their collisions with neutral complex atoms by taking into account all of the possible, including multiple, exci-
tations and ionizations of both projectile and target. We have been able to achieve a significant simplification
of the problem by considering multielectron targets and by restricting our analysis to highly charged structured
ions with charges much larger than unity, when the characteristic size of the electron coat of the projectile ion
is much smaller than that of the neutral target atom. The errors in the approximations used and in the calcula-
tions of inelastic cross sections are estimated. We have derived formulas for the effective stopping similar to the
well-known Bethe–Bloch formulas. To illustrate the contribution from multielectron excitations of the ion coat
to the effective stopping, we make a comparison with the calculations based on the perturbation theory. The
energy losses of Uq+ (10
q 70) ions in their collisions with argon atoms and the energy losses of Pb and Bi ions on several targets have been calculated. A comparison with experiment is made.