Shape resonances in ion–molecule reaction

Abstract

A simple analytical formula for the probability of reaction in low-energy ion–molecule collisions is given by Wentzel–Kramers–Brillouin and uniform approximations. By using this formula, one can deal with any type of shape resonances regardless of whether the collision energy is below or above a potential barrier. The reaction probability is completely determined by three parameters: the high-energy limit (P0) of the reaction probability obtained at a collision energy much above the potential barrier, a universal measure (α) of the difference between the collision energy and the barrier top, and a scattering phase shift (θ) due to short-range reactive interaction. It is very useful to draw a topographical map of the reaction probability by assuming that P0 is given as a constant and that (α, θ) are independent variables. The energy dependence of the reaction probability in a collision process is represented by the section view along a route actually allowed on this topographical map. A resonance structure appears when the actual route crosses a prominent mountain ridge. It is shown that the reaction probability can be unity at a resonance energy even if the probabilities at off-resonance energies are very small. No sharp tunnelling resonance would be expected in the collision system having .