Geodesic
Dispersion of the permittivity tensor of ionic crystals in the exciton region
Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 415-423

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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. 
@article{TMF_1974_21_3_a11,
     author = {A. F. Lubchenko and V. M. Nitsovich and N. V. Tkach},
     title = {Dispersion of the permittivity tensor of ionic crystals in the exciton region},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {415--423},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a11/}
}
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A. F. Lubchenko; V. M. Nitsovich; N. V. Tkach. Dispersion of the permittivity tensor of ionic crystals in the exciton region. Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 415-423. http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a11/