Cross-Section Uncertainty Propagation in the Multigroup Slowing-Down Equations Using Probability Table Formalism

In the frame of neutral-particle (neutron, gamma) transport, the uncertainty propagation calculation regarding the uncertainties on cross sections is often carried out without explicitly taking into account their probabilistic distribution. We investigate a new uncertainty propagation formalism where the cross-section uncertainty distributions are represented by probability tables.

This technical note develops this approach for the steady-state slowing-down equation without upscattering and in an infinite medium. This work is based on a deterministic multiband formalism that takes into account multilevel probability tables for cross sections. The first level represents the variation of cross sections versus lethargy (or energy) in each group of the multigroup lethargy mesh and thus corresponds to the classical cross-section probability tables. The higher levels represent the uncertainties on each step of the first-level cross-section probability table. This method is validated against a Monte Carlo calculation in a case of neutron slowing down in a ²³⁸U-hydrogen homogeneous mixture, showing fully consistent numerical results. The main interest of the deterministic multilevel multiband formalism is that it gives not only the mean value and the variance but also a probabilistic distribution of the fluxes.

In the near future, we plan to investigate more deeply the robustness of this new approach in relation to high values of cross-section uncertainties and to introduce cross-section uncertainty correlations as well. Meanwhile, the promise of this work is its extension to the general transport steady-state equation solved by the discrete ordinates (SN) or Monte Carlo methods.