Abstract
An accurate normalization prescription is derived and tested for approximate bound vibrational wavefunctions due to W. H. Miller [1]. These bound state- and single turning point uniform Langer transformed continuum functions then are used to approach all types of Franck-Condon transition elements via partially uniform mapping techniques in a three dimensional space of integration variables. The classical Franck-Condon principle, Mulliken's difference potential, various reflection approximations and many other of the more recent approaches are shown to be naturally included in our method. The excellent accuracy of the final results is demonstrated by comparing with exact Franck-Condon matrix elements of Stückelberg's bound-continuum model.
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Krüger, H. Approximate Franck-Condon factors from piecewise Langer-transformed vibrational wave functions. Theoret. Chim. Acta 57, 145–161 (1980). https://doi.org/10.1007/BF00574901
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DOI: https://doi.org/10.1007/BF00574901