Optical Response Functions of theFCenter

Abstract

The lattice dynamics of the $F$ center in its electronic ground state in NaCl, KCl, KI, and KBr crystals is considered in connection with the defect-induced electronic Raman spectra, and the lattice and electronic absorptions. Two different dynamical models are adopted: (a) a change in the central force constant $\lambda$ between the defect and the nearest neighbors (nn), and a change in the central force constant $\gamma$ between the nn ions and the fourth neighbors; (b) a change in the central and noncentral (${\lambda }^{\prime }$) force constants between the defect and nn's, and a change in central force constant (${\lambda }^{\prime \prime }$) between the defect and next-nearest neighbors. $\lambda$ and $\gamma$, are estimated by means of calculations based on the available wave functions. For the electronic absorption and Raman spectra, we work in the approximation of a linear electron-phonon interaction, and the coupling constants are derived from the experimental stress coefficients. The dynamical input data were taken at 0°K temperature. Good agreement is found between the experimental data and the absorption-band shape parameters, when the corrections coming from the anharmonic effects are taken into account. Some discrepancies between the theoretical results and experimental data are found for the first-order Raman scattering spectra. They are explained in part by means of the bulk anharmonicity, and in part by means of the local anharmonicity. The existence of a strong peak is predicted in KI Raman spectra, due to a Raman active mode in the gap. As regards the infrared properties of the $F$ center, we have found resonance and gap mode frequencies in the calculated absorption spectra of KBr ind KI; their dependence on the long-range forces of the lattice is briefly discussed.