A degenerate model of vibronic transitions for analyzing 4f-5d spectra

Vibronic coupling of the 4f-5d electronic transitions is investigated using Franck-Condon theory of vibronic interactions. To perform quantitative analysis of partially resolved experimental spectra given arise from a large number of vibrational modes and multiple electronic states, a semi-empirical model is established based on frequency degeneracy and line broadening. Instead of taking account all participating modes without experimental information on vibrational frequencies and vibronic coupling strength, this model includes a restricted number of degenerate modes with characteristic frequencies and line widths to simulate the experimental spectra. It is demonstrated that this model can be satisfactorily applied to quantitate the luminescence spectra of Ce3+ in Y3Al5O12 (YAG) and evaluate electronic energy levels, frequencies of leading vibrational modes and their vibronic coupling constant.