Contribution of the4f-core-excited states in determination of atomic properties in the promethium isoelectronic sequence

Abstract

The atomic properties of Pm-like ions were comprehensively studied using relativistic atomic codes. Excitation energies of the $4{f}^{14}nl$ (with $nl=5s$, $6s$, $5p$, $6p$, $5d$, $6d$, and $5f$) states in Pm-like ions with nuclear charge $Z$ ranging from 74 to 100 are evaluated within the framework of relativistic many-body theory (RMBPT). First- and second-order Coulomb energies and first- and second-order Breit corrections to the energies are calculated. Two alternative treatments of the Breit interaction are investigated. In the first approach we omit Breit contributions to the Dirac-Fock potential and evaluate Coulomb and Breit-Coulomb corrections through second order perturbatively. In the second approach were included both Coulomb and Breit contributions on the same footing via the Breit-Dirac-Fock potential and then treat the residual Breit and Coulomb interactions perturbatively. The results obtained from the two approaches are compared and discussed. The important question of what is the ground state in Pm-like ions was answered. Properties of the $4f$-core-excited states are evaluated using the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (hullac code) and the Hartree-Fock-relativistic method (cowan code). We evaluate excitation energies and transition rates in Pm-like ions with nuclear charge $Z$ ranging from 74 to 92. Our large scale calculations include the following set of configurations: $4{f}^{14}5s$, $4{f}^{14}5p$, $4{f}^{13}5{s}^{2}$, $4{f}^{13}5{p}^{2}$, $4{f}^{13}5s5p$, $4{f}^{12}5{s}^{2}5p$, $4{f}^{12}5s5{p}^{2}$, and $4{f}^{12}5{p}^{3}$. Trends of excitation energies as function of $Z$ are shown graphically for selected states. Excitation energies, transition rates, and lifetimes in Pm-like tungsten are evaluated with additional inclusion of the $4{f}^{11}5{s}^{2}5{p}^{2}$, $4{f}^{11}5s5{p}^{3}$, $4{f}^{10}5{s}^{2}5{p}^{3}$, and $4{f}^{10}5s5{p}^{4}$ configurations. This represents an unusual example of an atomic system where the even-parity complex [$4{f}^{14}5s+4{f}^{13}5s5p+4{f}^{12}5s5{p}^{2}+4{f}^{11}5s5{p}^{3}+4{f}^{10}5s5{p}^{4}$] and the odd-parity complex [$4{f}^{14}5p+4{f}^{13}5{s}^{2}+4{f}^{12}5{s}^{2}5p+4{f}^{11}5{s}^{2}5{p}^{2}+4{f}^{10}5{s}^{2}5{p}^{3}$] include so different configurations. Wavelengths of the $4{f}^{14}5s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}$-$4{f}^{14}5p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{J}$ transition obtained by the cowan, hullac, and RMBPT codes are compared with other theoretical results and available measurements.