Eigenvalue Spectrum of Multiplying Slabs and Spheres for Monoenergetic Neutrons with Anisotropic Scattering

Abstract

The transport equation for monoenergetic neutrons with linearly anisotropic scattering has been solved numerically with a method developed by Carlvik. Homogeneous multiplying systems in the form of spheres and infinite slabs were studied with boundary conditions of no incoming neutrons. Tables are given of six or more eigenvalues for an average cosine of the scattering angle ranging from 0 to 0.3 and for various dimensions of the bodies. With increasing anisotropy, there is an increasing number of complex eigenvalues that extend to lower modes and larger bodies. For spheres, tentative curves of the eigenvalue spectrum are given.