Intensities of multipole-induced zero-phonon transitions in solid parahydrogen

Theoretical expressions are given for the intensities of zero-phonon single and double transitions in solid parahydrogen arising from the isotropic $2^{\mathrm{l}}$ multipole induction mechanism. Comparisons between theory and experiment for l=2 and 4 [corresponding to $S_{v\mathcal{’}}$(0) and $S_{v\mathcal{’}}$(0)+$Q_{v\mathcal{’}\mathcal{’}}$(0) and $U_{v\mathcal{’}}$(0) and $U_{v\mathcal{’}}$(0)+$Q_{v\mathcal{’}\mathcal{’}}$(0) transitions, respectively] have been given previously, and the results are in reasonably good agreement. A direct comparison is not possible for the recently observed l=6 [$W_{v\mathcal{’}}$(0) and $W_{v\mathcal{’}}$(0)+$Q_{v\mathcal{’}\mathcal{’}}$(0)] transitions because of the unavailability of ab initio values of the vibration-rotational matrix elements of the 64-pole moment function, or for the as yet unobserved l=8[$Y_{v\mathcal{’}}$(0) and $Y_{v\mathcal{’}}$(0)+$Q_{v\mathcal{’}\mathcal{’}}$(0)] transitions. Modifications of the intensities of the $W_{v\mathcal{’}}$(0) transitions due to the mixing of rotational levels by the quadrupole-quadrupole interaction have been calculated, and they contribute less than 1%. These corrections are smaller than those due to phonon renormalization and thus will not appreciably affect the magnitudes of the 64-pole moment matrix elements deduced from the experimental intensities.