Application of a Variational Method to Milne's Problem

Abstract

An approximate solution of Milne's integral equation for the neutron density is obtained by a variational method with high accuracy in simple analytical form. The extrapolated asymptotic density at the boundary is given by this method correct to 0.4 parts in a million. The density itself has a maximum error of 0.3 percent which occurs at the boundary and of less than 0.05 percent for all distances beyond 0.05 mean free paths. A simple expression for the angular distribution of emerging neutrons is also obtained.