Direct Sampling of the Egelstaff-Schofield Scattering Law and the Phonon Sampling Method for Liquids

Abstract

The phonon sampling method (PSM) enables accurate and efficient simulation of thermal neutron scattering from solids; it obviates a substantial degree of discretization, enabling continuous representations of scattering law behavior across a variety of conditions. Despite these strengths, the PSM relies on the phonon expansion, which only applies to solid materials. To remove this limitation, we demonstrate an efficient sampling algorithm for the nonsymmetric translational 𝒮⁡(𝛼,𝛽) distribution of Egelstaff and Schofield, and show how this can be used to extend the PSM for the simulation of thermal neutron scattering in materials exhibiting mixed translational and vibrational behavior, such as water or molten salts. We demonstrate the correctness of the method with example results for scattering from room temperature water at a few incident neutron energies.