Expansion About a Local Maxwellian for Evaluating the Spatially Dependent Neutron Spectrum

The problem of the spatial variation of thermal-neutron fluxes is investigated in the framework of energy-dependent diffusion theory. Neutron flux is expanded here in terms of Laguerre polynomials in energy, weighted with a local Maxwellian distribution in which the neutron temperature depends on the space variable. The method proposed is applied to the diffusion of thermal neutrons in moderating systems with a nonuniform temperature profile.