Journal of Mathematical Chemistry

, Volume 24, Issue 1, pp 39–60

Derivation of closed analytical expressions for Rosen–Morse Franck–Condon factors

  • H. Hornburger
  • Geerd H.F. Diercksen

DOI: 10.1023/A:1019154115691

Cite this article as:
Hornburger, H. & Diercksen, G.H. Journal of Mathematical Chemistry (1998) 24: 39. doi:10.1023/A:1019154115691


The expressions for Rosen–Morse Franck–Condon factors derived previously yield a double sum with alternating terms. For higher values of the quantum number the numerical calculation of the Franck–Condon factors by electronic computers using these expressions leads to numerical overflow inspite of the use of double-precision (32 digits) arithmetic. High values for the quantum number in the final ground state of the Rosen–Morse potential occur in molecular nonradiative rate calculations. Furthermore, the expressions show a lack of clearness with respect to the parameters of the potential. For out-of-plane modes exact closed form expressions and exact recurrence relations are derived. Asymptotic expressions for the matrix elements are calculated. Exact closed form expressions for matrix elements with quantum numbers which correspond to regions close to the dissociation barrier are given.

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • H. Hornburger
    • 1
  • Geerd H.F. Diercksen
    • 2
  1. 1.Max-Planck-Institut für QuantenoptikGarching bei MünchenGermany E-mail:
  2. 2.Max-Planck-Institut für AstrophysikGarching bei MünchenGermany E-mail:

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