Inelastic processes in the collision of fast highly-charged ions with atoms

In the present work we propose 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 and is applicable for wide range of collision energy. This formula have a standard nonrelativistic limit and in the ultrarelativistic limit coincides with the exact solution [1] of Dirac equation. As an example we considered excitation and ionization of hydrogenlike atom, single and double excitation and ionization of heliumlike atom. We derived the simple analytic formulas for the cross sections of inelastic collisions and compared our results with the experimental data and the results of calculations of other authors. (author)