FCenter in Ionic Crystals. II. Polarizable-Ion Models

The states of the $F$ center are considered on the basis of models which treat the movement of the nearest neighbors to the $F$ center and the $F$ electron in a self-consistent manner. The lattice is first described in terms of a classical ionic-crystal theory. The theory is then extended to treat the nearest-neighbor ions in a quantum-mechanical manner. The one defect electron (the $F$ electron) is treated according to polarizable-ion models. The absorption energy, the emission energy, the lifetime of the first excited state, the zero-phonon transition energies, and the Huang-Rhys factors are evaluated for two models, which differ in the rigor used to compute the polarization of the nearest and next-nearest neighbors. It is found that the model that contains the more rigorous evaluation of the polarization agrees best with the experimental results for CaO and perhaps MgO. In addition, it is found that both these models are least successful for $F$ centers in NaCl and KCl. Not enough data exist to make judgments about the agreement for Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$.