Photoabsorption studies of some closed-shell ions in the La isonuclear sequence

Photoionization cross sections and dipole angular distribution asymmetry parameters, β, of $5s$ and $4d$ shells of the closed-shell ions $({\mathrm{La}}^{3+},{\mathrm{La}}^{9+}$, and ${\mathrm{La}}^{11+})$ in the La isonuclear sequence have been studied using the relativistic random phase approximation. The positions of the $5s$ Cooper minima in ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$ ions are found to be extremely sensitive to the details of electron correlation. The results show that the $5s$ cross sections of ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$ do not lie along the same curve near the thresholds; the $4d$ cross sections, however, do match well in overlap regions so they lie along the same curve, over the isonuclear sequence, except for a shift in threshold towards higher energies with increasing degree of ionization.

Figure 1

$5s$ photoionization cross sections, ${\sigma }_{5s}$, for ${\mathrm{La}}^{3+}$ calculated at various levels of truncation of the RRPA with each cross section labeled by the number of channels and the subshells included, and thresholds labeled and indicated by vertical lines for energies (a) 2.6–3.0 a.u., (b) 5.2–7.5 a.u. CM refers to the location of the Cooper minimum.

Figure 2

Same as Fig. 1 but for the photoelectron angular distribution asymmetry parameter, ${\beta }_{5s}$.

Figure 3

Same as Fig. 1 but for ${\mathrm{La}}^{9+}$ in the 5.5–7.0 a.u. energy range.

Figure 4

Same as Fig. 2 but for ${\mathrm{La}}^{9+}$ in the 5.5 to 7.0 a.u. energy range.

Figure 5

Same as Fig. 1 but for ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$. The lower thresholds are for ${\mathrm{La}}^{3+}$ and the higher for ${\mathrm{La}}^{9+}$.

Figure 6

Same as Fig. 2 but for ${\mathrm{La}}^{3+}$ and ${\mathrm{La}}^{9+}$. The lower thresholds are for ${\mathrm{La}}^{3+}$ and the higher for ${\mathrm{La}}^{9+}$.

Figure 7

Same as Fig. 1 but for the total $4d$ cross sections $\left(4d_{5/2}+4d_{3/2}\right)$ of ${\mathrm{La}}^{3+},{\mathrm{La}}^{9+}$, and ${\mathrm{La}}^{11+}$, with the $4d$ thresholds of each of the respective ion stages given.

Figure 8

Same as Fig. 2 but for the effective $4d$ β's of ${\mathrm{La}}^{3+},{\mathrm{La}}^{9+}$, and ${\mathrm{La}}^{11+}$ (as defined in text), with the $4d$ thresholds of each of the respective ion stages given.

Figure 9

$4d_{5/2}$: $4d_{3/2}$ branching ratios for ${\mathrm{La}}^{3+},{\mathrm{La}}^{9+}$, and ${\mathrm{La}}^{11+}$ as functions of photon energy with the $4d$ thresholds of each of the respective ion stage given.