Model studies of resonances and unimolecular decay of triatomic Van der Waals molecules

Abstract

The wave equation appropriate to describing the resonance states of atom–diatomic Van der Waals molecules in body-fixed coordinates is presented. The Van der Waals bond is described by a square-well attraction whose depth can depend on the internal state of the diatomic. With this simple model, the analytic structure of the scattering matrix is expressed by an exact partial fraction expansion in terms of simple poles due to the bound, antibound and resonance states of the complex. The expansion leads to partial fraction expansions for the collisional time delay and the spectroscopic transition probabilities, and the results are compared to the Breit–Wigner parametrization. The square well is idealized further to a delta-function attraction, and the scattering matrix for coupled channels is obtained. Poles corresponding to shape and Feshbach resonances are identified, and an expression for the decay probabilities of a resonance into the open channels is obtained for the model.