Ground-State Energy of a Wannier Exciton in a Polar Crystal

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Abstract
An analytic expression for the ground-state energy of a Wannier exciton, interacting with the longitudinal-optical-phonon field of the crystal lattice, is derived. The coupling between the constituents of the exciton, i.e., the electron and the hole, and the optical-phonon field is assumed to be weak, and hence second-order perturbation theory as formulated by Dalgarno and Lewis is used. The theoretically calculated value of the ground-state energy is then compared with its experimentally determined values in various polar crystals and a good agreement is found.