Effects of Dynamic Lattice Distortions on the Structure of theFBand in the Cesium Halides

The smooth, nearly Gaussian, optical absorption band of $F$ centers in most alkali halides contrasts with that observed at low temperatures in the cesium halides, where two or sometimes three components are partially resolved. A strong spin-orbit coupling could account for two components, but the third has remained a mystery because of the cubic symmetry of the alkali-halide lattice. The calculations of this paper show that the cesium halide $F$-band structure can be explained by the instantaneous distortion of the $F$ center's environment from cubic symmetry induced by the motion of the lattice. We calculate the optical absorption line shapes and the low-temperature magneto-optic properties of the $F$ center by using perturbation theory to describe the noncubic electron-vibrational interactions in the limit of strong spin-orbit coupling and by using the Frank-Condon approximation to treat the distribution of vibrational distortions of both cubic and noncubic symmetry. The approximate line shapes obtained have three components corresponding to the three excited state Kramers doublets and can be brought into good agreement with the experimental results for CsI, CsBr, CsCl, and CsF by a suitable choice of the interaction parameters for each material. The same parameters satisfactorily account for the observed circular dichroism and Faraday rotation. A qualitative explanation of the effect of changing the halogen is given in terms of the physical properties of the halogen ions and the manner in which their motion diminishes the cubic interactions and enhances the noncubic interactions. The influence of the temperature upon the structure is also discussed. The different relative strengths of the various interactions account for the striking contrast between the cesium-halide $F$ bands and those observed in the salts which have a relatively light alkali.