Effects of the Laurent and Taylor expansions on the calculations of the thermal neutrons inelastic scattering cross sections for crystalline moderators

The use of updated phonon spectra for the calculation of the scattering matrix, S(α,β,T), of graphite made apparent discrepancies more related to numerical artifacts than to genuine differences. Comparing results from the use of the codes GASKET and LEAPR, with improved phonon spectra, we found consistent results only when a consistent asymptotic region around zero frequency is used. This effect is produced by a second order pole at frequency zero that appears during the calculation of S(α,β,T) via a double Fourier transform. The pole also affects the quadratures at higher frequencies so it became natural to use the Laurent expansion rather than Taylor’s for a more robust numerical method. The results of this analysis were included in the local version of the codes GASKET and LEAPR.