A Solution of the Space-Energy-Angle-Dependent Neutron Slowing-Down Problem

A general procedure for solving the space-energy-angle-dependent neutron transport equation is presented. A complete set of eigenfunctions of the transport equation is found under the assumptions of plane symmetry, constant cross sections, and stationary nuclei. The eigenfunctions are shown to be orthogonal with a proper weight function. The slowing-down problem in a hydrogen medium is treated in detail. An analytical solution of this problem is compared with the results of a Monte Carlo experiment.