Theory of phase transitions in solid methanes. XIV. The total neutron scattering cross section in phase II of solid CH4

Abstract

The total neutron cross section in phase II of solid CH4 is calculated as a function of the incident energy E0 and the temperature in the ranges [Formula: see text] and [Formula: see text]. The sample is assumed to be a polycrystal and the neutron beam to be unpolarized. The total cross section consists of two parts: proton spin-independent and dependent parts. The latter is given by a sum of σ0 and σ′. Both the spin-independent part and σ0 come from the elastic scattering and can together be cast in the form [Formula: see text] for both Oh andD2d molecules, where [Formula: see text] is the mean squared proton spin angular momentum within a single molecule. The quantity σ′ depends on the details of the spin–rotational states. The calculated total cross section can again be expressed approximately as a linear function of [Formula: see text] as was empirically found by Lushington and Morrison (Can. J. Phys. 55, 1580 (1977)). A prediction is offered for a possible future experimental study.