An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part IV: PFNS and $\bar{\nu }$ Uncertainty Propagation

An analytic benchmark with continuous-energy cross sections was previously derived to validate criticality calculations.To extend the utility of the analytic benchmark to verify the implementation of and prompt fission neutron spectrum (PFNS) uncertainty propagation methods, new simplified forms that are dependent on the incident (fission-causing) neutron energy, as well as the outgoing neutron energy for the PFNS, are introduced in this work. The analytical forms for the flux and adjoint flux are derived for the extended benchmark and used to determine the -eigenvalue sensitivity to and PFNS. The -eigenvalue uncertainty due to and PFNS is calculated for the analytic benchmark using simplified and PFNS representations based on the ENDF-B/VIII.0 ²³⁹Pu evaluation. Because of the low sensitivity of the analytic benchmark to the physical PFNS, a nonphysical high-sensitivity PFNS is also presented.