k=0Libron Spectrum for Solid Hydrogen in thePa3 and CmmmStructures

The libron wave spectrum at zero wave vector for solid hydrogen in the $\mathrm{Pa}3\mathrm{} \mathrm{and} C_{\mathrm{mmm}}$ structures is calculated at zero temperature. Interactions other than the electrostatic interactions between molecular quadrupole moments are treated perturbatively. Comparison of our numerical and analytic results for libron frequencies and Raman intensities with the observed Raman spectrum gives strong evidence for the $\mathrm{Pa}3\mathrm{}$ structure. The scaling relation between the frequencies of the classical and quantum-librational systems is found to hold for the $\mathrm{Pa}3\mathrm{}$ but not for the $C_{\mathrm{mmm}}$ structure. The effects of zero-point librations and libron-libron interactions are studied to lowest order in $\frac{1}{z}$, where $z$ is the number of nearest neighbors. Although the static effects are quite small, the shifts in the libron frequencies due to these interactions are of order 15%.