Reconciliation of measured fully differential single ionization data with the first Born approximation convoluted with elastic scattering

An analysis of experimental fully differential data for single ionization in $100\mathrm{MeV}∕\mathrm{amu}$ ${\mathrm{C}}^{6+}+\mathrm{He}$ collisions is reported. We present a convolution of the first Born approximation with elastic scattering by using an event generator technique. Furthermore, the calculation is convoluted with all known experimental resolutions. Our analysis shows that elastic scattering is a viable explanation for surprising structures observed in the fully differential cross sections outside the scattering plane. Furthermore, it may even explain discrepancies in the “recoil peak” frequently observed for both ion and electron impact.

Figure 1

Single ionization cross sections differential in impact parameter $d\sigma ∕db=bP\left(b\right)$ for $100\mathrm{MeV}∕\mathrm{amu}$ ${\mathrm{C}}^{6+}+\mathrm{He}$ collisions. Solid curve, simulation using Eqs. (3, 4) for $a=0.5$; dash-dotted curve, same as solid curve, but $a=1.0$; dotted curve, CDW-EIS; dashed curve; TDCC.

Figure 2

Singly differential spectra as a function of the $x$ (top) and $y$ components (bottom) of the momentum transfer. Closed symbols, experimental data; dotted curve, unconvoluted FBA; dashed curve, FBA convoluted only with elastic scattering ($a=0.5$, see text); solid curve, FBA convoluted with both elastic scattering and experimental resolution.

Figure 3

Doubly differential spectra as function of the transverse momentum transfer component for electron energies of $10\mathrm{eV}$ (closed symbols) and $50\mathrm{eV}$ (open symbols). Theoretical curves as in Fig. 2.

Figure 4

Fully differential spectra for electron ejection into the scattering plane (top) and perpendicular plane (bottom). The electron energy is $E_{\mathrm{e}}=6.5\pm 3.5\mathrm{eV}$ and the momentum transfer $q=0.75\pm 0.25\text{a.u.}$ Theoretical curves as in Fig. 2.

Figure 5

Fully differential spectra for electron ejection into the perpendicular plane. The electron energy is $E_{\mathrm{e}}=3–50\mathrm{eV}$ and the momentum transfer $q=1.0–2.0\text{a.u.}$ Dashed curve, fully convoluted FBA with $a=0.5$ (see text); solid curve, fully convoluted FBA with $a=1.0$.

Figure 6

Same as Fig. 2, but fully convoluted FBA is shown for $a=1.0$.

Figure 7

Same as Fig. 4, but fully convoluted FBA is shown for $a=1.0$.