Z2dependence of the stopping power and the effective charge for MeV helium-ion beams

$Z_2$ (target atomic number) dependence of the electronic stopping powers for MeV helium-ion beams is investigated where the charge-state fractions before emerging from matter play a significant role. The electronic stopping powers for a single helium ion in various charge states and a proton ($S_{{\mathrm{He}}^{q+}}$, $q=1\mathrm{} \mathrm{and} 2$, $S_{{\mathrm{H}}^{+}}$) are calculated on the basis of Lindhard-Winther theory with the local-electron-density model. The ratio $\frac{S_{{\mathrm{He}}^{+}}}{S_{{\mathrm{H}}^{+}}}$ shows the $Z_2$ oscillation as well as $S_{{\mathrm{He}}^{+}}$ and $S_{{\mathrm{H}}^{+}}$. The relation between the effective charge $q_{\mathrm{eff}}$ and the mean charge $\overline{q}$ is elucidated in some cases of the incident energy where $q_{\mathrm{eff}}>\overline{q}$ is valid regardless of $Z_2$ and the $q_{\mathrm{eff}}$ values show the oscillatory $Z_2$ dependence with a small amplitude in contrast with a strong $Z_2$ oscillation of $\overline{q}$.