The aim of this article is to describe a mathematical model and an associated numerical method for the basic problem of evaluating the void fraction of a slab material from the responses of a typical source-detector system for backscattered neutrons. The mathematical model and void fraction evaluation method reported herein: i) enable us to treat explicitly and exactly a mixed neutron beam, i.e. a neutron beam consisting of a monodirectional component with normal incidence upon the slab material and a component that is a smooth function of the angular variable and ii) allow for an arbitrary order of anisotropy of the neutron scattering phase function. In addition, the associated void fraction evaluation method is free from computer overflow exceptions, even for the challenging problems where the angular quadrature set is of high order and/or the slab material is exceedingly thick. We perform a numerical experiment to illustrate the positive features of both the mathematical model and evaluation method reported here, and we conclude this article with a discussion and directions for future work.
mathematical modeling; discrete ordinates; mixed neutron beams; material void fraction
