On the direct energy transfer via exchange to moving acceptors

In a recent work [K. Allinger and A. Blumen, J. Chem. Phys. 72, 4608 (1980)] we derived expressions for the energy decay of an excited donor due to its interactions with moving acceptors. As we show here, this approach is related to path-integral methods which occur in different fields. We apply the formalism to interactions mediated by exchange. Analytic expressions are found for the decay due to acceptors moving slowly or rapidly on the time scale of the energy transfer. If the motion is frozen we retrieve the decay law for acceptors imbedded randomly in a solid matrix [A. Blumen, J. Chem. Phys. 72, 2632 (1980)]. For slow diffusive motion, as in the three-dimensional dipolar case [M. Yokota and O. Tanimoto, J. Phys. Soc. Jpn. 22, 779 (1967)], the decay may be expressed by means of a power series in the diffusion coefficients. Here we obtain the coefficients of the series from a recurrence formula and present the first ten terms. An approximate, compact formula for the decay law is also given. In the rapid motion case the decay law depends on the distance of nearest approach between donor and acceptors, but not on the details of the motion.