An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part III: Uncertainty Propagation and Multigroup Covariance Matrices

An analytic benchmark for nuclear data uncertainty propagation in k-eigenvalue calculations is demonstrated. Flat-flux-weighted cross-section covariance matrices are available in the ENDF/B library for many isotopes. For application-specific purposes, flux-weighted multigroup cross sections with carefully constructed energy group boundaries are desired. In this paper, we use the covariance information from ENDF/B-VII.1 for the defined continuous-energy cross section and an artificially inflated variance version of the same covariance matrix for first-order and Monte Carlo propagation of uncertainty calculations. A flat-flux weighting function is used for the continuous-energy cross-section uncertainty collapse resulting in a higher propagated uncertainty on the k-eigenvalue as the group structure becomes coarser. The results of this analytic benchmark suggest that the reporting of flat-flux-weighted multigroup cross-section covariance matrices at the ENDF level may lead to inaccurate predictions of the uncertainty on the k-eigenvalue for certain applications. This work implies that not only should the resonance parameter uncertainties that go into the calculation of the continuous-energy cross sections be published, but the parameter uncertainties should also be processed into continuous-energy cross-section uncertainties that can be collapsed to application-specific multigroup cross-section covariance matrices.