Proton-phonon interaction in ferroelectrics with hydrogen bonds (strong coupling approximation)

The role of the proton-phonon interaction in a crystal of a $\mathrm{KH_2PO_4}$ type is investigated in the strong coupling case. It is shown that the quasipolaron effect causes a renormalization of the tunneling frequency of the protons, in such a way that the latter decreases with the increasing of temperature. An expression for the self-consistent optical phonon frequencies is obtained. The spectrum of coupled proton-phonon vibrations is considered.