Role of Rate Equations in the Theory of Luminescent Energy Transfer

Abstract

In this paper we derive from first principles, equations describing the kinetics of luminescent transfer. We apply the Pauli equation to an appropriately defined density matrix to derive, under one formalism but under opposite limiting assumptions, both the usual nonlinear kinetic rate equations and the equations which form the starting point for the calculations of Forster and others. The transition probabilities entering these equations are discussed. It is shown that they permit multiparticle processes, with great increase in the possibility for resonances that exist if only two-particle processes are considered. Further, in the rate-equation approximation, the concentration dependence of the transition probabilities and of the yield reflects only the number of particles participating in one energy-conserving transfer, and is not associated with the spatial dependence of the interaction. Such an association does exist in the Forster approximation, but a direct correspondence between powers of concentration and multipole orders appears valid only under severe constraints. The observed nonlinearities of decays and of yields, and dependences on the excitation mode, are easily handled with rate equations. Some of the experimental evidence that the rate-equation approximation applies, in fact, to many systems, particularly to rare earths in inorganic hosts, is briefly discussed.