Half-space General Multigroup Transport Theory*

A method for solving various half-space multigroup transport problems for the case of a general transfer matrix is explained. A non-linear integral equation for the emergent distribution of the albedo problem is derived. Then, by using the full-range completeness of the infinite medium eigenfunctions, the distribution inside the half-space is obtained from the emergent distribution. Finally, the Milne problem and the half-space Green’s function problem are solved in terms of the emergent distribution of the albedo problem and the infinite medium eigenfunctions. One advantage of this method is that it readily yields numerical results for emergent distributions of half-space problems. Even for the numerical evaluation of a particular solution inside the halfspace, this technique is felt to be superior to other exact half-space methods since only full-range eigenfunction expansions are employed rather than the more difficult half-range expansion used in other techniques.