Band Shape The Huang-Rhys Coupling Parameter

5 BAND SHAPE THE HUANG-RHYS COUPLING PARAMETER 

The overall absorption probabihty at 0 K involves a summation of the probabilities from the ground vibrational state, = 0, to all of the excited m states (m = 0, 1, 2.), and so it can be written as follows  

The absorption (emission) band shape at 0 K can be estimated from Equation (5.30) if the square of the overlap integral of harmonic functions, l(Xm(2)l/o(2) P. is known for each excited (terminal) m level. Using the wavefunctions of the harmonic oscillator, these overlap functions can be expressed as a function of S  

we can predict the relative intensity of each 0 m absorption line using this expression together with Equation (5.30)  

We must recall that that, according to Equation (5.31), the full absorption intensity (the area under the absorption band) is independent of S. Thus, the factor e (which corresponds to /o o) represents the fraction of the absorption intensity taken by the zero-phonon line, while the intensity /o i = e x S represents the fractional intensity related to the 0 1 transition, Iq 2 = x (5 /2) the fractional intensity of the 0 2 transition, and so on. 

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