Slowing down of neutrons in mixtures by the method of green's functions

Abstract

The formulation and approximate solution to the slowing down problem in homogeneous media by the method of Green's functions for a binary mixture of nuclei is presented in this paper. Some numerical examples are included. As a first step, solutions to the purely scattering problem for a binary mixture are obtained in closed form. These elementary solutions are then used as Green's functions for the absorption case. This transformation yields a Volterra integral equation having the correct asymptotic limits for the flux when properly normalized. In general, the resulting integral equation cannot be solved in closed form, thus several approximate results were obtained.