The reflected slab and sphere criticality problem with anisotropic scattering in one-speed neutron transport theory

Abstract

Abstract The one-speed transport equation is applied to a homogenous, one-dimensional multiplying medium with linearly anisotropic scattering. Case's singular eigenfunction method is used to formulate the criticality conditions. In addition to available bi- ortogonality relations in the literature, some parallel relations are derived to obtain the solution. In a previous study dealing with only isotropic scattering, it has been shown that the normal-mode expansion of Case also serves to evaluate the complete spectrum of a critical system. As an extension, the spectrum of critical thicknesses and eigenvalues of a slab (also sphere because of its relation to the antisymmetric solution of a slab) are determined by using the formulation established here. The results of this study including some numerical data relevant to the method employed are presented.