Stopping power and effective charge of heavy ions in solids

We have measured the energy loss of several heavy ions (C, Si, Cl, Ti, Fe, Ni, Ge, Br, Nb, and I) in elemental targets (C, Al, Cu, Ag, and Au) at energies near the maximum in the stopping power versus energy curve. These measurements have been used to examine the charge dependence of heavy-ion stopping powers, as well as the magnitude of the ion's effective charge inside the target material. Inclusion of the Lindhard $Z_1^3$,$Z_1^4$ corrections provides the best fit to the data, and the use of these corrections results in a simple expression for the effective charge which is valid for all our measured projectile-target combinations ($Z_1=6-53\mathrm{}$ and $Z_2=6-79\mathrm{}$). Both the magnitude and the target dependence of this effective-charge expression are consistent with average equilibrium charge-state measurements made in gases. This suggests that the high charge states observed for ions leaving solid materials are due mainly to charge-changing effects (such as Auger deexcitation) at the exit surface.