Energy deposition by nonequilibrium charge states of MeV ${}^{127}\mathrm{I}$ in Au

The energy loss of iodine ions at initial charge states up to 25+ and energies up to 36 MeV in self-supporting gold foils between 37 and 107 nm of thickness was measured with an electron mirror type time-of-flight detector. An excess energy loss of 130 keV was observed at 36 MeV for charge state 25+ compared to 16+, and an energy loss deficit of 100 keV was observed for charge state 8+. The charge state equilibration length for 36-MeV iodine was estimated to lie between 3 and 7 nm, corresponding to an equilibration time between 0.4 and 0.9 fs. This result is relevant both for nanostructure fabrication with MeV ion beams and for depth profiling based on ion beam analysis data in cases where the charge state of the primary ion is far from the equilibrium value in the sample under study. A comparison to published data on charge state equilibration for various projectile-target combinations and energies from 10 keV to 6 GeV indicated that the energy scaling of the equilibration length observed at high energy is invalid for projectile velocities on the order of the Bohr velocity and below. The measurement further provided equilibrium values of the electronic stopping power for iodine in gold at ten energies between 10 and 36 MeV.

Figure 1

Au foils mounted on sample holder in measurement chamber. White x's indicate approximate points at which the foil thickness was measured with RBS.

Figure 2

Energy loss of 10- and 36-MeV ${}^{127}\mathrm{I}$ in Au foil as a function of foil thickness for different initial charge states. The lines present at foil thicknesses larger than $1.7\times {10}^{17}\mathrm{at}./\mathrm{c}{\mathrm{m}}^2$ are fits to the respective data sets, and the fine dash-dotted extensions of these lines down to 0 foil thickness suggest a modified stopping power during charge state equilibration. Note that a slightly larger drift between the two data points obtained without Au foil at the start and end of each measurement sequence was observed during the measurement with charge state 8+ at 36 MeV than with 16+ and 25+. The drift is discussed further in the Appendix.

Figure 3

Energy loss for additional charge state/energy combinations produced when selecting operating conditions to yield (a) 36-MeV ${}^{127}\mathrm{I}^{16+}$, (b) 36-MeV ${}^{127}\mathrm{I}^{25+}$.

Figure 4

Energy loss of 36-MeV ${}^{127}\mathrm{I}$ in Au calculated as per (3) with equilibrium charge state 12.7+, equilibrium stopping 18.17 keV/nm, and equilibration lengths 3 nm for charge state 8+, 6.7 nm for 16+, and 4.5 nm for 25+. Measurement points for the two thinnest Au foils are shown for comparison.

Figure 5

Charge state equilibration time for ion-target combinations listed in Table 2 plotted against projectile velocity relative to the Bohr velocity $v_0$. Error bars on data points obtained in this work indicate the ranges of equilibration times obtained when varying the assumed equilibrium charge state from 12.7+ as given by Bohr's simple formula [32] to 16.8+ by the formula for solid target in [26]. The dashed blue line gives an example of $v^2$ scaling of $t_{\mathrm{eq}}$, corresponding to the scaling of $d$ with ${\left(E/m\right)}^{1.5}$ proposed in [15], while the dash-dotted thin line is a fit to the data below $5v_0$ as a guide to the eye. The points denoted by teal, downward pointing triangles have been taken as the average values based on several initial charge states and/or projectile energies from [12, 13, 37, 38, 39] since several charge states yield similar equilibration lengths in [13], multiple charge states are required for calculating the equilibration time in [12] and multiple projectile velocities are required for calculating the equilibration time in [37, 38, 39].

Figure 6

RBS data (dots) and corresponding simnra calculations (lines) for all measurement points on each foil.

Figure 7

Energy converted ToF spectra for 10-MeV ${}^{127}\mathrm{I}^{8+}$ with and without Au foils, compensated for energy loss in the first EMTD foil. Solid lines represent data while dashed lines are Gaussian distributions fit to the channel range of interest for each peak.

Figure 8

Ions reaching the Au foil (or ToF detector) in configuration selected to produce (a) 36-MeV ${}^{127}\mathrm{I}^{16+}$: $V_{\mathrm{terminal}}\approx 4.05\mathrm{MV}, B_{\mathrm{magnet}}=4789\pm 1.2\mathrm{G}$; (b) 36-MeV ${}^{127}\mathrm{I}^{25+}$: $V_{\mathrm{terminal}}\approx 4.07\mathrm{MV}, B_{\mathrm{magnet}}=3065\pm 1.2\mathrm{G}$. Spectra were recorded once with each Au foil present, and twice without foil.

Figure 9

Energy converted ToF spectra obtained for primary ${}^{127}\mathrm{I}$ ion energy 36 MeV with three different initial charge states and three different Au foils, as well as a measurement without foil.