TEMPERATURE AND ENERGY-GAP DEPENDENCE OF ENERGY-TRANSFER BETWEEN RARE-EARTH IONS IN SOLIDS

In this paper we develop a model to explain the temperature dependence of energy transfer between rare-earth ions for situations in which th e energy gap is small. When the gap is large, and many phonons are req uired the transfer rate follows the well-known exponential law. When j ust a few phonons are required, however, the temperature dependence ma y be quite different, and may even be more efficient at low temperatur es; this is shown to be the case of Er to Ho transfer in YAG. We show that for small energy gaps, the redistribution of the ions with temper ature may be a driving factor in the transfer. As the number of phonon s increases, this redistribution becomes less important and the expone ntial law emerges.