Correlation effects in out-of-plane excitation-ionization collisions

We present theoretical three-dimensional fully differential cross sections (FDCSs) for electron-impact excitation-ionization of helium when the ionized electron is found outside of the scattering plane. Using our first Born approximation model, we examine the effects of electron correlation in the initial state and show that it significantly affects the shape of the out-of-plane FDCS.

Figure 1

Three-dimensional FDCS for electron-impact excitation-ionization of helium using the FBA-HY and FBA-VAR. Results are shown for an ionized electron energy of 3 eV and a projectile scattering angle of 4.1°. The incident projectile energy and final state of the ${\mathrm{He}}^{+}$ ion are labeled in the figure as are the incident projectile ($k_i$), scattered projectile ($k_f$), and momentum-transfer ($q$) directions.

Figure 2

The same as Fig. 1 but with an ionized electron energy of 20 eV.

Figure 3

Coordinate system showing the incident projectile momentum ($k_i$), scattered projectile momentum ($k_f$), and momentum-transfer vectors ($q$). The incident projectile momentum is in the $z$ direction; the scattered projectile momentum and momentum transfer both lie in the $x-z$ plane. The perpendicular plane is defined as the $x$′-$z$′ plane where a rotation about the $y$ axis by an angle ${\theta }_q$ has been performed to find the $x$′ and $z$′ axes.

Figure 4

Two-dimensional FDCS slices for electron-impact excitation-ionization of helium using the FBA-HY (solid line) and FBA-VAR (dashed line) models in the scattering plane and plane perpendicular to the momentum transfer. Results are shown for an ionized electron energy of 3 eV and a projectile scattering angle of 4.1°. The incident projectile energy and final state of the ${\mathrm{He}}^{+}$ ion are labeled in the figure as are the incident projectile ($k_i$), scattered projectile ($k_f$), and momentum-transfer ($q$) vectors.

Figure 5

The same as Fig. 4 but for an ionized electron energy of 20 eV.