Evidence for unnatural-parity contributions to electron-impact ionization of laser-aligned atoms

Recent measurements have examined the electron-impact ionization of excited-state laser-aligned Mg atoms. In this work we show that the ionization cross section arising from the geometry where the aligned atom is perpendicular to the scattering plane directly probes the unnatural parity contributions to the ionization amplitude. The contributions from natural parity partial waves cancel exactly in this geometry. Our calculations resolve the discrepancy between the nonzero measured cross sections in this plane and the zero cross section predicted by distorted-wave approaches. We demonstrate that this is a general feature of ionization from $p$-state targets by additional studies of ionization from excited Ca and Na atoms.

Figure 1

Geometry of the scattering experiments performed on Mg [17] and for the Ca experiments reported here. The incident electron has momentum ${\mathbf{k}}_{\mathbf{0}}$ and the outgoing electrons have momentum vectors ${\mathbf{k}}_{\mathbf{1}}$ and ${\mathbf{k}}_{\mathbf{2}}$. The target $p$ orbital is shown here to be aligned along the $y$ axis using the laser beam polarization, i.e., perpendicular to the scattering plane (in which the outgoing electrons lie).

Figure 2

Triple differential cross sections for the electron-impact ionization of excited-state Mg for equal energy sharing between the outgoing electrons of $E_1=E_2=20$ eV. The measurements of [17] are compared with TDCC calculations for various $({\theta }_T,{\varphi }_T)$ orientations of the target $3p$ orbital as indicated. We present TDCC calculations performed at a fixed ${\theta }_1$ angle of ${30}^{\circ }$ (the fixed angle reported in the measurements of [17]) (solid red lines) and at angles of ${25}^{\circ }$ (dashed blue lines) and ${35}^{\circ }$ (dot-dashed purple lines).

Figure 3

Same as Fig. 2, except now we show only the ${\theta }_1={30}^{\circ }$ TDCC calculation. We also present a TDCC calculation (purple dashed lines) in which the unnatural parity contribution is omitted.

Figure 4

Triple differential cross sections for the electron-impact ionization of excited-state Na for equal energy sharing between the outgoing electrons of $E_1=E_2=20$ eV. The cross sections are presented for a fixed electron angle of ${\theta }_1={30}^{\circ }$ and at various orientations of the $3p$ orbital as indicated. We compare the TDCC calculations (solid blue lines) with DWBA (dot-dashed red lines) and 3DW calculations (dashed green lines) made in a similar manner to the distorted-wave calculations presented in [20]. In this figure, the DWBA and 3DW calculations have been normalized to the TDCC calculations.

Figure 5

Triple differential cross sections for the electron-impact ionization of excited-state Ca for equal energy sharing between the outgoing electrons of $E_1=E_2=30$ eV. Measurements are compared with TDCC calculations (solid blue lines) and 3DW calculations (green dashed line) as described in the text. The measurements were made for a fixed electron angle of ${45}^{\circ }$. The upper panel shows the cross section for the $4p$ orbital in the scattering plane and the lower panel shows the cross section for the $4p$ orbital perpendicular to the scattering plane. The thick solid blue lines indicate a TDCC calculation averaged over the experimental angular uncertainties, while the thin (solid red, dashed light blue, dot-dashed purple) lines show the individual TDCC calculations at each fixed angle.