Isotropic finite surface sources in an infinite medium

In the course of providing numerical benchmarks to the nuclear and medical industries, it is desirable to continually obtain solutions that use the available computational facilities to the greatest possible extent. Analytical benchmarks are generally simple problems, yet they provide numerical results that are numerically accurate to a desired error. Greater accuracy can be obtained at the expense of computational time. The simplest types of problems are usually those that evaluate the scalar flux, and the simplest geometry is an infinite homogeneous medium. However, depending on the source configuration, the scalar flux in an infinite medium can have spatial variation in one, two, or three dimensions. This paper shows how a three-dimensional problem can be generated by considering two-dimensional finite disk and rectangular sources