Stopping power of some lightly ionized gold ions for protons

Calculations are presented for the stopping power of ${\mathrm{Au}}^{n+} \left(0\mathrm{}\le n\le 11\right)$ for protons with energy between 0.1 and 10 MeV. Over this range the proton stopping power changes by at least a factor of 2 between neutral and 11 times ionized gold. Explicit Born-approximation calculations are done for both excitation (for all ions considered) and ionization (for selected ions). For inner shells ($\mathrm{nl}\le 4d$) the explicit calculations are in excellent agreement with results obtained from scaling laws. For outer shells ($\mathrm{nl}\ge 4f$) there are differences of as much as a factor of 2 between the explicit calculations and the scaling laws for some subshells of some ions. A correction to the scaling laws using an integral over optical oscillator strength is developed which removes some of the disagreement between the explicit calculations and scaled values. The residual difference between the explicit calculations and the scaled values appears to arise from the spatial expansion of an ion subshell orbital compared to an atom subshell orbital even when the subshells have the same ionization energy.