Effective stopping-power charges of swift ions in condensed matter

The effective charge of energetic ions as it pertains to the stopping power of solids is calculated in a dielectric-response approximation. The density distribution of $N$ electrons bound in an ion of atomic number $Z_1$ is given by a variational statistical approximation. The effective charge $Z_1^{}{}_{}{}^{*}e$ is always larger than the ionic charge $Q_1=(Z_1-N)e$, because of close collisions. A comprehensive low-velocity formula predicts $Z_1^{}{}_{}{}^{*}e$ for given $Q$ as a function of the ratio between the ion size and the mean electron spacing in the medium. At high velocities one obtains a partition rule of stopping powers for the effective charge of ionic projectiles. The results are compared with new precision stopping-power measurements on C, Al, and Au with ${}_7{}^{}{}_{}{}^{}\mathrm{N}$ ions.