Dispersion of the permittivity tensor of ionic crystals in the exciton region

The Bogolyubov–Tyablikov method is used to allow simultaneously for the linear and quadratic terms of the exciton-phonon interaction in a calculation of the two-time retarded temperature Green's function of the excitons. It is shown that in the case of weak exciten-phonon coupling the imaginary part of the permittivity tensor can be described by a function of quasi-Lorentzian type, in which the temperature genesis of the parameters is determined by the linear, $\varphi$, and quadratic, $\Phi$, functions of the exciton-phonon coupling. For the interaction of excitons with high-energy phonons the contribution of $\Phi$ to the mass operator may be overwhelmingly important if $\Phi/\varphi>\varphi/\Omega$, where $\Omega$ is the phonon energy.