Theory of donor fluorescence in the diffusion limit

Time dependence of fluorescence from donors is studied in the diffusion limit when there is a large number of donors in the sphere of influence of an acceptor. The average $t$-matrix approximation is used to derive the Laplace transform of the normalized intensity in this limit. The time dependence of the decay of the fluorescence is compared with experimental data on ${\mathrm{Pr}}_{0.95}$ ${\mathrm{F}}_3$: ${\mathrm{Nd}}_{0.05}^{3+}$ and also with the results of the diffusion model of Yokota and Tanimoto.