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Chin. Phys. B, 2023, Vol. 32(1): 013101    DOI: 10.1088/1674-1056/ac90b0

Theoretical calculations on Landé $g$-factors and quadratic Zeeman shift coefficients of $n$s$n$p $^{3} {P}^{o}_{0}$ clock states in Mg and Cd optical lattice clocks

Benquan Lu(卢本全)1 and Hong Chang(常宏)1,2,†
1 National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;
2 The University of Chinese Academy of Sciences, Beijing 100088, China
Abstract  The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce. In this work, the hyperfine-induced Landé $g$-factors and quadratic Zeeman shift coefficients of the ${n{\rm s}n{\rm p}}$ $^3P^{\rm o}_0$ clock states for $^{111,113}$Cd and $^{25}$Mg were calculated by using the multi-configuration Dirac-Hartree-Fock theory. To obtain accurate values of these parameters, the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the Landé $g$-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy. Our calculations provide important data for estimating the first- and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.
Keywords:  optical lattice clock      hyperfine-induced Landé      g-factor      quadratic Zeeman shift coefficient      Mg and Cd  
Received:  13 July 2022      Revised:  29 August 2022      Accepted manuscript online:  09 September 2022
PACS:  31.15.aj (Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure)  
  31.15.vj (Electron correlation calculations for atoms and ions: excited states)  
  32.60.+i (Zeeman and Stark effects)  
  95.55.Sh (Auxiliary and recording instruments; clocks and frequency standards)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61775220), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030100), and the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004).
Corresponding Authors:  Hong Chang     E-mail:

Cite this article: 

Benquan Lu(卢本全) and Hong Chang(常宏) Theoretical calculations on Landé $g$-factors and quadratic Zeeman shift coefficients of $n$s$n$p $^{3} {P}^{o}_{0}$ clock states in Mg and Cd optical lattice clocks 2023 Chin. Phys. B 32 013101

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