Inelastic collisions of relativistic highly charged ions with atoms

A general expression for the cross sections of inelastic collisions of fast (including relativistic) multicharged ions with atoms which is based on the generalization of the eikonal approximation is derived. This expression is applicable for a wide range of collision energy and has the standard nonrelativistic limit; in the ultrarelativistic limit it coincides with Baltz's exact solution (Baltz 1997 Phys. Rev. Lett. 78 1231) of the Dirac equation. As an application of the obtained result the following processes are calculated: the excitation and ionization cross sections of a hydrogen-like atom; the single and double excitation and ionization of a helium-like atom; the multiple ionization of neon and argon atoms; and the probability and cross section of K-vacancy production in the relativistic U⁹²⁺-U⁹¹⁺ collision. Simple analytic formulae for the cross sections of inelastic collisions and the recurrence relations between the ionization cross sections of different multiplicities are also obtained. Comparison of our results with the experimental data and the results of other calculations are given.