Decay of thek→=0exciton mode at a finite trap concentration

We study the decay of the $\overrightarrow{\mathrm{k}}=0\mathrm{}$ exciton mode in the presence of a finite concentration of traps. It is assumed that the traps are distributed at random and that each trap can couple to a single donor. Particular attention is paid to the behavior of one- and two-dimensional systems where algebraic decay was predicted on the basis of the average $T$-matrix approximation (ATA). Using the coherent potential approximation (CPA), we find that the ATA and CPA give similar results at all times in three-dimensional systems with a low concentration of traps. In one- and two-dimensional systems the ATA and CPA agree at short times, while at long times the CPA predicts exponential decay with a complex decay rate. The variation of the decay rate with trap concentration is determined in the low-concentration limit.