Projectile-Charge Sign Dependence of Four-Particle Dynamics in Helium Double Ionization

Double ionization of helium by 6 MeV proton impact has been explored in a kinematically complete experiment using a “reaction microscope.” For the first time, fully differential cross sections for positively charged projectiles have been obtained and compared with data from 2 keV electron impact. The significant differences observed in the angular distribution of the ejected electrons are attributed to the charge sign of the projectile, resulting in different dynamics of the four-particle Coulomb system, which is not considered in the first Born approximation.

Figure 1

The ratio $R={\sigma }^{++}/{\sigma }^{+}$ of the total double-to-single ionization cross sections for helium as a function of the projectile velocity for protons (full circles [3]), antiprotons (full triangles [3, 4]), electrons (open circles [5, 6]), positrons (open triangles [7]), and ${\mathrm{N}\mathrm{e}}^{10+}$ (full square [8]). The dash-dotted lines denote the velocity dependence for the “pure” two-step 2 (TS2) mechanism and the high-velocity limit for shakeoff (SO) [9].

Figure 2

Angular distribution of the two ejected electrons (${\vartheta }_1,{\vartheta }_2$: polar angle with respect to the forward beam direction) in coplanar geometry for proton (a)–(c) and electron (d)–(f) impact at a momentum transfer of 0.2 to 0.8 a.u. (a),(d), 0.8 to 1.4 a.u. (b),(e), and 1.4 to 2.0 a.u. (c),(f), respectively. A symmetric energy sharing is chosen ($E_{\mathrm{e}\mathrm{1}}=E_{\mathrm{e}\mathrm{2}}<25\mathrm{e}\mathrm{V}$). The black area in the middle of the diagrams denotes the kinematically allowed momentum transfer directions, which ranges from about 0° to 75° (a),(d), 60° to 80° (b),(e), and 75° to 85° (c),(f), respectively. The symmetry axis obtained in the FBA (solid lines) and the nodes for dipole transitions (dashed lines) are shown for an averaged momentum transfer angle.