On the overestimation of ²³⁸U resonance capture by equivalence theory

Extensive analyses of resonance calculation based on equivalence theory have indicated that the resonance capture of ²³⁸U is usually overestimated in a heterogeneous system. We evaluate the overestimation by generating the multi-group absorption cross sections of ²³⁸U in a PWR pin cell problem using Dancoff method with equivalence theory and other rigorous methods. The integral resonance reaction rate over resolved resonance range obtained by an integration procedure based on Narrow Resonance (NR) approximation shows that rational approximation of neutron escape probability is not the primary contributor to the overestimation, and that preserving reaction rate within rational approximation is theoretically superior to pursuing accurate escape probability. It is also implied by our results and analysis that the main contributors are the constant distribution assumption of total cross section and the NR approximation. Consequently, a two-dimensional geometry dependent resonance integral table based on the homogeneous and heterogeneous components of background cross section is suggested as an alternative to the legacy one-dimensional on the sum of the two components.