Excitation and ionization cross sections of hydrogen-like atoms in collisions with relativistic highly charged ions

The relativistic eikonal approximation and a matching procedure are used to describe excitation and ionization of hydrogen-like atoms from an arbitrary discrete energy state by the impact of a highly charged relativistic bare ion. Bethe-type formulas are derived that are asymptotically valid in the limits of v → c and Z ? 1, where v is the relative collision velocity, c is the speed of light, and Z is the ion charge.