Journal of Statistical Physics, Vol. 30, No. 2, 1983. p. 345-354.
We investigate the trapping of excitation by a random array of acceptor ions embedded in an assembly of donors. The problem is formulated in terms of coupled rate equations. Exact results for the fraction of excited donors are obtained in the zero and rapid donor-donor transfer limits for arbitrary ratios of the donor to trap concentration. The average T-matrix approximation (ATA) is introduced to interpolate between these limits in situations where the concentration of traps is much less than the concentration of donor ions. In three-dimensional systems the ATA reproduces the results of earlier calculations in appropriate limits. The extension of the theory to higher trap ~concentration is discussed, as are problems connected with the application to one- and two-dimensional arrays.