Translational-invariant excitons

Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of excitons interacting with a phonon field leads to a nonzero contribution of phonons into the exciton ground state energy only in the case of weak or intermediate electron-phonon coupling. A conclusion is made that self-trapped excitons cannot exist in the limit of strong coupling. Peculiarities of absorption and emission spectra of translation invariant excitons in a phonon field are discussed. Conditions when the hydrogen-like exciton model remains valid in the case of electron-phonon interaction are found.