Abstract
In the present paper, the Frenkel exciton is discussed in the case of an amorphous solid, taking into account a three-fold degeneracy of the excited one-electron state. It is shown how this degeneracy gives rise to a supplementary diagonalization of a 3 x 3 matrix, resulting in the longitudinal and transversal p-like exciton eigenvalues. Extending a calculation technique of Born and Bradburn, an explicit expression, useful for numerical calculations, is obtained for the exciton energy. This expression depends on the radial distribution function and the interference function, which are the only available information we have about the geometrical structure of the amorphous material.
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