Competing radiative and nonradiative decay of embedded ions states in dielectric crystals: theory, and application to Co²⁺:AgCl_0.5Br_0.5

We present a generally applicable theoretical model describing excited-state decay lifetime analysis of metal ions in a host crystal matrix. In contrast to common practice, we include multi-phonon non-radiative transitions competitively to the radiative one. We have applied our theory to Co²⁺ ions in a mixed AgCl_0.5Br_0.5 crystal, and as opposed to a previous analysis, find excellent agreement between theory and experiment over the entire measured temperature range. The fit predicts a zero absolute temperature radiative lifetime τ_{r ad}(0) = 5.5 ms, more than three times longer than the measured e ective low-temperature one τ_e f_f (0) = 1.48 ms. Furthermore, the fit configuration potential dissociation energy has been estimated as D = 2500 cm⁻¹ and the lattice vibrational cuto frequency as ω_co = 180 cm⁻¹. We have experimentally verified the latter by optical reflection measurement in the far-IR.