Role of hyperfine interaction in Landé $g$-factors of ${}^3{P}_0^o$ clock states

Abstract

In the weak-magnetic-field approximation, we derived a general expression of hyperfine-induced Landé $g$-factors. By using this formula and the multi-configuration Dirac-Hartree-Fock theory, the $g$-factors were calculated for the $3s3p{}^3{P}_0^o$ clock state in ${}^{27}$Al${}^{+}$ and $5s5p{}^3{P}_0^o$ in ${}^{87}$Sr. The present results, $\delta g_{\mathrm{hfs}}^{(1)}{(}^3{P}_0^o)=-1.183(6)\times 10^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\mathrm{hfs}}^{(1)}{(}^3{P}_0^o)=7.78(30)\times 10^{-5}$ for ${}^{87}$Sr agree with experimental values very well. Our theory is also useful to predict hyperfine-induced Landé $g$-factors for other atomic systems.

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Cited by in corpus (1)

• Theoretical Calculation of the Quadratic Zeeman Shift Coefficient of the 3P0 clock state for Strontium Optical Lattice Clock