Vibronic Spectra and the Shell Models

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Abstract
The Cochran-Cowley shell model and the Schroeder breathing shell model for the lattice dynamics of ionic crystals have been checked against experimental vibronic sidebands. The latter accompany pure electronic transitions localized at optically active ions in the crystal. The structure of such sidebands depends directly on the vibrational eigenvectors, in contrast to inelastic neutron scattering results, which depend more directly on vibrational eigenvalues. Vibrational eigenvectors and eigenvalues for a number of alkalihalide crystals are computed throughout the Brillouin zone via the shell models. On the assumption that the coupling between the vibrations and the optically active ions is Coulombic, the amplitude and frequency distribution of the sidebands are calculated. Good qualitative agreement between theory and experiment is reached, although the over-all quantitative agreement is poor. Barring unexpected complications caused by the presence of probe ions in the crystals, or a breakdown of the Born-Oppenheimer approximation, the present results indicate that the shell models overestimate the magnitude of the dynamical electronic polarization in certain regions of the Brillouin zone.