Theory of interconfigurational nonradiative transitions in transition-metal ions in solids and application to the ${\mathrm{Ti}}^{3+}$:${\mathrm{Al}}_2$${\mathrm{O}}_3$ system

In this paper the nonradiative deexcitation of transition-metal ions in solids is discussed. It has been found that when the deexcitation of the system occurs due to the crossing of the configurational energies of ground and excited electronic manifolds (the internal conversion process) the system dynamics can be described by the perturbation method. Detailed investigation of two equivalent approaches, the adiabatic and the diabatic, shows that the diabatic attempt is usually more useful, since it allows the description of the vibronic problem in the harmonic-oscillator limit. The model has been successfully applied for describing the temperature quenching of ${\mathrm{Ti}}^{3+}$:sapphire luminescence.