Two-center exchange interactions in rare earth doped materials

摘要

Two-center exchange interactions between rare earth ion and ligands are taken into account as a source of new contributions to the energy transfer resulting in sensitized luminescence. The consequences of the exchange of two electrons are described in an algebraic form by the so-called Dirac's identity after prior transformation of the radial functions localized on ligand to the coordinate frame of the central ion. This procedure enables one to use for the description of electrostatic interactions a simple multipole one-center expansion. The energy transfer amplitude is defined within the free ionic system approximation adopted for the rare earth ion, and its value is modified in a perturbative way by the contributions caused by the influence of crystal field potential produced by the surrounding ligands. The general expressions are defined in the terms of double tensor operators that determine isotropic and anisotropic parts, symmetric and antisymmetric ones. (C) 2002 Wiley Periodicals, Inc. [References: 49]