Theory of phase transitions in solid methanes. XIII. The differential neutron scattering cross section in phase II of solid CH4

Abstract

Theoretical study of the differential neutron cross section in phase II of solid CH₄ is carried out with special emphasis upon the dependence of the incident energy of the neutron and the scattering angle. Spin–rotational wave functions given by T. Yamamoto, Y. Kataoka, and K. Okada [J. Chem. Phys. 66, 2701 (1977)] are employed, which are obtained on the basis of the extended James–Keenan model. The interference effect of spin‐dependent scattering by a tetrahedral four‐proton system is explicitly taken into account according to Hama and Miyagi’s formalism [Prog. Theor. Phys. 50, 1142 (1973)]. The effect of inter‐ and intramolecular vibrations is included in terms of a Debye–Waller factor. The proton spin‐dependent part of the cross section for an unpolarized neutron beam is calculated in the case of an equilibrium mixture of three nuclear spin species in a polycrystalline sample at around liquid helium temperature. The results are compared with available experimental data and the main features of observed spectra are reproduced by theory. Some predictions are made for future experimental work to deepen our understanding of solid methane.