Introducing electron capture into the unitary-convolution-approximation energy-loss theory at low velocities

Recent developments in the theoretical treatment of electronic energy losses of bare and screened ions in gases are presented. Specifically, the unitary-convolution-approximation (UCA) stopping-power model has proven its strengths for the determination of nonequilibrium effects for light as well as heavy projectiles at intermediate to high projectile velocities. The focus of this contribution will be on the UCA and its extension to specific projectile energies far below 100 keV/u, by considering electron-capture contributions at charge-equilibrium conditions.

Figure 1

Typical behavior of basic single-electron processes as a function of the reduced projectile velocity $v_p$/$v_o$ for a fixed projectile charge state ($v_o$ is the mean orbital velocity of a certain specific state). The energy dependences of stopping cross sections related to excitation, ionization, and electron capture are shown schematically in the plot. The corresponding stopping cross sections have been extracted from experimental and theoretical cross sections and mean energy transfers for H and He targets (from Ref. [3]).

Figure 2

Bound-state energetics for electron capture from the valence-band states for different relative speeds and binding energies in the target and projectile systems. (a) and (c) refer to low projectile speeds $v_p$ and (b) and (d) refer to high speeds. (a) and (b) refer to low target binding energies (compared to the projectile) and (c) and (d) refer to high target binding energies.

Figure 3

Scaled cross-section ratio for projectile energy losses as discussed in the text (evaluated for neutral H and He target potentials interacting with H 1$s$, He 1$s$, and C 2$s$ electrons of neutral H, He, and C projectiles).

Figure 4

Projectile-energy dependence of the electronic energy loss of charge-equilibrated hydrogen beams in different heavy rare gases (Ne, Ar, and Kr). Experimental values (red diamonds) are taken from the data collection of Paul [55]. Dashed, dotted, and dashed-dotted curves are charge-weighted partial energy-loss cross sections. The solid black curve denoted Σ corresponds to the sum of these partial contributions. The open arrows and shell indicators ($L_1$,$M_1$,$N_1$,$M_{45}$) are explained in the text.

Figure 5

Ab initio electronic energy loss of charge-equilibrated sulfur ions in Ar, similar as in Fig. 4. Experimental values are taken from the data collection of Paul [55]. The dash-dot-dot curve corresponds to the trim2000 stopping-power fit [56].