Rotation—Translation-Coupling Effect in Noble-Gas Crystals Containing Molecular Impurities

Abstract

A generalized perturbation theory has been developed, valid in the case where the perturbation can no longer be considered as small relative to the separation between successive unperturbed energy levels. This is applied to the problem of coupling between the rotational and translational motions of a molecule trapped in a spherically symmetric cell. A representation which is diagonal with respect to the total angular momentum and parity operators has been used, taking advantage of the rotation—inversion symmetry presented by the cell model. It has been found possible to obtain closed expressions for the perturbed energy levels valid in the case of near resonance between rotational and translational frequencies. General expressions for the intensity of rotation—translation transitions have also been derived. A quantitative discussion is given of the effect of finite linewidth on the position of maxima of ``hot'' lines. The theory is applied to the interpretation of the spectra of hydrogen halides trapped in noble-gas crystals. The anisotropy of the crystal field is included and leads to an estimate of 0.5×10−42 esu for the hexadecapole moment of HCl. The limitations of the cell-model treatment due to coupling between molecular rotation and lattice vibrations are discussed.