Unified model of the temperature quenching of narrow-line and broad-band emissions

Abstract Temperature quenchings of narrow-line and broad-band emissions are pictured through the quantum-mechanical single-configurational-coordinate model. The model is taken in the thermal-Condon approximation with the overlap integrals evaluated through the Manneback recursion formulas. The multiple activation energies mħωυ to the initial vibrational states produce an increase in the non-radiative rate poorly described, in general, by a single activation energy. The model applies to energy parabolas with large Franck- Condon offset and a consequent crossover and to energy parabolas with small Franck- Condon offset and no relevant crossover. For large offset, the model gives approximately Mott's single-activation-energy rate AM exp(-EX/kT) for upward transitions but faster rates poorly described by a single activation energy for downward transitions. For small offset, the model gives approximately Kiel's multiphonon-emission rate AKϵp[1+〈m〉υ]p for downward transitions. A numerical matrix method is described which can handle all cases and which explicitly exhibits the multiple activation energies mħωυ in every case. This method is used to work out examples of the various types of quenchings which can occur: a fast bottom crossover, an outside crossover, small-offset multiphonon emission, a tunneling crossover, and two-step quenchings through a higher offset state.