Anisotropic Collision Probabilities in Cell Problems

Abstract

A new first-flight collision probability that takes into account the effect of the anisotropic scattering in the moderator is derived in a cylindrical cell. This probability is obtained by expanding the scattering kernel, angular flux and angular source into spherical harmonics series and retaining the first two terms in the integral Boltzmann equation. Making use of a new reciprocity relation and the conservation law, we introduce the probability relevant to a lattice cell under the condition that all neutrons impinging on the cell boundary should reflect with isotropic distribution back into the original cell. This probability also satisfies both the usual reciprocity theorem and the conservation law. Though we have here treated only a 2-medium problem, the method can be easily extended to the problem of a cell containing many regions. As an example of application, we calculate the flux ratios in a two region cell by one-group theory and the neutron spectra in fuel and moderator using the Fermi-age kern...