Reciprocity analysis of electronic stopping of slow ions

Abstract

Reciprocity denotes the (approximate) equality of the electronic stopping cross section of element A in element B with the one of element B in element A. Reciprocity is expected in the energy range below ∼ 0.1 MeV/u. For ions heavier than protons, most measurements are performed by the transmission technique. In order to minimize nuclear energy loss, only a narrow beam of penetrating ions is allowed to enter the detector. This implies that also the electronic energy loss is underestimated. We have estimated the magnitude of the necessary correction on the basis of the PASS code and its influence on the expected reciprocity and find that reciprocity is not necessarily violated, even if the reported cross sections differ significantly. However, we also find differences between reported stopping cross sections and computed reduced stopping cross sections that we cannot reconcile on the basis of the PASS code. These differences are found to reflect the well-known Z 1 structure, which is not inherent in the present version of PASS.

Expanded PASS stopping code

“…We note that amongst numerous ion-target combinations considered in Figures 2-6, several have been analysed previously, such as H ions in N, Al, Si and Ag in [54], H-Au and Ni-Au in [59], as well as He-N, Ne-N and Si-Al in [60]. In Figure we show that these effects also occur at relatively high energies for the heaviest projectiles.…”

“…• In those cases that we have analyzed explicitly [54,59,60] and Figure 8, we argue that estimates from PASS come closer to the true electronic stopping cross section than do the reported values.…”

“…We have studied stopping in gas targets, especially He, Ne and Ar extensively in two recent papers [59,60]. Therefore we here only consider nitrogen as a target.…”

“…In the literature we have identified papers that do not mention nuclear stopping at all [60]. More often, the description of the applied correction for nuclear stopping is incomplete [70], and cases have been identified, where the full nuclear stopping has been subtracted from the measured energy loss, neglecting the fact that when energy loss is measured in transmission, ions that experience large nuclear energy losses are deflected by large angles and do not enter the detector [54,59].…”

“…A more general source of error is the neglect of the dependence of electronic energy loss on impact parameter in an individual ion-atom collision. We have studied this effect extensively for the most-frequently applied transmission technique for measuring electronic energy loss [54,59,60], but some influence is also expected on alternative techniques, including inversion of ion ranges.…”