Abstract :
The source-sink method has recently assumed some importance in the understanding of the neutronic behaviour of spatially stochastic media. In view of this it is important that one of the fundamental parameters used in the method, namely Galaninʹs constant, γ, be accurately known. To this end we describe herein methods for calculating γ for isolated slabs and spheres using integral transport theory. The problems solved are the cases of a slab and a sphere embedded in an infinite moderating material which contains a spatially constant source. The problem is simplified by using a special transformation by which the infinite reflector is effectively replaced by a modified kernel of the integral equation and integration is over the slab or sphere only. For the slab problem, this procedure is valid for arbitrarily spatially varying cross sections, but for the sphere it is restricted to the case of a spatially constant total cross section. Very accurate results are obtained for some important integral parameters, e.g. the average flux in the body, the blackness, the extrapolation distance and Galaninʹs constant. We believe that some results for the sphere have not appeared before and therefore offer them as benchmark values. We have also noted that simple diffusion theory gives remarkably accurate values for Galaninʹs constant over a wide range of material properties and optical thicknesses. For this range, it is never more than 12% in error. Some illustrative tables and figures are given to show typical values and also how the flux varies within the slab and its reflector.
