Mutual influence of the composite exciton-phonon states and impurity states on the spectra of doped molecular crystals

We have calculated the energy eigenvalues of the localized energy states arising from the interaction between the composite exciton-phonon states and isotopic impurity states for 0-0 and 0-1 phonon transitions in molecular crystals. The exciton-phonon-impurity state interaction Hamiltonian is derived, and the results are obtained at low temperatures where the participation of the low-energy acoustic phonons is assumed to be dominant. A condition on the localized energy states as a function of the trap depth is obtained. The results are found to be in good agreement with experiments on doped naphthalene crystals, and with the theoretical results already established.