Microscopic model for the neutron dynamic structure factor of solid methane in phase II

We have constructed a microscopic model for the neutron dynamic structure factor S(Q,ω) of solid methane in phase II. We expect this model to apply for neutron energies below 1 eV at pressures near 1 bar and temperatures below 20 K where methane possesses both free rotation and hindered rotation modes of the tetrahedral molecules in the unit cell. The model treats the motions of molecular translations, intra-molecular vibrations and the free and hindered rotations of methane molecule as independent. Total scattering cross-sections calculated from the model agree with the cross-section measurements for incident neutron energies of 0.5 meV-1 eV. The effective density of states is extracted from the model. We also present the quantitative calculation of the separate contributions of the two different rotational modes to the inelastic cross-section for different methane temperatures in phase II.