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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 Z₁ is given by a variational statistical approximation. The effective charge Z₁^_^*e is always larger than the ionic charge Q₁= (Z₁-N) e, because of close collisions. A comprehensive low-velocity formula predicts Z₁^_^*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 ₇N ions.
Brandt et al. (Sat,) studied this question.