Solution of the thermal neutron diffusion equation for a two-region system by perturbation calculation

Abstract

The paper presents a method of solving the diffusion equation for the thermal neutron flux in a heterogeneous medium. Perturbation calculation is successfully applied for a cylindrical concentric system after testing this method for a spherical concentric geometry, analytically solved by Czubek (1981). The method makes possible the calculation of the thermal neutron decay constant and the space distribution of the thermal neutron flux in a two-region system. The condition of a constant value of the neutron flux in the inner part of the system must be met in this method. This method has an application in the measurement of the thermal neutron absorption cross-section (Czubek 1981).