FCenters in Ionic Crystals: Semicontinuum-Polaron Models and Polarizable-Ion Models

The three lowest-lying $F$-center states for KCl, CaO, and Ca${\mathrm{F}}_2$ are calculated within the framework of five semicontinuum-polaron models and one polarizable-ion model. The movement of the nearest-neighbor ions to the $F$ center and the $F$ electron are treated in a self-consistent manner in these models. Exact solutions to these models for the states involved in the transitions of optical absorption and emission are obtained numerically. In addition, the internal Stark effect due to noncubic phonons is estimated. The absorption energy, the emission energy, and the lifetime of the first excited state are evaluated for the six models. It is shown that a semicontinuum-polaron model agrees best with the experimental results for KCl and that the polarizable-ion model gives the best results for CaO and Ca${\mathrm{F}}_2$. In addition, the semicontinuum-polaron model and the internal Stark effect predict that the relaxed excited state in KCl consists of a strong mixing of $2p$-like and $2s$-like states which are spatially diffuse.