The neutron flux in a spherical void

Using the basic theory developed in our earlier work (Cassell, J.S., Williams, M.M.R., 2005. Particle flux in an annular gap about a sphere, Annals of Nuclear Energy 32, 457, we have evaluated the neutron flux across a spherical void due to a point source in a moderating and absorbing medium. Neutron motion in the moderator is described by diffusion theory and that in the void by the free streaming Boltzmann transport equation. An explicit solution is obtained in the form of an infinite series. This is evaluated numerically for a number of practical cases and comparison is made with an exact transport calculation using a Monte Carlo code. The hybrid method is seen to be highly accurate.