Analytical solutions to the moment transport equations--i : One-group one-region slab and sphere criticality

Abstract

Analytical PN and AN moment criticality solutions are obtained for uniform infinite slabs and finite spheres using Mark, Marshak and importance-weighted vacuum boundary conditions. Comparison with 'exact' criticality results leads to reevaluation of the literature-reported 'belief' in the relative accuracy comparisons of Mark and Marshak boundary conditions. The ranking for these problems is Mark, Marshak, importance-weighted in order of increasing accuracy.