Exciton Polarons of Molecular Crystal Model. I. –Dynamical CPA–

Energy spectrum of exciton polaron is studied with the dynamical CPA (coherent potential approximation), which is introduced for inelastic scattering by Einstein phonons at every lattice site. The coherent potential at energy E is determined by the potentials at energies apart from E by integral times the phonon energy. We determine applicability ranges of the concepts used in the limiting cases; (I) the nearly free exciton for weak coupling, (II) multiple bands of the vibronic excitons for small excitation transfer, and (III) the self-trapped exciton for strong coupling. An ambiguous boundary separating (II) and (III) lies about S ≃6, with S representing the ratio of the energy gain of exciton localization to the phonon energy. The change with increasing excitation transfer for a fixed S is characterized by the sharp crossing of (III) with (I) for \(S{}6\), while by the gradual merging of (II) into (I) for \(S{}6\).