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ANP PROJECT QUARTERLY PROGRESS REPORT
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LFWi'IX OF
TRANSITION
SECTION (in.)
.
POSITlON
Y( cm)
I
z( cm)
I1
Y( cm)
111
Y( cm) Y( c d
IV
z( cm)
___
0
6
12
18
The neutron dose €or this con-
figuration has been obtained from the
data with water alone by using asiinple
assumption. The dose at a distance r
in water frorn an isotropic point-source
of strength dS(') is
-- . ____ ..........
G(r)
d D(r) = dS - ,
&rr
where G(r) is an undetermined functiori
of r. Integration of this expression
over a source disk of radius a gives,
for a point on the axis at a distance
Z from the source,
where w is the specific source st,rength
in neutrons/cm2-sec, and R is the
distance from the edge of the source
to the detector,
Now, consider the case in which
there is a plane-bounded void of
thickness (r-r' between source and
detector, which are still separated by
a distance r. For a point source,
assume the dose to be
Integrating this as before gives
Since the ratio of r to r' is a con-
(2)This calculation i s mainly based on the
work of E. P. Blizard, Zntroductron to Shreld
Desrgn, Part Z, ORNL CF-51-10-70 (Jan. 30, 1352).
70
43. 1 97.0 61.0 90.9 45.9 23.3
44.8 111.3 62.4 91.9 45.1 40.2
46.0 128 7 63.7 93.7 43.4 55.5
45.4 144.2 62. 3 92. 2 44.5 71.5
- .
stant throughout this integration,
.-I__
--.-._.I
where A' is the distance, in water,
between the edge of the source and the
detector. By referring to a sketch of
the geometry, Fig. 6.8, and to the
previous integral, it is immediately
apparent that this expression is just
the dose at a distance 2' in water
alone from a source of reduced radius
a', where a' is given simply by the
ratio
_I a' - Z' ._
a Z
To find the dose that would be
measured with a source of different
radius, an approximation given by
Blizard to the Hurwitz transformation
from a disk to ari infinite plane
source is used; that is, the trans-
formation is made from the data for
water alone and the actual source
radius, to an infinite plane source,
and from this back to a source of
smaller radius. The approximate ratio
of dose with infinite source to that
with source of radius a is
D(Z',m) ~ 1
>--fa,
8(Z',a) 2
where h is the relaxation length of
the water.