A general formula for calculation of the two-dimensional Franck-Condon factors

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Koc H., Mamedov B. A. , ESER E.

CANADIAN JOURNAL OF PHYSICS, vol.95, no.4, pp.340-345, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 95 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1139/cjp-2016-0475
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.340-345
  • Keywords: Franck-Condon factor, Duschinsky effects, binomial coefficients, Hermite polynomials, OSCILLATOR WAVE-FUNCTION, OVERLAP INTEGRALS, MOLECULES, SPECTRA, SPECTROSCOPY
  • Ankara Haci Bayram Veli University Affiliated: No


Knowledge of the Franck-Condon factors (FCFs) and related quantities is essential to understand and to estimate many important aspects of the astrophysical molecules, such as kinetics of the energy transfer, radiative lifetimes, band intensity, and vibrational temperatures. In this view, we propose a new analytical formula of the Franck-Condon integral for two-dimensional harmonic oscillators taking into account the Duschinsky effect. This method is based on the use of the binomial expansion theorem and the Hermite polynomials. With the formula obtained, the FCF of any transition can be computed independently. In this study, the method for FCF calculations was applied to the NO2 molecule.