A relativistic many-body calculation is performed for the low-lying states of the alkaline earth ions ${}^{43}\mathrm{Ca}^{+}$ and ${}^{87}\mathrm{Sr}^{+}$. The zeroth-order hyperfine structure constants are evaluated with Dirac-Fock wave functions, and the finite basis sets of the Dirac-Fock equation are constructed by $B$ splines. With the finite basis sets, the core polarization and the correlation effect are calculated. The final results for ${}^{43}\mathrm{Ca}^{+}$ are $a\left(4S_{1∕2}\right)=-805.3\mathrm{MHz}$, $a\left(4P_{1∕2}\right)=-143.1\mathrm{MHz}$, $a\left(4P_{3∕2}\right)=-30.5\mathrm{MHz}$, $b\left(4P_{3∕2}\right)∕Q=151.8{\mathrm{MHz}\mathrm{b}}^{-1}$, $a\left(3D_{3∕2}\right)=-47.8\mathrm{MHz}$, $b\left(3D_{3∕2}\right)∕Q=68.1{\mathrm{MHz}\mathrm{b}}^{-1}$, $a\left(3D_{5∕2}\right)=-3.6\mathrm{MHz}$, and $b\left(3D_{5∕2}\right)∕Q=100.2{\mathrm{MHz}\mathrm{b}}^{-1}$. The results for ${}^{87}\mathrm{Sr}^{+}$ are $a\left(5S_{1∕2}\right)=-1003.2\mathrm{MHz}$, $a\left(5P_{1∕2}\right)=-178.4\mathrm{MHz}$, $a\left(5P_{3∕2}\right)=-35.1\mathrm{MHz}$, $b\left(5P_{3∕2}\right)∕Q=274.3{\mathrm{MHz}\mathrm{b}}^{-1}$, $a\left(4D_{3∕2}\right)=-47.4\mathrm{MHz}$, $b\left(4D_{3∕2}\right)∕Q=118.2{\mathrm{MHz}\mathrm{b}}^{-1}$, $a\left(4D_{5∕2}\right)=2.5\mathrm{MHz}$, and $b\left(4D_{5∕2}\right)∕Q=169.5{\mathrm{MHz}\mathrm{b}}^{-1}$.

• Received 28 February 2004

DOI:https://doi.org/10.1103/PhysRevA.70.012506