An improved mathematical model for a void fraction problem in nondestructive testing

The aim of this article is to describe an improved mathematical model for the basic problem of evaluating the void fraction of a slab material by using the responses of a collimated detector from a typical neutron source-detector system. In contrast to previous work, the model reported here: (i) is able to treat explicitly and exactly a parallel neutron beam with normal incidence; (ii) allows for an arbitrary order of anisotropy of the neutron scattering phase function and (iii) provides us with a void fraction evaluation method that is free from computer overflow exceptions even for angular quadrature sets of high order and arbitrarily thick slabs. We perform a numerical experiment in order to illustrate the positive features of the mathematical model and the void fraction evaluation method reported here, and we conclude this article with closing remarks and directions for future work.