Energy straggling of light-ion beams

The dielectric function method is applied to investigate the energy straggling of protons and helium ions using the atomic and the solid local-electron-density models. A partially stripped ion is treated as well as point charges. At low energies, the conventional stragglings of a proton (${\Omega }_{{\mathrm{H}{}^{+}}^2)}$ and of helium ions (${\Omega }_{{\mathrm{He}{}^{+}}^2}$,${\Omega }_{\mathrm{He}}^{2+}$ ${}_{}{}^2{}_{}{}^{}$) due to the fluctuation in electronic excitations are proportional to the kinetic energies of the ions even when the local-electron-density models are adopted, and at high energies they approach the values predicted by Bohr. Here we do not consider the bunching term since we assume the probability of exciting an electron is small. The straggling ratio ${\Omega }_{{\mathrm{He}{}^{+}}^2/{\Omega }_{{\mathrm{H}{}^{+}}^2}}$ shows a remarkable feature that it is nearly constant up to ∼50 keV/amu, and increases gradually beyond this energy for solid targets. The estimation of the collisional straggling of helium-ion beams is performed using the charge-state fractions, resulting in displaying $Z_2$ (target atomic number) oscillations similar to those of ${\Omega }_{{\mathrm{He}{}^{+}}^2}$ and ${\Omega }_{{\mathrm{He}{}^{2+}}^2}$. The straggling caused by charge-state fluctuations, which enhance the $Z_2$ oscillations of the total straggling of helium-ion beams more sharply at the energies considered, is also estimated.