Resonance Energy Transfer in Condensed Media from a Many-Particle Viewpoint

Abstract

The F\orster-Dexter (FD) theory of transfer of electronic energy by the resonance interaction between an excitation localized at one impurity and an unexcited state at another is based on a model consisting of an ensemble of inert continuous dielectric hosts in each of which are imbedded one sensitizer and one activator at random positions; there are only two relevant electronic energy levels associated with each impurity, and these levels are merely broadened by lattice vibrations. In spite of the apparently crude approximations involved in the two-impurity model for resonance transfer, the FD theory has been vital to the understanding of energy-transfer phenomena in solids, liquids, and biological systems, and most of the predictions of the theory have been verified at least semiquantitatively. Clearly the two-impurity model must not be so crude as it appears to be at first glance, and many of the complicated effects which one might expect from a more elegant theory must be hidden in the parameters of the model. In this paper, the resonance-energy-transfer mechanism is treated from a many-particle viewpoint, and the collective nature of the excitation migration is taken into account. Assuming a nonmagnetic monatomic crystal with two substitutional impurities, the initial and final states of the energy-transfer process are taken to be localized excitons, or excited states of the entire system of impurities plus host crystal. First, on a linear-chain model it is found that the host states modify the bare interaction between impurities and also provide a short-ranged virtual-exciton mechanism for energy transfer. Then the long-ranged part of the effective interaction is treated for a three-dimensional model of a tight-binding crystal, with the effects of the impurities on the host treated within the framework of linear response theory. For long-ranged excitation migration, the connection between the collective picture and the two-impurity picture is established by performing a unitary transformation on the crystal Hamiltonian and showing that an effective two-atom Hamiltonian consistent with the FD theory can be extracted from it. Therefore, the two-impurity picture of sensitized luminescence is shown to be a suitable limit of a many-body treatment of migration of localized excitons; and, in this limit, all the effects of the medium can be included in a simple frequency-dependent dielectric response function. The approximations implicit in the FD theory are discussed, with particular attention paid to the effects of low-lying host-crystal states on the rate of energy migration. It is argued that the usual weak-coupling criterion is not sufficient to guarantee the validity of the FD theory and that multiple-scattering effects not included in the theory become important at relatively low concentrations.