Resonant Energy Transfer between Localized Electronic States in a Crystal
Abstract
We propose a model Hamiltonian to describe resonant energy transfer between discrete electronic states each of which is coupled to the same boson field. In this model, the calculation of the transition probabilities for resonant energy transfer, radiationless intraimpurity electronic transitions, and phononbroadened electromagnetic transitions among the electronic states of a given impurity are rendered formally equivalent, differing only in the selection of various model parameters. The relation of those parameters to microscopic models is described in detail for the case of resonant energy transfer between localized impurity states. A calculation of the energytransfer probability is presented which is valid to arbitrary order in the electronphonon interaction, but is the linearresponsetheory treatment of the electronictransfer term. Explicit comparison between the predictions of our model and those of the FörsterDexter model are given. We present an analysis of the timedependent Schrödinger equation which permits us to distinguish between dissipative and multiply periodic solutions to the Schrödinger equation and gives a precise definition of weak and strongcoupling limits. Finally, we indicate the application of our results to describe experimental systems involving radiationless energy transfer and electronic relaxation in rareearth impurities in crystals.
 Publication:

Physical Review B
 Pub Date:
 January 1971
 DOI:
 10.1103/PhysRevB.3.262
 Bibcode:
 1971PhRvB...3..262S