Vibration–Rotation Interaction Effects in Calculated Franck–Condon Factors. I. The Ionization of H2 and D2

Abstract

Computed Franck–Condon factors for the ionization of H2 and D2 are reported which include previously neglected vibration–rotation interaction effects. Eigenfunctions were obtained by direct solution of the Schrödinger equation in which the exact centrifugal potential is explicitly included. Only υ″ = 0 and small K″ states of the neutral molecule have been considered and attention is confined to those transitions for which |K″ − K| = 0, 2. The results show a clear dependence of the computed Franck–Condon factor on rotational quantum number. For K″ = K, this effect is small except for transitions to the uppermost vibrational states of the ion. For |K″ − K| = 2, the effect is substantial even for transitions to low-lying vibrational states of the ion. By using a sum rule, it is shown that the probability of dissociative ionization exhibits a similar dependence on rotational state. Comparison of the present results for the case K″ = K = 0 with previous computation shows that adiabatic corrections for nuclear motion, explicitly included in this work, have a wholly negligible influence on computed Franck–Condon factors.