ORNL-1771 - Oak Ridge National Laboratory

AM? QUARTERLY PROGRESS REPORT
w i tll
-aRpQ
+(Q,P) = e
4.nR2pQ
Since the Fourier transform of a convolution is the
product of the transforms of the individual func-
tions, for an isotropic source with no energy loss
after each collision the transform TF-n becomes
with
In taking the inverse of 'i'F,, the path of integration
is deformed intothe closed curve about the negative
real axis to the left of -0. Calculations of these
scattering functions for the first- and second-
scuttered flux give
F1 = 1.635 I
F2 = 0.19167 ,
These figures are to be multiplied by 1/4n2 AD,
for X = 130 meters, to obtain the number of fast
neutrons at a distance D feet from the source.
GROUND SCATTERlNG OF NEUTRONS
A. Simon H. E. Stern
An investigation is being carried oiut to derive
formulas for the ground-scattered neutron flux to
be obtained froin Q general source distribution. The
model used is that of a source whose axis, or
direction of maximum intensity, forms an arbitrary
angle 0 with the source-receiver axis but lies in
the same horizontal plane as the latter. The
differential source strength is assumed to be a
function of only the angle between the emergent
ray and the source axis. The receiver is isotropic
under the assumptions of no air attenuation and a
constant albedo for the ground. The following
expressions for the flux at the receiver are ob-
tained:
162
1,
For isotropic re-emission from the ground,
N ,A
F = ~-
87i2b2
I" /( a,) sin a da
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._
For cosine re-emission from the ground,
h =
o =
D =
total source strength (neutrons/sec),
reflection coefficient of the ground
(a1 bedo),
relative source strengfh per steradian at
ungle a between emergent ray and source
axis,
height of source and receiver above the
ground,
~-
1
sin' acos2 4
(? - 2 - cos Oeot asec +
angle between source axis and source-
receiver axis,
separation distance between source and
receiver.