Simple benchmark for evaluating self-shielding models

Accounting for self-shielding effects is paramount to accurate generation of multigroup cross sections for use in deterministic reactor physics neutronics calculations. Historically, equivalence in dilution and subgroup techniques have been the preeminent means of accounting for these effects, but recent work has proposed new solutions, including the Embedded Self-Shielding Method (ESSM). This paper presents a very simple benchmark problem to compare these and future self-shielding methods. The benchmark is perhaps the simplest problem in which both energy and spatial self-shielding effects are important, a two-region problem with a lumped resonant material. A single resonance in a single energy group is considered. Scattering is approximated using the narrow resonance approximation, decoupling each energy value and allowing an easily-computed reference solution to be obtained. Equivalence in dilution using two-term rational expansions and the subgroup method were both found to give very accurate solutions on this benchmark, with errors less than 1% in nearly all cases. One-term rational expansions and ESSM showed much larger errors