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Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

Information was received from
ference

of lead and bismuth gamma shielding. The shield thickness used there is

8"; our calculations had indicated that 4" of Pb was adequate, for which it

As a check on the
for an 8" spherical shell, as sketched below.

Analysis: the flux equations for the carbon and shield are

In the three regions, solutions are assumed

Boundary conditions are taken as follows:
φ

I = 1 at the surface of the core. Normalization to

A comparison between the coefficients E for lead and bismuth serves to
termine

shape of the flux curve will be

By the application of standard, methods of solution (
including calculation of the K's (reciprocals of the thermal neutron diffusion

lengths) and the λ's (transport mean free paths), the coefficient E is

The general solution is:

The constants used were:

c = 0.020 cm-1 ;c = 2.72 cm1 = 66 cmpb = 0.085 cm-1 ;Pb = 2.33 cm2 = 86.3 cmBi = 0.0187 cm-1;Bi = 3.85 cm

For the case of 8" of lead, E is 0.185; for 8" of bismuth E is approximately
1, (which is expected because the diffusion lengths for C and Bi are about

the same). Thus the flux with a lead shield is about 1/5 that with a bismuth

shield. No account is taken of impurities in either case. A separate

calculation with a 4" lead shield leads to a factor of 1/3, which would not

be too serious a drop. The problem thus rests on the necessary shield