Development of an equivalent homogenization method with anisotropic scattering few-group constants in the RMC code

The Legendre expansion, widely adopted for representing anisotropic scattering in Monte Carlo multi-group cross section generation, suffers from truncation artifacts that can lead to negative scattering cross sections. This paper develops an angle-discretized macroscopic scattering matrix representation, generated by direct track-length tallying during continuous-energy Monte Carlo transport and used as the working representation throughout a complete Monte Carlo two-step workflow in the Reactor Monte Carlo code RMC. The representation is non-negative by construction across all angular bins, avoiding the negative scattering cross sections that arise from Legendre truncation. Supporting engineering elements required for the complete workflow—including a full-core tallying scheme that mitigates environmental-effect errors associated with reflective single-assembly boundary conditions, and a Monte Carlo–adapted SPH iteration for use within the workflow—are also described. The methodology is validated on a PWR assembly, a MOX fuel assembly with control-rod insertion and withdrawal, a four-assembly mini-core, and the C5G7 benchmark. Reference solutions are obtained from continuous-energy RMC simulations, and the angle-discretized scattering matrices are compared against OpenMC Legendre-expansion results to illustrate the non-negativity property of the proposed representation. Key results include a reduction of the mini-core eigenvalue deviation from approximately 600 pcm under reflective-boundary group constants to 6 pcm under full-core group constants.