Subcriticality and supercriticality of energy dependent neutron transport in slab geometry

The energy dependent transport system in an anisotropic medium in slab geometry subjecting possible internal source q and incoming fluxes psi0, psi1 is discussed. It has been shown in an earlier paper that under certain conditions on the average number of secondary neutrons per collision c, the scattering cross section sigma, and the optical slab length 2a, this system has a unique nonnegative solution for all inputs q, psi0, psi1. The aim of this paper is to establish analogous conditions on c, sigma, a so that the system has no nonnegative solution when there is either internal source or incoming fluxes (or both), and it only has the trivial solution when neither internal source nor incoming fluxes are present in the system. This conclusion together with the earlier results yield explicit conditions for insuring the supercriticality and the subcriticality of the energy dependent system and therefore lead to analytical upper and lower bounds for the critical value c* in terms of sigma and a