Theoretical calculations on lifetimes of the low-lying excited states in Lu⁺

The lifetime of the 5d6s ³D₁ clock state in Lu⁺ exhibits a large discrepancy between experimental and theoretical values. To resolve this discrepancy, we perform calculations of the magnetic dipole transition rate between the 5d6s ³D₁ and 6s²¹S₀ states using the multi-configuration Dirac–Hartree–Fock method. The effects of electron correlations, Breit interaction, and quantum electrodynamics (QED) corrections on the transition parameters are analyzed systematically. The calculated 5d6s ³D₁–6s²¹S₀ magnetic dipole transition rate, 1.69(7) × 10⁻⁶ s⁻¹, shows excellent agreement with the experimental measurement. To accurately determine the lifetime of the ³D₁ clock state, the hyperfine-induced electric quadrupole transition rate between the ³D₁ and ground states is also calculated. Furthermore, the rates of various transitions between states in the 5d6s configuration are obtained. The lifetimes of the ³D_2,3 and ¹D₂ states are consistent with previous theoretical calculations.