Theoretical calculations of the Landé g -factors, electric quadrupole moments, and quadratic Zeeman shift coefficients of the clock states in the Lu + optical clock

In this study, the multiconfiguration Dirac-Hartree-Fock method was employed to calculate the Landé g -factors and electric-quadrupole moments of the 5 d 6 s 3 D 1 , 2 , 3 and 1 D 2 states, as well as the quadratic Zeeman shift coefficients of the 3 D 1 , 2 clock states in Lu + . The electron correlation, particularly higher-order electron correlation effects, along with the Breit interaction and quantum electrodynamics corrections, are systematically taken into account. Our calculated Landé g -factors, electric-quadrupole moments, and quadratic Zeeman shift coefficients for the 5 d 6 s 3 D 1 , 2 clock states are in agreement with experimental measurements within 1 % . The influence of hyperfine interactions and perturbing states on these parameters was also analyzed. Our results demonstrate that both the magnetic-dipole and the electric-quadrupole hyperfine interactions contribute significantly to the hyperfine-induced Landé g -factors and electric-quadrupole moments of the 3 D 1 , 2 states. In particular, for Lu + 176 , the electric-quadrupole hyperfine interaction accounts for approximately 15 % of the total hyperfine-induced electric-quadrupole moment of the 3 D 1 , 2 states. This study provides valuable theoretical support for evaluating frequency shifts in the Lu + optical clock.