Inelastic transitions in slow heavy-particle atomic collisions - art. no. 052702

It is a generally held belief that inelastic transition probabilities and c ross sections in slow, nearly adiabatic atomic collisions decrease exponent ially with the inverse of the collision velocity v [i.e., sigma (alpha)exp( -const/v)]. This notion is supported by the Landau-Zener approximation and the hidden crossings approximation. We revisit the adiabatic limit of inn-a tom collisions and show that for eely slow collisions radial transitions ar e dominated by the topology of the branch points of the radial velocity rat her than the branch points of the energy eigensurface. This can lead to a d ominant power-law dependence of inelastic cross sections, sigma alphav(n). We illustrate the interplay between different contributions to the transiti on probabilities in a one-dimensional collision system for which the exact probabilities can be obtained from a direct numerical solution of the time- dependent Schodinger equation.