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

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Abstract

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.

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Authors and Affiliations

  1. Max-Planck-Institut für Quantenoptik, D-85748, Garching bei München, Germany E-mail:

    H. Hornburger

  2. Max-Planck-Institut für Astrophysik, D-85740, Garching bei München, Germany E-mail:

    Geerd H.F. Diercksen

Authors
  1. H. Hornburger
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  2. Geerd H.F. Diercksen
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Hornburger, H., Diercksen, G.H. Derivation of closed analytical expressions for Rosen–Morse Franck–Condon factors. Journal of Mathematical Chemistry 24, 39–60 (1998). https://doi.org/10.1023/A:1019154115691

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