Optical response function from Jahn-Teller systems: TheFband in Cs halides

We present the theory for the absorption-band shape of the $F$ band in Cs halides, taking into account the spin-orbit interaction as well as the electron-phonon interactions that induce the dynamic Jahn-Teller effect. We divide the electron-phonon interactions transforming according to the irreducible representations ${\Gamma }_1^{+}$, ${\Gamma }_3^{+}$, and ${\Gamma }_5^{+}$ in intrastate interactions that act on the ${\Gamma }_8^{-}$ and ${\Gamma }_6^{-}$ electronic excited states and in interstate interactions that mix the two electronic states. The evaluation of the imaginary part of the dielectric constants ${\epsilon }^{\prime \prime }\left(\Omega \right)$ is then performed by resumming all the Feynman diagrams determined by the intrastate interactions and by the interstate interactions that enter the Hamiltonian and the dipole-moment operators expressions in the first-order perturbation-theory approximation. We give the results for the absorption-band shape by considering the $t^2$ and $t^3$ terms in the time-dependent phonon propagators. Very good agreement with the experimental data for the $F$ band in CsF and CsBr is found.