Intermediate-and strong-coupling scheme ions

Whether or not energy transfer will occur between identical ions with S 1, depends in the first place on the spectral overlap of their emission and absorption spectra. The reader will feel intuitively that for ions with strongly Stokes-shifted emission (S 10) this spectral overlap will be very small or even vanish, so that energy transfer becomes impossible. 

It is easy to make these feelings more quantitative [10]. Consider a system of two identical luminescent centers. The ground state of each center is denoted by g(i)v(i) , and the excited state by e(i)v (i) . Here g and e indicate the electronic states (ground or excited state) and v and v the vibrational states, and i numbers the centers, i.e. I or 2. 

If H presents the interaction causing enctgy transfer, the transition matrix element is given by 

The transfer probability is proportional to M, i.e. to yfOKfl) . At low temperatures the transfer transitions are restricted to the zero-vibrational levels, so that at OK 

Here 0 denotes the zeio-vibrational level. At low temperatures, therefore, the transfer probability vanishes if the spectra do not show vibrational. structure with a zero-phonon line. 

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