Correlation and relativistic effects for the4f−nlmultipole transitions in Yb III ions

Abstract

Wavelengths, transition rates, and line strengths are calculated for the multipole (E1, M1, E2, M2, and E3) transitions between the excited $[\mathrm{Xe}]4{f}^{13}ns$, $[\mathrm{Xe}]4{f}^{13}nd$, and $[\mathrm{Xe}]4{f}^{13}np$ and the ground $[\mathrm{Xe}]4{f}^{14}$ state in Yb III ion with the nuclear charge $Z=70$ $([\mathrm{Xe}]=[\mathrm{Ni}]4{s}^{2}4{p}^{6}4{d}^{10}5{s}^{2}5{p}^{6})$. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in this hole-particle system. This method is based on the relativistic many-body perturbation theory that agrees with multiconfiguration Dirac-Fock calculations in lowest-order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a $[\mathrm{Xe}]4{d}^{14}$ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. Evaluated multipole matrix elements for transitions from excited states into the ground states and transitions between excited states are used to determine the lifetime of the 20 $[\mathrm{Xe}]4{f}^{13}5d(J)$ levels, four $[\mathrm{Xe}]4{f}^{13}6s(J)$ levels, 12 $[\mathrm{Xe}]4{f}^{13}6p(J)$ levels, and four $[\mathrm{Xe}]4{f}^{13}7s(J)$ levels.