An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving flux as neutrons downscatter across resonances nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting resonance structure single-largest cause reactivity uncertainty. Any additional reference solution for critical downscattering problem with phenomena would be a boon to verification validation neutronics codes.This paper establishes benchmark verify accuracy criticality solvers along dimension. For first time, analytic amplitude derived particular case an infinite homogeneous medium isotropic scattering center mass arbitrary number no-threshold, neutral particle reaction (e.g., radiative capture, fission, scattering). Original expressions are established quantify discrepancy between ?k(E) ??(E) amplitudes, respective solutions multiplication factor k, or exponential time-evolution frequency ? eigenproblems. The physical study these relations led analysis their first-order relative difference near condition ?=0. Finally, numerical provided constituted 239Pu, 6.67-eV 238U, isotope flat section, allowing computational resolution current codes. Through novel results, this can serve sensitivity calculations.