Temperature interpolation of the phonon distribution for accurate preparation of the thermal neutron scattering law

Accurate computational modeling of nuclear reactor systems requires that appropriate nuclear data be provided for the relevant materials. In systems where slow-moving neutrons are of great importance, thermal neutron scattering distributions are prepared using either a free-gas model or, more accurately, a phonon distribution. For materials that experience significant thermal expansion, the phonon distributions are temperature dependent and thus the thermal scattering distribution generated at a certain temperature should use a phonon distribution corresponding to that same temperature. In Monte Carlo simulations when a phonon distribution is not readily available at the desired temperature, the scattering cross sections and angular distributions can be generated at nearby, bounding temperatures, and a neutron can sample which distribution to follow. An alternative to this approach would be to interpolate the phonon distribution prior to generating a scattering kernel, and this interpolated phonon distribution would be processed at the desired temperature. In this paper, we compare these two approximations, and find that interpolating the phonon distribution better replicates the true behavior (that is, the results generated using the true phonon distribution that corresponds to the desired temperature). Additionally, the option to simply process the desired thermal scattering data using the phonon spectrum of a nearby temperature is also briefly discussed and compared to the two aforementioned interpolation methods. (authors)