Evaluation of Resonance Integrals in Homogeneous and Heterogeneous Systems–An Intermediate Approximation

A theoretical approximation, which bridges the gap between NR and NRIA approximations for resonance integrals, is derived, making use of the concept of escape probability in energy space for a single line. The nature of this approach is similar to Goldstein and Cohen λ method, and may be considered a physical interpretation of it, leading to simpler, nearly equal results. The method is applied to the heterogeneous case. Numerical calculations, but neglecting interference scattering, lead to simple fitting formulae for UO₂ and ThO₂ rods at different temperatures; the calculations are in good agreement with experiment.