Effect of Equivalence on Calculations of the Doppler Effect in Thin Lumped Absorbers

Calculations of the Doppler effect on resonance absorption, which assume equivalence, are shown to underestimate the effect in thin lumped absorbers where the mean chord length is of the order of the resonance-neutron mean-free-path. This error results from the deviation of Wigner’s rational approximation, both the original and as modified by Otter, from the exact escape probability in this region. Results for ²³⁸U using the computer programs ZUT (with exact escape probabilities) and TRIX (assuming equivalence) are compared. A new temperature-dependent modification to Wigner’s rational approximation is developed and shown to improve agreement between calculations using equivalence and those using exact escape probabilities. Calculations are made for thin ²³⁸U metal and oxide slabs in the surface area-to-mass range of 1 to 40 cm²/g and at temperatures up to 2000°C.