Some Applications of a Spectral Representation of the Linear Multigroup Transport Problem

The spectral representation of the linear multigroup transport problem is applied to two examples. In the first example, we obtain the dispersion relations, normalization coefficients, and eigenfunctions for any order N of scattering by using the eigenfunctions for isotropic scattering as the basis. In the second we obtain the dispersion relations, normalization coefficients, and eigenfunctions for N+1 order scattering by using the eigenfunctions for Nth order scattering as the basis. New identities relating quantities referring to different orders of scattering are obtained as well as identities involving spectral integrals and moments of eigenfunctions. Independent calculations are carried out to verify relations obtained using the spectral representation. In 1981, Kanal and Davies obtained similar results for the case of the one-velocity transport theory.