The Neutron Density Near a Plane Surface

Abstract

The exact solution of Milne's integral equation is expressed as a real integral with nonoscillating integrand. This expression has been derived from the Wiener-Hopf solution for the Laplace transform of the density. The integrand involves the angular distribution of neutrons emerging from the surface, and the tabulation of this function by the Mathematical Tables Project given by Placzek has been used in the numerical evaluation of the integral. The values of the first three moments of the difference between the density and the asymptotic density, and an expansion of the density for points near the boundary are also given. Various authors have proposed or obtained approximations to the solution of this problem, and some of these approximations are referred to and compared with the exact solution.