Second-Order Analysis: Effects of Scattering Cross Sections

Abstract

This chapter presents the results of the computations of the second-order sensitivities of the PERP (polyethylene-reflected plutonium) benchmark’s computed leakage response with respect to the benchmark’s 21,600 parameters underlying the group-averaged isotopic scattering cross sections. The numerical results obtained indicate that the vast majority of the (21,600)² second-order sensitivities with respect to the scattering cross sections were much smaller than the corresponding first-order ones. Consequently, it shows that the effects of variances in the scattering cross sections on the expected value, variance, and skewness of the response distribution were negligible in comparison to the corresponding effects stemming from uncertainties in the total cross sections, which were presented in Chap. 2. On the other hand, it was found that 52 of the mixed second-order sensitivities of the leakage response with respect to the scattering and total microscopic cross sections had values that were significantly larger than the unmixed second-order sensitivities of the leakage response with respect to the group-averaged scattering microscopic cross sections.