Energy Spectrum of a Bound Polaron

Energies of the ground state and of a few low lying excited states of a conduction electron coupled simultaneously to an attractive Coulomb potential and to a longitudinal optical phonon field of the crystal lattice are obtained in analytic forms. The coupling describing the interaction between the electron and the phonon field is assumed to be weak and therefore second order perturbation theory as formulated by Dalgarno and Lewis is used. The values of 1s → 2p and 1s → ∞ transitions thus obtained are compared with those observed experimentally in the far infrared optical absorption in silver halides and semiconducting CdF2 and a good agreement is found. A comparison between the theoretical results, obtained and those of others is presented.