Abstract
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.
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