Energy-transfer processes induced by exchange interactions

A study is made of energy-transfer processes by conventional direct exchange in condensed matter within the conceptual framework of the crystal model. The study is presented in two stages. As a first approximation, a simple model is obtained developed along an isotropic interaction approximation that depends exponentially on the distance of the donor and acceptor ions, and in which the angular factors are considered as averages. In that case, the statistical analysis of the crystal model leads to a formalism reminding one of the master equation obtained previously for electric dipole-electric dipole interactions, and showing the need for this analysis in order to know how many and which of the acceptor ions actually contribute to the rate of energy transfer. In a second stage, the problem is worked out using the approach originally proposed by Levy [Phys. Rev. 177, 509 (1969)] to calculate the matrix elements of the interaction, in which the bipolar system is referred to one of the centers. The formalism is completely general and rigorous, analyzing in detail the anisotropy factors of the conventional direct exchange mechanism for a pair of interacting ions, and their consequences on the global rates of energy-transfer processes. Work has been focused on the general derivation of the equations and on the analysis of its formal, rather than specific, calculations. However, for the sake of completeness, the LnCl(3) and LnF(3) systems are used as examples. [S0163-1829(99)11735-8].