Resonant elastic scattering of polarized electrons on H-like ions

We study the polarization properties of elastic electron scattering on H-like ions using the relativistic QED theory. We calculate the complete set of parameters which describe the scattering of a polarized electron on an initially unpolarized ion and analyze them for both nonresonant and resonant scattering focusing on the LL-shell resonances. The study is carried out for ${\mathrm{B}}^{4+}, {\mathrm{Ca}}^{19+}, {\mathrm{Kr}}^{35+}$, and ${\mathrm{Xe}}^{53+}$ ions. We demonstrate that for the resonant electron scattering on ions with $Z$ up to 50 both the relativistic spin-orbit and the exchange interaction are equally significant. The possible spin exchange between the incident and bound electrons can fundamentally change the polarization of the scattered electron. We show that the involvement of the autoionizing states leads to quantitative and qualitative changes in the polarization parameters, in particular, to a significant increase in the spin asymmetry.

Figure 1

Functions $D\left(\theta \right)/I\left(\theta \right)$ (left column), $F\left(\theta \right)/I\left(\theta \right)$ (middle column), and $G\left(\theta \right)/I\left(\theta \right)$ (right column) for nonresonant scattering on ${\mathrm{Ca}}^{19+}$ and ${\mathrm{Kr}}^{35+}$ (black solid line) and Coulomb scattering by the screened potential of the nucleus (red dashed line). The kinetic energy of incident electron is 2.77 keV for ${\mathrm{Ca}}^{19+}$ and 9.22 keV for ${\mathrm{Kr}}^{35+}$.

Figure 2

Functions $H\left(\theta \right)/I\left(\theta \right)$ (black solid line) and $K\left(\theta \right)/I\left(\theta \right)$ (red dashed line) for nonresonant scattering on ${\mathrm{Ca}}^{19+}$ and ${\mathrm{Kr}}^{35+}$. The kinetic energy of incident electron is 2.77 keV for ${\mathrm{Ca}}^{19+}$ and 9.22 keV for ${\mathrm{Kr}}^{35+}$.

Figure 3

Function $D\left(\theta \right)/I\left(\theta \right)$ for electron scattering on ${\mathrm{Ca}}^{19+}$ near the resonances for five different angles $\theta$ of the scattered electron. The vertical gray dashed line denotes the resonance energy.

Figure 4

Function $D/I$ for scattering of electrons on ${\mathrm{B}}^{4+}, {\mathrm{Ca}}^{19+}, {\mathrm{Kr}}^{35+}$ and ${\mathrm{Xe}}^{53+}$ to the angle $\theta ={120}^{\circ }$. The vertical dashed lines mark the positions of resonances. The corresponding autoionizing states are presented in Table 1.

Figure 5

Same as in Fig. 3 but for $F\left(\theta \right)/I\left(\theta \right)$.

Figure 6

Same as in Fig. 4 but for $F/I$.

Figure 7

Same as in Fig. 3 but for $G\left(\theta \right)/I\left(\theta \right)$.

Figure 8

Same as in Fig. 3 but for $H\left(\theta \right)/I\left(\theta \right)$.

Figure 9

Same as in Fig. 3 but for $K\left(\theta \right)/I\left(\theta \right)$.

Figure 10

Parameter $S_{\widehat{\mathit{k}}\widehat{\mathit{k}}}$ for scattering of electrons on ${\mathrm{B}}^{4+}, {\mathrm{Ca}}^{19+}, {\mathrm{Kr}}^{35+}$, and ${\mathrm{Xe}}^{53+}$ to the angle $\theta ={180}^{\circ }$. For the backward scattering $S_{\widehat{\mathit{n}}\widehat{\mathit{n}}}$ coincides with $S_{\widehat{\mathit{k}}\widehat{\mathit{k}}}$. The vertical dashed lines mark the positions of resonances. The corresponding autoionizing states are presented in Table 1.

Figure 11

Same as in Fig. 4 but for $S_{\widehat{\mathit{q}}\widehat{\mathit{q}}}$.

Figure 12

Parameters $S_{\widehat{\mathit{n}}\widehat{\mathit{n}}}$ (black solid line) and $S_{-\widehat{\mathit{n}}-\widehat{\mathit{n}}}$ (red dashed line) for scattering on ${\mathrm{B}}^{4+}$ to the angle $\theta ={120}^{\circ }$ in the vicinity of ${\left(2s2p_{1/2}\right)}_1, {\left(2s2p_{1/2}\right)}_0$, and ${\left(2s2p_{3/2}\right)}_2$ resonances.

Figure 13

Plot of $D^{\mathrm{ion}}\left(\theta \right)/I\left(\theta \right)$ for scattering on ${\mathrm{B}}^{4+}$ as a function of incident electron energy $\varepsilon$ in the vicinity of ${\left(2s2p_{1/2}\right)}_0$ and ${\left(2s2p_{3/2}\right)}_2$ resonances (graph on the left) and as a function of $\theta$ at energies marked by black dotted lines on the left graph (graphs on the right).