Inelastic transitions in slow heavy-particle atomic collisions

It is a generally held belief that inelastic transition probabilities and cross sections in slow, nearly adiabatic atomic collisions decrease exponentially with the inverse of the collision velocity v [i.e., σ∝exp(-const/v)]. This notion is supported by the Landau-Zener approximation and the hidden crossings approximation. We revisit the adiabatic limit of ion-atom collisions and show that for very slow collisions radial transitions are dominated by the topology of the branch points of the radial velocity rather than the branch points of the energy eigensurface. This can lead to a dominant power-law dependence of inelastic cross sections, σ∝vⁿ. We illustrate the interplay between different contributions to the transition probabilities in a one-dimensional collision system for which the exact probabilities can be obtained from a direct numerical solution of the time-dependent Sch\"odinger equation.