Variation of photoelectron angular distributions along the Ar and Ca isonuclear sequences

The dipole angular distribution asymmetry parameter, $\beta$, for photoelectrons resulting from $2p$ photoionization of Ar, ${\mathrm{Ar}}^{6+}$, and ${\mathrm{Ar}}^{8+}$ and Ca, ${\mathrm{Ca}}^{2+}$, and ${\mathrm{Ca}}^{8+}$ of the Ar ($Z=18$) and Ca ($Z=20$) isonuclear sequences, respectively, have been studied using the relativistic random-phase approximation over a broad range of photon energy. In the absence of relaxation, it is known that inner-shell cross sections are essentially unchanged, as a function of photon energy, upon the removal of outer-shell electrons. The present results show that this is not true for the photoelectron angular distribution asymmetry parameters, particularly near the ionization thresholds.

Figure 1

Photoionization cross sections for the $2p$ subshell of Ar, ${\mathrm{Ar}}^{6+}$, and ${\mathrm{Ar}}^{8+}$. Vertical lines indicate the DHF $2p_{1/2}$ thresholds.

Figure 2

$2p$ dipole angular distribution asymmetry parameter for the Ar isonuclear sequence. Vertical lines indicate the DHF $2p_{1/2}$ thresholds.

Figure 3

Cosine of the phase-shift differences for the photoionization channels from the $2p_{3/2}$ subshell (upper panel) and the $2p_{1/2}$ subshell (lower panel) for three ions of the Ar isonuclear sequence. The phase-shift differences $\delta (p_{3/2}\to s_{1/2})-\delta (p_{3/2}\to d_{3/2})$ and $\delta (p_{3/2}\to s_{1/2})-\delta (p_{3/2}\to d_{5/2})$ are almost identical so the difference is designated as $\delta (p_{3/2}\to s_{1/2})-\delta (p_{3/2}\to d)$. Cosines of the phase-shift difference $\delta (p_{3/2}\to d_{3/2})-\delta (p_{3/2}\to d_{5/2})$ for Ar, ${\mathrm{Ar}}^{6+}$, and ${\mathrm{Ar}}^{8+}$ are essentially unity and are not shown.

Figure 4

Photoionization cross sections for the $2p$ subshell of Ca, ${\mathrm{Ca}}^{2+}$, and ${\mathrm{Ca}}^{8+}$. Vertical lines indicate the DHF $2p_{1/2}$ thresholds.

Figure 5

$2p$ dipole angular distribution asymmetry parameter for the Ca isonuclear sequence. Vertical lines indicate the DHF $2p_{1/2}$ thresholds.

Figure 6

As in Fig. 3, but for the Ca isonuclear sequence.