Coulomb Four-Body Problem: Electron-Impact Double Ionization of Helium in the Threshold Regime

Double ionization of helium by electron impact is studied in a kinematical complete experiment in the threshold regime at 5 eV excess energy. As expected the recoil ion carries the full initial projectile momentum and the emitted electrons’ sum momentum in average is zero. The electron emission is revealed to be completely dominated by the symmetric 120° configuration predicted by many threshold theories but never observed experimentally before. Fully differential cross sections show a more complex structure than expected for a pure threshold collision dynamics.

Figure 1

The distribution of the final-state electrons’ sum momentum $p_{\mathrm{sum}}$ and the respective recoil-ion momentum distribution projected onto a plane containing the incoming beam direction (indicated). (a) For the projectile energy $E_0=106\mathrm{eV}$ ($p_0=2.8\mathrm{a}.\mathrm{u}.$). (b) For $E_0=84\mathrm{eV}$ ($p_0=2.5\mathrm{a}.\mathrm{u}.$). The incoming projectile momentum ${\mathit{p}}_0$ is indicated. The limiting momentum ranges for the case that one electron carries the full excess energy are marked by circles.

Figure 2

Cross section differential in the relative emission angles of the final-state electrons. Left diagrams: Cross section as a function of ${\theta }_{12}$ and ${\theta }_{23}$ (see text). (a) For $E_0=106\mathrm{eV}$ ($E_{\mathrm{exc}}=27\mathrm{eV}$). (b) For $E_0=84\mathrm{eV}$ ($E_{\mathrm{exc}}=5\mathrm{eV}$). In this representation the solid angle correction factor $(\sin {\theta }_{12}\times \sin {\theta }_{23}{)}^{-1}$ was applied and gives rise to an increased data scattering along the boundaries of the diagrams. Right diagrams: Cross section summed over ${\theta }_{23}$. (b) For $E_0=106\mathrm{eV}$, (d) For $E_0=84\mathrm{eV}$.

Figure 3

Fully differential cross sections for symmetric energy sharing $E_1=E_2=E_3=1.6\mathrm{eV}\pm 1\mathrm{eV}$ among the final-state electrons. All three outgoing electron momentum vectors are in a common plane containing the incoming electron beam axis ${\mathit{p}}_0$ (indicated as an arrow). Two-electron emission angles are fixed along the directions indicated by arrows. The gray lobes are meant for guiding the eye.