Calculation of neutron cross sections and thermalization parameters for molecular gases using a synthetic scattering function. I

Based on a synthetic scattering function describing the interaction of thermal neutrons with molecular gases, we developed analytical expressions for cross sections of interest in reactor-physics calculations; these are the zero- and first-order angular moments of the double-differential cross section, ${\sigma }_0$($E_0$,E) and ${\sigma }_1$($E_0$,E), respectively, and the total scattering cross section σ($E_0$). The formulas presented here allow then a very fast and reliable evaluation of thermalization parameters and transport coefficients at any desired temperature of the moderating media. One of the main applications of this study is the generation of (thermal) nuclear data libraries for reactor codes, using a minimum set of input information. In the following paper, calculations based on our formulas are compared with experimental data and other theories for some commonly used moderators under different physical conditions.