Kinetic-energy transfer in highly-charged-ion collisions with carbon

We present an accurate theoretical model for the charge dependence of kinetic energy transferred in collisions between slow highly charged ions (HCIs) and the atoms in a carbon solid. The model is in excellent agreement with experimental kinetic-energy-loss data for carbon nanomembrane and thin carbon foil targets. This study fills a notable gap in the literature of charged-particle energy loss in the regime of low incident velocity ($v_p\lesssim 2.188\times {10}^6$ m/s) where charge states greatly exceed the equilibrium values.

Figure 1

(a) Mean energy loss of ${\mathrm{Xe}}^{Q+}$ transmitted through C nanomembranes. Triangles are data from Fig. 3 in Ref. [16] ($E_p=40$ keV). Dashed and solid lines are calculated from $T(Q,b)$ by using the small-angle approximation [Eqs. (3) and (4)] and exact calculation [Eqs. (3) and (5)], respectively. (b) Impact parameters extracted from fits to data: $b_{\mathrm{c}}$ from the small-angle approximation and $b_1$ from the exact calculation (left axis). ${\theta }_{1,\mathrm{LAB}}$ is the scattering angle in the laboratory frame for impact parameter $b_1$ (right axis).

Figure 2

Mean energy loss of (a) ${\mathrm{Au}}^{Q+}, {\mathrm{Xe}}^{Q+}, {\mathrm{Kr}}^{Q+}$ and (b) ${\mathrm{Ar}}^{Q+}, {\mathrm{O}}^{Q+}$ with $v_p\approx 0.3 [{\mathrm{Xe}}^{Q+}$: $E_p$ = ($312.4\pm 2$) keV] transmitted through C foils ($\mathrm{\Delta }x=104$ Å) [15]. Markers are data, solid lines are calculations of $(S_n+S_e)\mathrm{\Delta }x$, and dashed lines are calculations of $S_n\mathrm{\Delta }x$.

Figure 3

(a) Calculated $T(Q,b)$ for ${\mathrm{Xe}}^{Q+}$ at $E_p=312.4$ keV. The dashed line indicates $T_{max}$. (b) $Q_{\mathrm{eff}}\left(b\right)$ from Eq. (2) plotted for the same $Q$ as in panel (a).