Effective Hamiltonians and bindings energies of Wannier excitons in polar semiconductors

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Abstract
The interaction of Wannier excitons with an LO-phonon field is investigated in detail. We derive effective local Hamiltonians which may be used to calculate the whole exciton spectrum in a polarizable medium. The constituents of the exciton are no longer treated as two independent polarons. The coupling of the polarons is described by new displacement amplitudes. The ground-state energy is evaluated variationally as an example and the analytic expression for the exciton's self-energy is discussed as a function of the binding-strength. We do not reproduce numerical results for various materials which have been given in previous letters and have been found to compare satisfactorily with experimental data. Meanwhile our results have been used with great success in a variety of more complex problems due to its formal simplicity and its quantitative accuracy.