Coupling strength in the theory of radiationless transitions: f → f and d → f relaxation of rare-earth ions in YAIO3 and Y3AI5O12

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Abstract
The dependences of the radiationless relaxation rate constant on the effective mediating phonon energy, the equilibrium displacement of the adiabatic surfaces, the energy gap, and the temperature are numerically examined in terms of a generalized theoretical rate expression derived from quantum statistical theory. Special emphasis is placed on the effect of the coupling strength on the behavior of the relaxation rate process. The validity of the generalized rate expression is illustrated by its application to the fit of the temperature dependences of several f → f and d → f radiationless relaxation rates observed for Er3+, Eu3+, Ho3+, and Pr3+ in YAIO3 and Y3Al5O12.