Orbital collapse and the photoionization of the inner4dshells for Xe-like ions

Photoionization of the inner $4d$ shells for Xe, ${\mathrm{Cs}}^{+}$, ${\mathrm{Ba}}^{2+}$, and ${\mathrm{La}}^{3+}$ are studied with the use of the relativistic random-phase approximation. Total cross sections, partial cross-section branching ratios, and angular-distribution asymmetry parameters are calculated, and their systematic trends along the isoelectronic sequence are studied. Important dynamic effects of electron correlations are obtained from an eigenchannel analysis involving the eigenquantum defects, the eigendipole amplitudes, and the transformation $U$ matrices. We find that there are shape resonances in the effective potential for $f$ electrons, and that the collapse of the $4f$ orbital along the isoelectronic sequence is closely related to changes in $f$ orbitals in passing through these resonances.