches with an overall length of
48 inches. Both sections of the slot were 24 inches long by 34 inches
wide and the offset distance, D, was varied from zero to a few inches.
This variation was small compared with the 40-inch source plate, so that
the source remained effectively infinite in size. Fig. 1 is a sketch in-
dicating the essentials of the experiment. An infinite offset was ac-
complished approximately by having the bottom section filled with water.
An experiment, to be discussed later, included a horizontal gap connecting
the two vertical air slots.

Thermal neutron data were taken in the water above the upper
slot with both fission and BF3 counters. The usual procedure was to make
a vertical traverse along the upper slot centerline. For small values of
offset, when the transmission was large, the fission counter was employed.
For larger offsets, the 1 x 6 inch BF3 counter was used. Horizontal tra-
verses were also taken in the thickness direction at vertical positions
corresponding to about 1.5 and 7.5 inch water separations between the top
of the aluminum box and the detection center of the counter. The vertical
traverses for the 0.5 inch thick slot are presented in the semilog plot of
Fig. 2. Ordinates are thermal flux per unit pile power and abcissae repre-
sent the height of the detector above the bottom of the water tank. The
top of the slot holder assembly was at Z = 52.5 inches. Nomenclature ap-
pearing in the figure is described in Part I of this series of reports.

Qualitative features of the traverses which bear comment are
the following:
For large Z, the l/e length is approximately 7 cm;
characteristic of fastneutrons.
For small Z; i.e., 54 inches, the 1/e length varies
with offset and is larger for smaller offset. The be-
havior is consistent with the assumption that with large
offsets the emergent spectrum of neutrons is softer than
with small offsets.

The peaks of horizontal traverses made in the neighborhood of
Z = 54 inches have been normalized to the flux measured in the vertical
traverses at 54 inches. The assumption is made that the shapes of hori-
zontal traverses taken with Z differing by fractions of an inch are closely
the same. These normalized data are presented in Fig. 3.

From the peak flux measured at 54 inches, using different values
of offset, D, one obtains curve A given in Fig. 4. Curve B results from
peak fluxes corresponding to Z = 60 inches. The characteristic to note is






the slow decrease followed successively, as the offset is increased, by a
rapid decrease, and then a slow decrease. Shown at the right hand side are
fluxes obtained with the bottom slot filled with lucite; i.e., an infinite
offset. For large offset curve B is much flatter than curve A. This is
interpreted to mean that the higher energy component which is detected at
the larger water separation of curve B is better collimated and that the
interaction effect is smaller.

A question of interest is whether the features observed for
the 0.5 inch thick slots are the same for slots of different thickness.
Data were obtained with 1.5 inch thick slots which allowed comparison with
the 0.5 ibh data. Figs. 5 and 6 show vertical and horizontal traverses
obtained when the upper half of the 1.5 inch thick slot was displaced.
In Fig. 7, corresponding to Fig. 4, the qualitative behavior for the 1.5
inch thick gap is observed to be the same as with the 0.5 inch gap.

The similarity of shape for the two thicknesses is demonstrated
in Fig. 8. Ordinates for the 1.5 inch points were.determined by dividing
the flux by the square of the ratio of slot thicknesses; i.e., factor of
32, or ninefold. Abcissae are in slot thickness units; i.e., offset divided
by slot thickness. It is seen that the lower curve shape is essentially
independent of slot thickness, whereas the unper curve, which included
softer radiation, after transformation is not independent of slot thickness.
It appears that for the more energetic neutrons, as a first approximation,
the offset shape is independent of slot thickness.

For displacements from zero to one slot unit, it is reasonable
to assume that, as a first approximation, the transmitted flux will be due
to unscattered neutrons. The response function can then be calculated over
this range of displacements if one assumes that the problem is two dimen-
sional and that the detector integrates the emergent flux. This calculation,
for those neutrons which do not penetrate water, is done in appendix A, and
yields a T2 D2 dependence, where T is the slot thickness and D is the slot
offset. In Fig. 9, curve B of Fig. 8 is replotted and a calculated curve
is shown for which Phe flux is normalized at D = 0, and decreases with D
according to T2 D .

