Adiabatic limit of inelastic transitions - art. no. 032103

The widely used assumption that transitions induced by slowly changing pert urbations are completely described by the topology of adiabatic energy surf aces in the plane of a complex perturbation parameter is reexamined. This a ssumption is the basis for the hidden crossings theory and most two-state m odels and yields an exponential decrease of transition probabilities and cr oss sections with decreasing speed of the perturbation v. We show that for a large class of problems, these approximations do not describe correctly t ransitions in the adiabatic limit. Contributions neglected lead, instead, t o dominant power-law dependences in inelastic collisional cross sections, s igma infinityv(4). We illustrate the interplay between different contributi ons for a collisional model system for which exact transition probabilities can be determined.