Donor fluorescence at high trap concentration

We investigate the time development of the donor fluorescence in the presence of a high concentration of acceptor ions which act as traps for the excitation. It is assumed that the transfer rates between donors are symmetric and independent of the energy mismatch and that there is no back transfer from the traps. The donor and acceptor ions are randomly distributed on a lattice with site occupation probabilities $c_D$ and $c_A$, respectively. We specialize to the case of dipole-dipole transfer between donors and from donors to acceptors. For a dilute system, $c_D$, $c_A\ll 1$, we use a coherent-potential approximation to calculate the Laplace transform of the donor fluorescence-decay curve for all values of the ratio $\frac{c_A}{c_D}$. It is argued that the theory should apply when the microscopic transfer rate between donor ions is at least as large as the corresponding transfer rate from donors to acceptors.