Critical Concentration for Single-Ion-Single-Ion Energy Transfer in Ruby

Abstract

The critical concentration for single-ion-single-ion energy transfer in ruby is calculated using Anderson's method for transport between ions which are characterized by inhomogeneously broadened energy levels. The excitation on the chromium impurity is assumed to propagate by virtue of superexchange interactions. Using a continuum approximation, we find that the single-ion excitation is localized below concentrations of \ensuremath{\sim}0.3-0.4%, a range not inconsistent with that concentration at which a sudden change in the fluorescent lifetime of ruby occurs.