Energy Loss and Effective Charge of Heavy Ions in Aluminum

Heavy-ion beams of fixed initial energy ($\frac{{E}^{0}}{m}\ensuremath{\approx}10$ Mev/amu) are passed through aluminum absorbers of known thickness, and the emergent ions are analyzed by means of a magnetic spectrograph to determine their charge and energy distributions. Accurate measurements of the mean emergent ion energy as a function of absorber thickness are reported for beams of ${\mathrm{He}}^{4}$, ${\mathrm{B}}^{10}$, ${\mathrm{B}}^{11}$, ${\mathrm{C}}^{12}$, ${\mathrm{N}}^{14}$, ${\mathrm{O}}^{16}$, ${\mathrm{F}}^{19}$, and ${\mathrm{Ne}}^{20}$ ions with emergent energies in the range $10>\frac{E}{m}>1$ Mev/amu. The results can be interpreted as measurements of the range-energy relation for heavy ions. While the absolute accuracy of the range measurements is approximately \ifmmode\pm\else\textpm\fi{}1 mg/${\mathrm{cm}}^{2}$, the range difference $R({E}^{0})\ensuremath{-}R(E)$ is measured (as a function of $E$) with a typical accuracy of \ifmmode\pm\else\textpm\fi{}0.1 mg/${\mathrm{cm}}^{2}$. In the analysis the shape of the heavy-ion range-energy curve is compared with the accurately known shape of the proton range-energy curve (using the conversion factor $\ensuremath{\Delta}R=m{{Z}_{p}}^{2}{({m}_{p}{Z}^{2})}^{\ensuremath{-}1}\ensuremath{\Delta}{R}_{p}$) and the differences in shape are attributed to deviations of the effective charge of the ion from its nuclear charge. No detectable difference is found between the shape of the range-energy curve for ${\mathrm{He}}^{4}$ ions and for protons. For heavier ions, deviations in the curve shape do occur. A simple empirical formula is found for the effective charge of an ion as a function of its velocity which is consistent with the deviations of the observed range-energy curves and presumably can be used to predict the range-energy curves for ions not investigated experimentally. By an independent analysis of the spectrograph data the equilibrium distribution of charge states in the ${\mathrm{O}}^{16}$ beam is determined as a function of emergent beam energy. The effective charge implied by the charge state distribution is found to be consistent with the effective charge as given by the empirical formula.