A simple analytical estimate of the bound-free Franck–Condon factors for a transition to a repulsive exponential potential in a diatomic molecule Original Research Article

An analytical study of the bound-free (b-f) Franck–Condon (FC) factors is proposed for an electronic transition in a diatomic molecule. The case where the continuous state is characterized by an exponential repulsive potential curve is investigated. The paper focuses on the qualitative characterization of the b-f FC factors in terms of physical parameters. A simple analytical estimate is proposed which matches exactly the b-f FC factors for small kinetic energy. This analysis allows us to define the short- and long-range domains of the exponential repulsive potential curve. Depending on the equilibrium position of the bonding curve (which may fall into the short- or long-range domain), the behaviour of the b-f FC factors is qualitatively different. The relation with the Wigner threshold laws is established.