Deterministic modeling of higher angular moments of resonant neutron scattering

An exact scattering kernel formulation for anisotropic scattering up to angular order 10 has been developed and implemented into a deterministic code. The effects of accounting for lattice dynamics on the modeling of neutron scattering in 235U, 238U, 238Pu, and other nuclides have been demonstrated. The new formulation essentially reproduces other investigators previous results for isotropic scattering and quantifies the departures from the isotropic values when higher angular orders are accounted for. The correct accounting for the lattice effects influences the estimated values for the probability of neutron absorption and scattering, which in turn affect the estimation of core reactivity and burnup characteristics. It is shown that, when using the exact scattering kernel formulation, the probability for upscattering significantly increases with increasing temperatures. For example, upscattering for 238U from below the 20.67 eV resonance increases from 5.57% at 300 K to 30.41% at 1000 K, respectively. Thus, it is shown that the exact scattering kernel is strongly sensitive to temperature, a fact of major importance for High Temperature Reactor fuels. The slowing down process is important in thermal reactors because it results in the neutrons entering the thermal energy range in which the majority of fission events occur. Correctly modeling the slowing down and hence slowing down source into the thermal energy range and consequently allowing the correct modeling of the thermal energy neutron fluxes (or the correct thermal range portion of the spectrum) is paramount to the correct prediction of criticality and safety features such as the Doppler effect. These artifacts are important for all thermal spectrum reactors. In High Temperature Reactors such as the NGNP or the Deep Burn HTR these effects are even more important.