A four-group analytic rod transport problem for (n, γ) and (n, n′γ) verification

Forward and adjoint transport problems are solved analytically on a homogeneous rod (the forward-backward model) with four energy groups. Groups 1 and 2 represent fast and thermal neutrons; groups 3 and 4 represent gamma rays born from thermal neutron capture and fast neutron inelastic scattering, respectively. Neutron scattering includes self-scattering and downscattering. There is no fission. Gamma rays are treated as lines, so gamma-ray scattering is ignored. Neutron scattering and gamma production are isotropic. In the forward problem, there are neutron sources incoming at the rod endpoints but no internal neutron sources; there are no extrinsic gamma sources. In the adjoint problem, there are gamma detectors at the rod endpoints but no neutron detectors anywhere. PARTISN results agree to seven significant figures with the analytic results in a numerical benchmark problem using hydrogen and carbon. The equivalence among the rod transport problem, diffusion theory, and the S2 discrete ordinates method is demonstrated for didactic purposes.