Rotational Correlation Functions in Neutron Scattering by Molecular Gases

Abstract

The incoherent neutron scattering cross section of molecular gases is evaluated in terms of classical rotational time correlation functions. The calculation emphasizes the Gaussian behavior of the intermediate scattering function but also treats non-Gaussian effects. Explicit expressions applicable to spherical, linear, and symmetric molecules are given and applied to C${\mathrm{H}}_4$, HCl, and N${\mathrm{H}}_3$. Comparisons with exact quantum-mechanical calculations and experimental data show the Gaussian approximation to be reasonably accurate. In the case of C${\mathrm{H}}_4$, the inclusion of the leading non-Gaussian term brings the agreement to within about 1% of the exact results. The present approach considerably reduces the amount of computation relative to exact calculations; moreover, it permits a physically intuitive and potentially tractable extension to liquids and solids.