The orientational relaxation of methane molecules in the solid phase II at low temperatures

A model for the dynamics of the coupling between the orientations of the ordered CH₄ molecules in phase II of solid methane at low temperatures is proposed. The model is equivalent to the dynamics of disordered solid hydrogen. The effective interaction strength is determined by the overlap of the librational ground states in the molecular field potential and vanishes in the classical limit. An approximate expression for the effective interaction strength is derived, showing an exponential dependence on the uncertainty of orientation in the librational ground states. This parameter is estimated from the experimental values of the tunnel energies. The second moments of the spectral densities of several anisotropic operators are evaluated in the infinite temperature limit. The resulting gaussian approximations for the spectra are applied in a derivation of the spin lattice relaxation time. The calculated values of the spin lattice relaxation time are compared to experiment.