The effect of localized modes on radiationless electronic transitions. II. Dependence on impurity concentration

The nonradiative decay of electronically excited impurities in a linear crystal is studied. For isolated isotropic impurities lighter than the host atoms [i.e., ε=-(ΔM/M)>0] localized modes exist which, however, cannot accept energy in the relaxation process since the Franck-Condon factors vanish due to parity selection rules. This is not the case if there is a second impurity at a finite distance. The effect of the localized modes on the nonradiative rate is studied as a function of the impurity distance, the relative mass change, and the temperature. For low temperatures and weak coupling the rates may be enlarged by several orders of magnitude for neighboring impurities. This is important for increased impurity concentration. The time-dependent decay is in general nonexponential, and in the simplest case a superposition of two exponentials.