Third-order relativistic many-body calculations of energies, transition rates, hyperfine constants, and blackbody radiation shift in ¹⁷¹Yb⁺

Relativistic many-body perturbation theory is applied to studying the properties of singly ionized ytterbium, Yb⁺. Specifically, energies of the [Xe]4f¹⁴ns_1/2, [Xe]4f¹⁴np_j, and [Xe]4f¹⁴nd_j (n≤9) are calculated through third order. Reduced matrix elements, oscillator strengths, and transition rates are determined for electric-dipole transitions including the 6s, 7s, 8s, 6p, 7p, 5d, and 6d states. Lifetime values are determined for the 6p states. Electric-dipole (6s_1/2−np_j, n=6–12) matrix elements are calculated to obtain the ground-state E1 polarizability. The hyperfine A values are determined for the low-lying levels up to n=7 of ¹⁷¹Yb II. The quadratic Stark effect on hyperfine structure levels of ¹⁷¹Yb II ground state is investigated. The calculated shift for the (F=1, M=0)↔(F=0, M=0) transition is −0.1796 Hz/(kV/cm)², in agreement with the previous theoretical result −0.171±0.009. These calculations provide a theoretical benchmark for comparison with experiment and theory.