Bondarenko method for obtaining group cross sections in a multi-region collision probability model

Correct multigroup cross sections are essential to modeling the physics of nuclear reactors. In particular, the presence of resonances leads to the well-known self-shielding effect that complicates any procedure for obtaining group cross sections. The Bondarenko method for producing self-shielded group cross sections is widely used. For heterogeneous systems, the approach requires the use of an escape cross section that captures the probability that a neutron will leave a cell without interaction, and simple approximations are typically used for this purpose. Here we provide a concise derivation for how to determine group cross sections using the Bondarenko method with an extension to multi-region collision probability models. The accuracy of the method is demonstrated by comparing group cross sections derived this way with those produced by Monte Carlo simulations of thermal and fast spectrum reactors.

► A concise derivation for how to determine group cross sections using the Bondarenko method.
► A general extension to multi-region collision probability models.
► The method is demonstrated by comparison to Monte Carlo simulations.