In polar semiconductors, resonances occur due to the interaction of excitonic states (discrete and continuous) with excitations involving virtual excitons plus a longitudinal-optical (LO) phonon. A theory is presented which starts with bare electrons, holes, and phonons, interacting via Coulomb attraction and Fr\"ohlich coupling. Within a self-consistent one-phonon treatment, a nonlinear and nonlocal Schr\"odinger equation for the exciton Green's function is derived. Only after extracting a Haken type effective potential as zeroth-order, perturbation theory with respect to the dynamical nature of the exciton-phonon interaction can be applied. Accurate measurements of the exciton absorption continuum in CdTe and, recently, in GaAs display around the resonance energy a slight change of slope which can be quantitatively explained by the present exciton-phonon model. For GaAs, first-order perturbation theory with respect to exciton-LO-phonon coupling is found sufficient, whereas for CdTe, a full solution of the nonlocal exciton equation is necessary.
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Zimmermann et al. (1997) studied this question.