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

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 biortogonality 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. Copyright © 1996 Elsevier Science Ltd.