Ionization of highly charged relativistic ions by neutral atoms and ions

Ionization of highly charged relativistic ions by neutral atoms and ions is considered. Numerical results of recently developed computer codes based on the relativistic Born and the equivalent-photon approximations are presented. The ionization of the outer shells dominate. For the outer projectile electron shells, which give the main contribution to the process, the non-relativistic Schr\"odinger wave functions can be used. The formulae for the non-relativistic reduction of the Dirac matrix-elements are obtained for ionization of electrons with arbitrary quantum numbers $n$ and $\ell$.