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where
I = radius of source (taken as the average
radius of each fuel shell),
R = distance from center of fuel shell to
field point,
H(x) 3 heating at a field point due to an infinite
plane source of monoenergetic gamma
rays a distance x away from the field
point.
The second term of Eq. 1 was dropped for these
calculations because of the large radii involved.
The assumptions made were certainly not
consistent with the geometry, inasmuch as the
region between the source shells and the field
point is not everywhere homogeneous. The justification
for this approach was that it appeared to
be as good as could be done without going to a
much more detailed numerical integration over all
source points for each energy group to calculate
the heating at one field point.
In deriving H, it was assumed that the attenuating
medium between the plane source and field
point consisted of infinite slabs of materials
whose thicknesses were determined by their
thicknesses at the equatorial plane of the ART.'
The buildup factor used was of the form
us /.Liti
(2)
where
A(e -1) + 1 ,
A,a parameters of the equation,
pi 3 linear total gamma-ray absorption cross
section (cm-1) for material i,
ti = thickness of material i (cm).
Under these conditions,
r 1
ing (w/cm3) at the fi
S = source strength (w/cm2),
pe E linear gamma-ray energy
section (cm-') for the fi
ti e thickness of the ith slab (c
The S term was determined f
and each energy group by multiplying the source
strength for each group (in w/cm3) by the thickness
PERIOD ENDING JUNE 70, 7956
of the shell. The buildup factor parameters, A and
a, were taken to be those for beryllium. The
p"s, A's, and a's were evaluated at each energy
group.3
The spectrum of prompt gamma rays reported
in ref. 7, 8.8 e-l*OIE photons/Mev*fission, is
different from that reported in ref. 3, 9.61 e-l*OIE
photons/Mev*fission. The former value, which
neglects the variation of (~=/u,)"~~ with energy,
was used in these calculations befiore the correction
was pointed out, Use of the latter spectrum
would change the results reported here by less
than 2%.
The heating by the capture gamma rays in the
outer core shell was calculated with the use of
the same assumptions as those used for the calculations
of the heating by the fuel-region sources,
thqt is, a sphere-to-plane transformation was
made and slab geometry was used for the intervening
mediums betweeh the plane source and
field point. The absorption rate in the outer core
shell was calculated from the output date of
multigroup calculations.5
The spectrum of capture gamma rays in lnconel
was divided into seven energy groups in ref. 3,
but, for this calculation, the first three groups
were combined into one group, and the average
energy of this combined group was taken to be
2 Mev. The fourth and fifth groups in ref. 3 were
taken as the second and third energy groups for
this calculation, and the average energies were
taken to be 4 and 6 Mev, respectively. The sixth
and seventh energy groups in ref. 3 were combined
into one group with an average energy of 8 MeV.
Thus a total of fow energy groups was used in
this calculation. The buildup factor used was that
for beryllium at each energy group. The outer
core shell has an inside radius of 26 cm and a
thickness of 0.381 cm.8
he capture gamma rays in the island core shell
e neglected because of the shielding properties
of the fuel. The heating by the capture gamma
rays in the beryllium reflector was calculated by
using the sphere-to-plane transformation and the
bove, The reflector
spherical shells, that
is, the same shells as those used by the Curtiss-
Wright Corp. in their multigroup calculations of
reactor No. 675.6 The capture gamma-ray source
*Calculations performed by C. M. Copenhaver,
QRNL, private communication to H. Bertini.
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