Neutron transport theory

Steady state solutions to the Boltzmann transport equation were obtained
for the transport of neutrinos across a finite, plane parallel slab
using discrete ordinate methods. Semi-analytic solutions were obtained
in the case of isoenergetic, isotropic scattering for one energy group
and in the restricted case of isoenergetic and nonisoenergetic (Compton),
isotropic scattering between two energy groups where the isoenergetic
and the Compton scattering rates are the same for the two groups. For
these two cases solutions were obtained for total optical thicknesses
of 0.2, 2, and 20. When the Compton scattering rates of the two energy
groups are allowed to be different, the transport equation becomes nonlinear
due to the exclusion principle. For this case a numerical scheme
was developed which yielded solutions for slabs having optical thicknesses
up to unity.