Non-radiative transitions in the anharmonic oscillating field model

Non-radiative transitions (NRT) between electron states of an impurity ion are considered in the framework of the energy levels crossing model. NRT is supposed to take place when two electron levels involved into the transition are crossing due to the ligands thermal vibrations. The Morse potential used to describe the ligands vibrations allows for taking into account the anharmonicity effects. The analytical expression for the thermal dependence of the NRT probability between two arbitrary levels is derived. An application of the developed model to the Y3Al5O12:Cr4+ crystal is described; the results obtained are compared with those for harmonic approximation and experimental measurements of the Cr4+ ion excited state lifetime; an improved agreement (compared with harmonic approximation) between the theoretical and experimental results is demonstrated.