Propensity for distinguishing two free electrons with equal energies in electron-impact ionization of helium

We report a combined experimental and theoretical study on the electron-impact ionization of helium at $E_0=70.6\mathrm{eV}$ and equal energy sharing of the two outgoing electrons ($E_1=E_2=23\mathrm{eV}$), where a double-peak or dip structure in the binary region of the triple differential cross section is observed. The experimental cross sections are compared with results from convergent close-coupling (CCC), $B$-spline R-matrix-with-pseudostates (BSR), and time-dependent close-coupling (TDCC) calculations, as well as predictions from the dynamic screening three-Coulomb (DS3C) theory. Excellent agreement is obtained between experiment and the nonperturbative CCC, BSR, and TDCC theories, and good agreement is also found for the DS3C model. The data are further analyzed regarding contributions in particular coupling schemes for the spins of either the two outgoing electrons or one of the outgoing electrons and the $1s$ electron remaining in the residual ion. While both coupling schemes can be used to explain the observed double-peak structure in the cross section, the second one allows for the isolation of the exchange contribution between the incident projectile and the target. For different observation angles of the two outgoing electrons, we interpret the results as a propensity for distinguishing these two electrons—one being more likely the incident projectile and the other one being more likely ejected from the target.

Figure 1

Sketch of the $(e,2e)$ reaction for the direct scattering process (a) and the exchange process (b).

Figure 2

Three-dimensional representation of the TDCS for $(e,2e)$ on He at equal energy sharing ($E_1=E_2=23$ eV) as a function of the emission angle ${\theta }_2$ of one electron with the other electron's detection angle ${\theta }_1$ being fixed to (a) and (b) ${\theta }_1$ = $-{35}^{\circ }$; (c) and (d) ${\theta }_1$ = $-{40}^{\circ }$; (e) and (f) ${\theta }_1$ = $-{45}^{\circ }$; (g) and (h) ${\theta }_1$ = $-{50}^{\circ }$. Left column, experiment; right column, CCC calculation.

Figure 3

Experimental data compared with CCC, BSR, and TDCC predictions for the TDCS in the scattering plane ($E_1=E_2=23$ eV) as a function of one-electron emission angle (${\theta }_2$) with the other electron emission angle ${\theta }_1$ fixed to $-{35}^{\circ }$ (a), $-{40}^{\circ }$ (b), $-{45}^{\circ }$ (c), and $-{50}^{\circ }$ (d). Also shown are the TDCC results for the contributions from the final-state (FS) singlet and triplet spin channels constructed from coupling the spins of the two outgoing electrons. See text for details.

Figure 4

Same as Fig. 3, except that the BSR theory is used to compare with the experimental data. Also shown are the contributions from excitation of the target-state (TS) singlet and triplet. See text for details.

Figure 5

Same as Fig. 3, except that the DS3C theory (solid line) is used to compare with the experimental data. Also shown are the separate direct and exchange contributions. See text for details.