Cross-section model for cold neutron scattering in solid and liquid methane

Incoherent neutron scattering cross-sections for solid CH4 in the temperature range of 20.4–90.7 K and liquid CH4 at temperatures between 90.7 and 111.7 K are evaluated. A space–time correlation approach is used to describe a double-differential scattering cross-section which is basically expressed by a generalized frequency distribution. The cross-section model includes molecular translations and rotations as well as intramolecular vibrations. The former are concerned with very short-time free-gas like translation, short-lived vibration and long-time diffusion (only in liquid state). The latter consists of short-time free rotation and long-time isotropic rotational diffusion. Numerical calculations on double-differential and total cross-sections are carried out for incident neutron energies covered 0.1 μeV to 10 eV. Good agreement with experimental results at many different temperatures is found.