ORNL-1771 - Oak Ridge National Laboratory

these integral 5 become
Let
and then
+ -+
Z: Fm+1,? yi(0) = r), F,,z,c 1 Ayp lPc Y,(w)
P
Equating coefficients of identical Y's gives
where
I
I
and
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PERIOD ENDING SEPTEMBER 70, 1954
The source function may be ani sotropic; however,
if an isotropic source is present or if the scattering
law possesses axial symmetry, some simplifications
occur.
When the scattering density has been obtained by
a Fourier inversion, one further integration gives
the flux into an arbitrary unit volume from any
direction; if the detector sensitivity depends on
direction, the total scattering to be counted at any
point P'is represented by o convolution and can be
calculated by another Fourier transformation and
inversion. The method is to be applied to air
scattering measurements taken at the TSF and will
make possible subsequent calculations for unusual
reactor shield shapes,
Thus, if Fm,c is represented as a vector (F,,l,0,F,72, ,,Fm,2, . . .) for al I rn,
Method for isotropic Source and Scatfering. If
the scattering is isotropic after each collision, the
formula to be used for calculating the total flux at
the point P after the nth collision is a convolution:
Fp) = us J j- 1 Fn- ,(P) dVQ +(Q,P) I
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