Jahn-Teller effect and asymptotic behavior of the recursion-method coefficients

In the study of the strongly coupled electron-phonon systems by the recursion procedure, we have examined the asymptotic behavior of the continued-fraction coefficients. Such a knowledge allows us to extend the continued-fraction coefficients and to calculate accurately the absorption band. Furthermore a new technique based on the properties of continued fractions to include Gaussian or other types of broadening has been introduced. This procedure has been applied to the study of the Jahn-Teller effect in the absorption band shape for the 2s-2p electron transition in Ag:Ar. The relevant electron-phonon interaction considered is linear; the phonon symmetries taken into account are ${\Gamma }_3^{+}$ or ${\Gamma }_5^{+}$, and spin-orbit coupling in the p state is included. The theoretical line shape exhibits three different absorption bands, in agreement with previous theoretical calculations and experimental results.