It is apparent, however, that when D approaches T substantial
contributions to the transmitted flux must come from neutrons which have
traversed some water in the region of the offset. In appendix B are out-
lined calculations which estimate the contribution coming through the
corners. For this purpose, it is assumed that fast neutrons are attenuated
with a 1/c length in water of 2.0 inches. The. calculation for D/T greater
than unity was made at only two points; D = 1.625 and 2.0 inches for
T = 1. inches. A summary of those calculations will be found in Table I
in appendix B. It is seen that the simple assumption of line-of-sight
behavior, including exponential attenuation in the water medium at the
corners, fits the data fairly well up to r/T = 1.1. This suggests that
the first an.roximation theory is good so long as the offset is not much
larger than the slot thickness. For larger separations, one may conjecture
that the interacting neutrons are not all removed from the beam, and that
some of them reach the detector. This would make the experimental points
lie higher than the calculated ones, particularly for D greater than T.







The difference between the experimental value and the sum of the infinite
offset result and the calculated value would then represent the "inscat-
tered" component: at D/T = 1.33 something like 8 x 10-3 of that obtained
at zero offset.

The effect of a horizontal connecting air gap on the trans-
mission of a stepped slot is indicated in Fig. 10. Curve B is run No. 1828
reported in Fig. 2 for the 0.5 inch thick slot with 1.8 inch offset.
Curve A was obtained with the same setup, except that there was a 3 inch high
connecting air space at the offset. It is seen that with the air space an
increase in flux is noted, and that curves A and B are almost parallel.
At Z = 54 inches, the increase is a factor of 1.48 and at 60 inches it is
1.39. If the process of transmission at the offset involved a twofold large
angle scattering, the low energy neutrons from the lower slot would scatter
through the horizontal section with greater probability than the high energy
neutrons because the cross sections are larger for the smaller energies.
This would imply that curve A would initially be steeper than curve B. There
is no evidence for this. In terms of curve B in Fig. 4, the effect of the
air gap was to reduce the offset from 1.8 inches to about 1.2 inches. It is
fair to state that for an offset a few times the slot thickness, inclusion
of a horizontal connecting gap affects the neutron transmission of the slot
in a minor way.








APPENDIX A


In order to approximate the flux trans-
mitted through offset slots, let us as-
sume that we have a two dimensional
problem, that the detector integrates
the emergent flux, and that we are
dealing with only neutrons which travel
straight line paths between source and i*
detector. The calculation then can be
broken into two parts depending upon
whether the neutron path is entirely in
air or whether it also includes some
water. In part A, we consider that the
complete path is in air, and in part B, -
include the effect of water on the as-
sumption of exponential attenuation in
the water.

For a source point lying at x, one ap-
proach is to calculate the angle sub-
tended at x, Fig. 11, by that part of
the top of the slot which is defined by
the corners halfway up and at the top.
The assumption is made that the emergent
flux is proportional to the angle sub-
tended. The desired result is then ob- -
tained by integrating over x. For off-
sets, D, less than or equal to half the
slot thickness, T, the desired function
is: Fig. 11


o D oD+T-x -T-D-. x-D.I D+T-xxj
I = dxlarcot-- arcot 2L ) dx + arctanj- arcet -
02L 'D2L 2L 2L


rT
+ Idxl + arctan(ll- arcotI(T-x
JT-D L2 '1 L

(1)








For D greater than or equal to T/2, and less than i, the function is:


,T-D I 'D x -D
O dxarcot 2 arcot + dx arcot ) arcrt


T -
+ xi + arctan ? )- arcot&-)
"n { '


In all cases, the angles are very small since L = 24 inches, T = 1.5 inches.
We can replace the arcot and arctan functions by the first term in their
series expansions and obtain to a good approximation:


T-D

JD 2L


T
dx + 2T-D-x dx
JT-D 2L


T2D2
2L


.D
I0 T-D+x d



0 4 2L


1 T-D+x
Io-Jo 2


-' T
dx + a- x
JT-PL


+T 2T-D-x dx = T-D
D 2L 2L


Equations 3 and 4 can be written directly on the assumption that the angles
involved are given by the chord divided by the radius, rather than the arc
by radius.







