Franck-Condon factors for band systems of molecular hydrogen. I.

TLDR: In this paper, the potential energy function was computed for all vibrational levels up to the dissociation limit by numerical solutions of the radial Schrodinger equation, and the resulting sets of Franck-Condon factors were given for all allowed bands of each system.

Abstract: Franck-Condon factors are reported for the ( B 1 Σ + u - X 1 Σ + g ), ( I 1 Π g - B 1 Σ + u ) and ( d 3 Π u - a 3 Σ + g ) band systems of molecular hydrogen. In each electronic state, wavefunctions were computed for all vibrational levels up to the dissociation limit by numerical solutions of the radial Schrodinger equation in which the potential energy function was entered in tabular form at equally spaced intervals of 0·01 A in the range of nuclear separations r = 0–25 A. In the X and B states the potential curves were obtained by interpolation and extrapolation of Rydberg-Klein-Rees (RKR) potential data; in the I, a and d states the potential curves were constructed from the Morse formula. The resulting sets of Franck-Condon factors are given for all allowed bands of each system. It is shown that the row and column sums in these matrices do not and should not all equal unity.