XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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FRANCK-CONDON FACTORS FOR DIATOMIC MOLECULES FOR AN ARBITRARY ANHARMONIC POTENTIAL
L. Sandoval*, I. Urdaneta and A. Palma
*Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma
de Puebla. Puebla, Pue. 72570, Mexico

Instituto de Fisica, Benemerita Universidad Autonoma de Puebla. Puebla, Pue. 72570, Mexico
In this work we develop a harmonic approximation of the Franck-Condon Factors (FCF) for any anharmonic potential of diatomic molecules.

The method is based on the Taylor series expansion of the potential and the second quantization formalism. Well known recurrence relations are used to calculate the FCF, which are incorporated in the hamiltonian. Keeping then only the quadratic terms, by the Bogoliubov-Tyablikov transformation the hamiltonian is found to be equivalent to an harmonic oscillator. The derivation is an alternative route to the Iterative Bogoliubov transformation (IBT), widely used to treat anharmonic potentials in a non-perturbative way. The FCF obtained by our method for the Morse potential are compared with numerical techniques like the RKR method and the Morse itself. Our results are in agreement with these numerical methods, being our technique entirely analytical and much simpler to use.


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