The Greenʹs function method for effective multiplication benchmark calculations in multi-region slab geometry

There are relatively few benchmark-quality solutions for effective multiplication calculations in multi-region multiplying systems. The purpose of this paper is to describe and add a benchmark-quality calculation for such test problems. Greenʹs functions are used to model a multi-region, one-group, isotropically scattering, multiplying system in Cartesian geometry to obtain boundary flux values for an eigenvalue search and subsequent eigenfunction calculation. As usual with multi-region Cartesian systems, the solution is facilitated using (1) Placzekʹs lemma, which allows us to consider a multi-region system one region at a time as an infinite medium, and (2) the calculation of the Greenʹs function solution for a nonphysical infinite multiplying medium. The Greenʹs function method is aesthetically pleasing both for its calculational efficiency and pedagogical clarity, and can, under certain circumstances, perform better than a discrete ordinates code.