Abstract
A study is made of the effect of disorder on the frequency and linewidth of a zone-center Frenkel exciton. It is assumed the disorder is sufficiently weak that the crystal momentum selection rules are approximately obeyed. As a consequence, the k=0 exciton is identified with the zero-phonon line in the optical spectrum. Two examples of disorder are studied in detail. In the first, disorder is introduced in the form of a small number of substitutional impurities. The average T-matrix approximation is used to obtain the shift in the transition frequency to first order in the impurity concentration for arbitrary impurity-host interactions and impurity transition frequency. In the second example, the effect of randomness in the transition frequencies is studied. A coherent potential approximation is introduced, and the shift and width of the optical transition are calculated as a function of the ratio of the rms width of the transition frequency distribution to the unperturbed exciton bandwidth. Possible experimental tests of the theory are mentioned.
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