Raphael Aronson

Critical problems for bare and reflected slabs and spheres

High-order P /SUB N/ calculations of critical radii are carried out for both bare and reflected spheres in the one-speed model and also of critical half-thicknesses for slabs. Results are compared with published data where possible. It is found that P /SUB N/ calculations diverge for sufficiently large N, although good results are still obtained provided that the critical radius is not too small.

Subcritical Problems in Spherical Geometry

The results of high-order P /SUB N/ calculations for the one-speed albedo and Milne problems in spherical geometry are presented. The computations were performed by the transfer matrix approach. The analysis is included in the paper. Reflection probabilities are given for spheres of various radii and for the region exterior to spheres: reflection and transmission probabilities for spherical shells and extrapolation lengths for the exterior Milne problem. The method is found to diverge for sufficiently high values of N--the smaller the radius, the more rapidly divergence sets in. For moderate and large radii (greater than or equal to 2 mfp), the method nevertheless gives generally excellent results.

Nonuniqueness of boundary conditions in the spherical harmonic method-a reprise

The authors rederive the Federighi-Pomraning boundary conditions for spherical harmonic calculations in transport theory in order to make explicit the original implicit assumptions in Federighis derivation. In so doing, they put into perhaps its clearest form the old controversy about the uniqueness of these boundary conditions. One new point is that even Federighis final equation does not have a unique solution, though the recursive procedure that he uses to get numbers does have only one stable solution.

Some Results of Transfer Matrix Calculations for Thermal Neutrons

The transfer matrix method is used to solve the Milne problem for a half-space for neutrons interacting with a moderator at temperature T. Two different scattering models are considered. They are the free monatomic gas of arbitrary molecular mass with constant cross sections in the center-of-mass system, and the Nelkin kernel for water. Both models permit an additional 1/v absorption cross section. The authors have obtained accurate numerical values for the diffusion length, the extrapolated end point, the critical absorption strength, and the boundary heating for a variety of values of the parameters. Comparison is made both with other calculations and with experiments.