Binding of carriers by an external potential in the presence of electron-phonon coupling

The binding of carriers by an external potential in the presence of a weak long-range electron-phonon coupling with longitudinal optical phonons is considered. This coupling results in a nonlocal effectively attractive contribution in the Schroedinger equation that makes the formation of a bound state possible in weaker potentials. As a physical example the potential of a charge cluster in heavily doped polar semiconductors is considered