Some Results Concerning the Singular Solution of the Conservative Transport Equation in Spherical Geometry

Abstract

We examine in this work one of the exact solutions of the conservative transport equation for isotropic scattering in spherical geometry, specifically the solution that is singular at the origin and vanishes at infinity. Two representations are known for that solution: one expressed as an infinite divergent series that is derived from the spherical harmonics method and another given by an integral that results from the technique of integration along the particle path and is confirmed here by the method of characteristics. We establish a connection between these representations by showing that the Borel sum of the first reproduces the latter. We also examine computational aspects of the solution expressed in various forms and discuss some standing issues related to it.