Franck-Condon factors based on RKR potentials with applications to radiative absorption coefficients

Abstract

Digital computer codes for calculating Franck-Condon factors based on arbitrary potentia function inputs and for numerical construction of diatomic potential curves by the RKR (Rydberg-Klein-Rees) method have been developed and are described in this paper; tests of the computational accuracy of these procedures are also shown. These codes have been used to compute Franck-Condon factors for the red and violet band systems of CN and for the Swan and Phillips systems of C 2. The calculations were performed using both Morse and RKR potential functions. For the electronic states of the CN red and violet bands and for the C 2 Swan bands, the RKR curves were taken from data published in the literature. For the electronic states of the C 2 Phillips system, The RKR potentials were constructed from the data of Ballik and Ramsay. The results of the CN Morse potential Franck-Condon factor calculations were compared with the earlier results of Nicholls and the agreement is excellent. The RKR calculations for the C 2 Swan system compare favorably with the more limited results of Jain. Comparison of Morse and RKR Franck-Condon factors shows differences which are particularly noticeable at high vibrational quantum numbers. The results of these calculations are used to compute spectral absorption coefficients using a local average model for the rotational structure. The effect of the RKR-Franck-Condon factors on these absorption coefficients is shown.