In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in ${}^{27}$Al${}^{+}$ and ${}^{87}$Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=-1.183\left(6\right)\times {10}^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=7.78\left(30\right)\times {10}^{-5}$ for ${}^{87}$Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the $g$-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in these two atomic systems.

在弱磁场近似中，我们计算了超精细感应的朗德 $G$的因素 ${}^3{P}_0^{Ø}$ 时钟状态 ${}^{27}$铝${}^{+}$ 和 ${}^{87}$通过使用多配置Dirac–Hartree–Fock方法来实现Sr。目前的结果，$\delta G_{\text{高频头}}^{（\mathrm{1个}）}（{}^3{P}_0^{Ø}）=-1.183（6）\times {10}^{-3}$ 为了 ${}^{27}$铝${}^{+}$ 和 $\delta G_{\text{高频头}}^{（\mathrm{1个}）}（{}^3{P}_0^{Ø}）=7.78（30）\times {10}^{-5}$ 为了 ${}^{87}$先生，非常同意实验值。相对论效应和电子相关性对涉及的超精细相互作用和塞曼矩阵元素以及能量分离的影响进行了详细研究。我们还估算了扰动国家对政府的贡献。$G$相关因素，以便在不损失准确性的情况下截断扰动状态的总和。在此基础上，系统分析了超细致Landé的计算不确定性。$G$的因素 ${}^3{P}_0^{Ø}$ 这两个原子系统中的时钟状态。