Concentration dependence of the phonon-assisted energy transfer between rare-earth ions

Abstract

In this paper we derive an expression for the rate constant of phonon-assisted energy transfer in which the donor ion interacts with $N$ acceptors. This expression is compared with the appropriate expression for the rate constant of resonant energy transfer. It is postulated that in the system with nonresonant energy transfer the rate constant is proportional to the number of acceptors. The results are discussed in connection with the linear concentration dependence of cross relaxation in the ${\mathrm{Nd}}^{3+}$ stoichiometric crystals.