The Frenkel exciton lattice sum is evaluated for a simple cubic crystal using a retarded dipole-dipole interaction. Long-range terms in the retarded interaction cause a singular behaviour of the exciton energy E q when the exciton quasi-momentum q approaches the retardation wave number k = ( E ξ - E 0 )/ hc . However, it seems likely that this singular behaviour of the exciton energy would not occur to such an extent in an improved model which took damping and linewidth into account.
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John Avery (1966) studied this question.
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