APPENDIX B


For those cases in which neutrons traverse water along part of the straight
line path from the source to the top of the air slot, it is not always pos-
sible to get an algebraic expression to describe the process. "e shall con-
sider four cases:


a. D less than T;
b. D greater than T, neutrons do not
traperse either of ends R or S;
c. D greater than T, neutrons traverse
end R; and,
d. D greater than T, neutrons traverse
end S.

Case a: For the experiments under dis-
cussion, the fast neutrons are attenu-
ated in the water with a 1/e length of
approximately 1/u = 2 inches**. Since
the length L = 24 inches, then uL-;1,
and for significant contributions l. L.
From the geometry shown in Fig. 12, we
can write

L+o
-T---"-
x-y x


K ~(






I'









I I


. X- L2 X
r x 2 .


Fig. 12


The contribution to the flux at y due to
to exp (-ul). The contribution emergent
passing through R is proportional to the


-D x -u
I dx.
a 00 2L
jrO 0


a source element
through the slot
angle dy/2L, henc


SD -x -uL x-)1
2L dx dy 2 -
2L 0 0o 2L


dx is proportional
top for rays


-uL D x ul
2- dx dy 2 x
'0 '0


-uL

2L


-D
dx
0


uL 1 -_uL 2

L2uL2
By~ ~~1L symer a siia2eulti bandfrryspsigtruhS


2u L 2
2u- L


By symmetry a similar result is obtained for rays passing through S.
Therefore, the total contribution is:


a D2






Case b: For simplicity consider the
case where T D 3T/2; i.e., in Fig. 13
d e T/2. Then the path length in water
is given by e = d 2LA+y+d, and one
can write

.d -x+d -yL
Ib dx 5 d
0 2L


T-d
+T dx



+1 dx
T-d


x+d -uL
-x-d 2L

T dy -uL
2L


Jx-dUL


= A + B + C.


Each of the integration
y is of the form
2uLd
xdyc-


with respect to


Fig. 13


which can be expressed in terms of the exponential integrals.
one can substitute


2uLd = K; x+d = a;


K
CI 2a
(dx dz

a


For example,


Z = ; dy = -2 dz


e2
Z2


K -,.d
= d0 [E 2 -M)


Similarly the terms B and C may be expressed in terms of exponential integral
of the second order giving

I( di Ex +T-d ( j
b ^ x & -EEA K(x+d j dJ E2(2) 2(x+d)


+ dx E2 ) -E2 +x+d)


Hence,

A K-
2L


-E2 L
2(7li K \l






The integration with respect to x can be carried out graphically for parti-
cular values of d and K.

Case c: For those rays which traverse end R of Fig. 13 one has

/ L x+d-y
x+d+y


-T x-d
I% )) dx f d
Id 0O


-uL x+d-
x+d+y d
2L


letting

x+d = m; uL = c; z = 2- ; dy = -2mc d ;
m+y z
z2


-cM-y c -2mc
Sm+y = c I-
(tL.M+y


mc
c -T+d T -z .T+d
Ic mdm c- dz = j mdm IE
c 2L 2d 2c z2 L d 2


Case d: For those rays which traverse end S of Fig. 13, one has


I' uL y-^
y+d+x

and analogous to case c, can write

.T +d-x
-T .y-d -uLy Tg-
II dx = T
d }d 2L 0 c

The following table contains a summary of computations for Fig. 9. The con-
stants involved are: u = 0.5; T = 1.5 inches; and L = 2? inches.

TABLE I
Surimary of Computat ions
IJORi4AIIZED TO UNITTY AT D = O I!5ORALIZED TO 1.08x10O AT D=-a3
D/T I- I, Total Total
O 1-0 0 1.0 1.08(3)
0.5 .75 .0O16 .792 8.56(2)
0.75 .438 .0936 .532 5.75(2)
0.90 .19 .135 .325 3.51(2)
1.00 0 .167 -2) (-2) (-2) .167 1.8 (2)
1.083 2.81 1.47 1.47 5.75 (- 6,21(1)

1..3. j33 .17 d 17 3.72-3 4.01
a (n) means times 10n

SIre wish to acknowledge the contribution of Bruce Knight to these calcu-
lations.
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UNIVERSITY OF FLORIDA
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