Integral equation approach to the exciton problem for intermediate binding

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Abstract
A new method for computing the exciton states is presented. Fredholm solutions to the integral equation for the expansion coefficients of the exciton wavefunction are obtained making use of Wannier functions. This method seems appropriate to give numerical solutions in the cases where neither the Frenkel-Peierls nor the Wannier-Mott schemes apply, such as in the low lying exciton levels of large gap insulators. The singlet-triplet splitting and the longitudinal transverse splitting are considered. This approach can be naturally extended to the case of resonant excitons and of core excitons.