A Burnup-Compensated Madland-Nix Prompt Fission Neutron Source Term for Multigroup Nuclear Reactor Shielding Calculations

Prompt fission neutrons (PFNs) constitute the most important component of the source term for nuclear reactor shielding calculations. The determination of the PFN source term for reactor shielding calculations has traditionally been performed using a number of simplifying assumptions. Very simple closed analytical expressions are normally used for the PFN spectrum. The Watt PFN spectrum for ²³⁵U, with coefficients determined by Cranberg et al., has become a virtual industry standard in the reactor shielding community. The source term is usually treated as a separable function of spatial location and energy, only the ²³⁵U spectrum is considered, and the effect of burnup on the source term is neglected. In reality, the PFN spectra of ²³⁵U, ²³⁸U, and ²³⁹Pu differ markedly, and their fractional contributions to fission are a function of burnup, which, in turn, is a time-dependent function of the spatial position within the reactor core. Recent theoretical developments have led to the advent of sophisticated microscopic models for the calculation of PFN spectra and multiplicities of various fissioning systems. Spectra for ²³⁵U, ²³⁸U, and ²³⁹Pu, calculated with the Madland-Nix model with fragment spin correction, were used in this investigation. An improved reactor source term model that calculates spectrally and spatially burnup-compensated source terms for nuclear reactor shielding calculations is developed and applied to a typical light water reactor (LWR).,Neutron, gamma-ray, and total absorbed dose rate distributions were calculated through four diverse biological shields with a thickness of 250 cm. At end-of-life core conditions, the traditional source term model leads to an underestimate of the transmitted absorbed dose rates by slightly more than a factor of 2. This discrepancy lies within the error margins quoted for LWR shielding calculations. We conclude that despite their age and simplicity, the Watt formula and the simple source term model are of sufficient accuracy for continued service. The more rigorous source term model presented here may be useful for accurate benchmark calculations and for the design of highly efficient shields for high-burnup reactors.