Derivation of the relation between non-radiative and radiative decay rates in rare-earth ions with comparison to experimental energy gap, parameters and the consequences for non-radiative selection rules

Abstract

Experimentally the electronic coupling element for non-radiative decay in rare-earth ions has been derived from the energy gap law. We derive that the effective energy gap to be used in the energy gap law is about two phonons smaller than the energy difference between initial and final state. The effective electronic coupling element determined in this way from experiment varies little for all known solids and is in good agreement with our theoretical calculation of this parameter. Also we can predict exceptions to the energy gap law with our theory.