Analytic solutions to several forms of the one-dimensional multigroup diffusion equation

A simple benchmark problem is defined as a demonstration of analytic techniques for solving various forms of the one-dimensional multigroup diffusion equation. Exact solutions are presented for the forward and regular adjoint fluxes for the fundamental and several higher modes. In addition, the generalized importance functions for two particular response functionals are obtained, and several perturbation integrals are tabulated. All computations are performed using four energy groups and an one-dimensional axial model of an HTGR core configuration