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

Min Feng1,2,3, Ting Liang1,2,3, Jin Cao1,2,3, Yiming Wang1,2, Tingxian Zhang4, Benquan Lu1,2,*, and Hong Chang1,2,3,†

  • *Contact author: lubenquan@ntsc.ac.cn
  • †Contact author: changhong@ntsc.ac.cn
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Phys. Rev. A 113, 032821 – Published 27 March, 2026

DOI: https://doi.org/10.1103/98z8-wv5d

Abstract

In this study, the multiconfiguration Dirac-Hartree-Fock method was employed to calculate the Landé g-factors and electric-quadrupole moments of the 5d6s3D1,2,3 and 1D2 states, as well as the quadratic Zeeman shift coefficients of the 3D1,2 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 5d6s3D1,2 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 3D1,2 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 3D1,2 states. This study provides valuable theoretical support for evaluating frequency shifts in the Lu+ optical clock.

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Phys. Rev. A 113, 032821– Published 27 March, 2026
  • Received 26 September 2025
  • Accepted 3 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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