Electronic Polarons in Alkali Halides

The effect of electronic polarization on an electron in the $s$-like conduction band, described by the tight-binding approximation, is studied using both the Green's function and perturbation methods. A criterion for the validity of the second-order perturbation method is derived. It turns out that the second-order perturbation method is valid even for large values of the coupling constant due to the exciton energy being considerably larger than the conduction-band width. The behavior of the polaron band and effective mass is examined as a function of the coupling constant, of the parameter $\lambda$, which represents the extent of localization of the atomic orbital, and of the exciton energy. For a given crystal, polarization effects are found to increase as the wave vector $\overrightarrow{\mathrm{k}}$ increases. The present results are compared with previous results which apply only near $\overrightarrow{\mathrm{k}}=0\mathrm{}$, and with the results obtained by classical theory.