Probing Scattering Wave Functions Close to the Nucleus

Recently, three-dimensional imaging of the ejected electrons following $100\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ ${\mathrm{C}}^{6+}$ single ionization of helium led to the observation of a new structure not predicted by theory [M. Schulz et al., Nature (London) 422, 48 (2003)]. Instead of the usual “recoil lobe” centered on the momentum-transfer axis, a ring-shaped structure centered on the beam axis was observed. New measurements at $2\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ exhibit a similar structure, which is now predicted by theory. We argue that the same theory failed at $100\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ because the faster projectiles probe distances much closer to the nucleus, where our multiple-scattering model is expected to break down.

Figure 1

Comparison of theory and experiment (Expt) for single ionization of helium by $100\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ ${\mathrm{C}}^{6+}$ ions. The fully differential cross section is shown. The momentum of the incident projectile is ${\mathbf{p}}_0$ and the momentum transfer is $\mathbf{q}$. The energy of the ejected electron is 6.5 eV and $|\mathbf{q}|=0.75\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ The 3DW-FBA model is discussed in the text.

Figure 2

Same as Fig. 1 for $2\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{m}\mathrm{u}$ collision energy, 1 eV electron energy, and $|\mathbf{q}|=1.5\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ The FBA, PCI, 3DW-FBA, and 3DW-EIS models are discussed in the text.