Relaxed Excited States of theFCenter: A Study of the Nearly Degenerate States of a Bound Lattice Polaron

A method of calculating the nearly degenerate states of a bound lattice polaron is formulated treating the Hartree-type Hamiltonian as the unperturbed Hamiltonian and the interaction omitted in the Hartree-type approximation as a perturbation. This method is applied to study theoretically the relaxed excited states associated with the $F$ emission in a typical alkali halide such as KCl. The resultant theoretical results imply that the lowest relaxed excited state contains about 70% $2s$ character and about 30% $2p$ character and that among all the higher relaxed excited states there are no states which can be well approximated either by the $2s$ or $2p$ type. In addition, adopting the Franck-Condon principle we extend the electronic-effective Hamiltonian derived for the relaxed excited state to the $1s$-like state to which the $F$ emission occurs and calculate this $1s$-like state and thereby the $F$-emission energy. Finally, an expression for the radiative lifetime of a point defect is derived for the case in which the initial states are nearly degenerate and applied to investigate the temperature dependence of the radiative lifetime of the $F$ center.