Vibronic Model for the Relaxed Excited State of theFCenter. II. Perturbation Analysis for Weak-Coupling Limit

A perturbation solution is given for a vibronic model for the relaxed excited state of the $F$ center, in the limiting case of weak electron-phonon coupling. The resulting predictions of the model are compared with available data on radiative lifetimes, Stark effects, magnetic circular polarization, and stress-induced polarization of $F$-band luminescence in alkali halides. It is shown that a consistent quantitative interpretation of most of these data is possible on this basis if the $2s$ electronic state lies below the $2p$ state in the relaxed cubic configuration by an energy difference which is ∼ 0.09 eV for KCl and ∼ 0.15 eV for KF. The long radiative lifetime should then be attributed predominantly to the $2s$ state being only weakly coupled to the $2p$ state by the phonons, rather than to spatial diffuseness of the $2p$ state. The model also accounts for the observed ratio of the electric-field-induced change in the radiative lifetime to the field-induced polarization of the luminescence, for the temperature dependence of the radiative lifetime and field-induced polarization, and for the absence of any such temperature dependence in the stress-induced polarization.