Unified treatment of Franck–Condon Factors over harmonic oscillator wave function using binomial expansion theorems

In this article an alternative analytical formula is proposed for Franck–Condon (FC) factors. The proposed method enables us to accurately determine the various level intensities in the spectrum of dia- and polyatomic molecules. This method is based on the use of binomial expansion theorem for the analytical representation of the FC factors. As an example of the effectiveness of the method, we present the calculation results of the FC factors of the molecules AlO, CeO, CrH, CrO, LaO, and NiH. The calculated results are in good agreement with other calculations obtained by theoretical and experimental methods.