Ionization of helium by slow antiproton impact: Total and differential cross sections

We investigate theoretically the single and double ionization of the He atom by antiproton impact for projectile energies ranging from 3 keV up to 1000 keV. We obtain accurate total cross sections by directly solving the fully correlated two-electron time-dependent Schrödinger equation. The cross sections are in excellent agreement with the available experimental data. We also present fully ab initio doubly differential data for single ionization at 10 and 100 keV impact energies and compare to classical-trajectory Monte Carlo calculations. In these differential cross sections we identify the binary-encounter peak along with the anticusp minimum. Furthermore, we also point out the importance of the postcollisional electron-projectile interaction at low antiproton energies, which significantly suppresses electron emission in the forward direction.

Figure 1

Total ionization cross sections for the single ionization of He by antiproton impact. The present TDCC results are compared with the experimental data of Andersen et al. [1] (CERN90), of Hvelplund et al. [2] (CERN94), and of Knudsen et al. [3] (CERN08). In panel (a) we also compare with the TDDCC results of Foster et al. [7, 8] (TDCC-Foster) and of Guan et al. [9] (TDCC-Guan). In panel (b) we compare with other fully correlated theoretical calculations of Abradurakhmanov et al. [11] (CCC-MC) and of Baxter et al. [18] (TDDFT). In panel (c) we compare with calculations of McGovern et al. [10] (CP), the CDW-EIS calculations [12], the frozen core CCC (CC-FC) calculations [11], and our frozen-TDCC calculations (see text).

Figure 2

Total ionization cross sections for the double ionization of He by antiproton impact. Experimental data of Andersen et al. [1] (CERN90), of Hvelplund et al. [2] (CERN94), and of Knudsen et al. [4] (CERN09) are compared with the present TDCC and other fully correlated theoretical calculations of Baxter et al. [18] (TDDFT), of Foster et al. [7] (TDCC-Foster), and of Guan et al. [9] (TDCC-Guan).

Figure 3

Doubly differential cross section (Mb/a.u.${}^2$) for SI as a function of the parallel ($p_{\parallel }$) and perpendicular ($p_{\perp }$) momentum components of the ejected electron. (a), (b) TDCC and (c), (d) CTMC calculations are compared at (a), (c) 10 keV and (b), (d) 100 keV antiproton energies. Both models show the characteristic features of the cross sections with the deep anticusp minima around the projectile velocity and the distribution of the continuum electrons around the binary-encounter ridge (half circles); see text.

Figure 4

The Gamow factor in the truncated angular basis with maximum angular momentum $l_{\max }$ for 10 keV (first row) and 100 keV (second row) projectile velocities and cuts along (first column) and perpendicular (second column) to the projectile velocity.

Figure 5

Singly differential cross section ${\sigma }^{\mathrm{SI}}\left(\theta \right)$ for SI as a function of electron ejection angle. $\theta =0^{\circ }$ corresponds to ejection in the direction of the outgoing antiproton. The figure illustrates the suppression of electron emission in the forward direction for low projectile velocities.

Figure 6

Singly differential cross sections ${\sigma }^{\mathrm{SI}}\left(E_e\right)$ integrated over a forward cone with cone angle ${\theta }_{\max }$ at 10 keV (upper) and 100 keV (lower) antiproton energies. For an easier comparison, the cross sections were normalized to the maximum of the SDCS at ${\theta }_{\max }={30}^{\circ }$. The wiggles in the 10 keV differential cross section are caused by partially resolved Beutler-Fano resonances due to doubly excited states which are excited by the projectile; see text.