Excitation decay due to incoherent energy transfer: A comparative study by means of an exact density expansion

In this paper we consider a system of identical, randomly distributed donors, between which incoherent energy transfer takes place, described by coupled rate equations. It is proved, that the well-known diagrammatic series expansion of Gochanour, Andersen, and Fayer for the self-energy, while not an expansion in terms of the density of donors, does in fact imply an exact density expansion for the configuration averaged probability ρ(t), that an initially excited donor will still be excited at time t. Although this diagrammatic expansion has derived its greatest appeal from the search for approximate self-consistent solutions to the generalized diffusion coefficient, the exact density expansion for ρ(t) can also serve very useful purposes. This is demonstrated by a comparative study of model results for ρ(t), whose absolute accuracy or validity can be assessed.