Excitation of atoms and molecules by highly relativistic ions

We study the cross section for inelastic collisions of atoms and small molecules under the influence of highly relativistic charged ions as they occur in storage rings and accelerators. Starting from fully time-resolved calculations of the electronic dynamics, we study a set of complementing approximations, a sudden approximation for the extremely fast collision at low impact parameter combined with time-dependent perturbation theory for the weak and slow collisions at large impact parameters. This leads eventually to a simple, yet reliable, estimate in terms of the ion-hydrogen cross section and the variance of the dipole moment for the actual system. We discuss, in particular, the systems H, He, C, N, O, Ne, H₂, and N₂.