Role of two-electron excitation-ionization processes in the ionization of lithium atoms by fast ion impact

We study excitation and ionization in the 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collision system, which was the subject of a recent reaction-microscope-type experiment [D. Fischer et al., Phys. Rev. Lett. 109, 113202 (2012)]. Starting from an independent-electron model based on determinantal wave functions and using a single-electron basis generator method calculation and a single-electron continuum distorted-wave with eikonal initial-state calculation, we show that pure single ionization of a lithium $K$-shell electron is too weak a process to explain the measured electron-energy-differential cross section. Rather, our analysis suggests that two-electron excitation-ionization processes occur and have to be taken into account when comparing with the data. Good agreement is obtained only if we replace the independent-electron calculation by an independent-event model for one of the excitation-ionization processes and also take a shake-off process into account.

Figure 1

Total excitation, capture, and ionization probabilities according to Eqs. (6)–(11) for 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collisions obtained from TC-BGM calculations for Li($1s$) (upper panel) and Li($2s$) (lower panel) initial states. In addition, CDW-EIS ionization probabilities are displayed as (black) dotted curves.

Figure 2

Impact-parameter-weighted probabilities for $2s$ vacancy production [Eq. (14)], exclusive $2s$ ionization [Eq. (20)], and single-particle $2s$ ionization [Eq. (11)] for 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collisions. All curves shown are obtained from TC-BGM calculations. The curves displaying the probabilities (14) and (20) sit on top of each other.

Figure 3

Impact-parameter-weighted probabilities for $1s$ vacancy production [Eq. (15)], exclusive $1s$ ionization [Eq. (22)], $1s$ ionization with $2s$ excitation [Eq. (23)], $1s$ excitation with $2s$ ionization [Eq. (24)], the sum of (22), (23), and (24) ($\sum$), and single-particle $1s$ ionization multiplied by 2 [Eq. (10)$\times 2$] for 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collisions. All curves shown are obtained from TC-BGM calculations.

Figure 4

Single-differential cross sections for single-particle $2s$ ionization [Eq. (11)], exclusive $2s$ ionization [Eq. (20)], single-particle $1s$ ionization multiplied by 2 [Eq. (10)$\times 2$], exclusive $1s$ ionization [Eq. (22)], $1s$ ionization with $2s$ excitation [Eq. (23)], $1s$ excitation with $2s$ ionization [Eq. (24)], and the sum of (22), (23), and (24) ($\sum$) as functions of the electron energy for 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collisions. Experimental data are from [7].

Figure 5

Single-differential cross sections for $2s$ ionization with $1s+$ excitation extrapolated to $n\to \infty$ [Eq. (26) for all $n$], the shake-off model as explained in the text, exclusive $1s$ ionization [Eq. (22)], and $1s$ ionization with $2s$ excitation extrapolated to $n\to \infty$ [Eq. (23) for all $n$] as functions of the electron energy for 1.5-MeV/amu ${\mathrm{O}}^{8+}$-Li collisions. The solid thick curve dubbed “final total EI” is obtained from adding the four other calculated SDCSs shown here and represents our final result for total EI. Experimental data are from [7].

Figure 6

The OPM potentials and $1s$ and $2p$ radial orbital densities for Li and ${\mathrm{Li}}^{+}$. The Li($1s$) and ${\mathrm{Li}}^{+}$($1s$) densities sit on top of each other. The horizontal lines indicate the binding energies of the $1s$ and $2p$ orbitals.