Using the configuration-interaction plus coupled-cluster approach, we calculate the electric-field gradients $q$ for the low-lying states of alkaline-earth atoms, including magnesium (Mg), strontium (Sr), and barium (Ba). These low-lying states specifically include the $3s3p{}^{3}P_{1,2}$ states of Mg; the $5s4d{}^{1}D_2$ and $5s5p{}^{3}P_{1,2}$ states of Sr; as well as the $6s5d{}^{3}D_{1,2,3}, 6s5d{}^{1}D_2$, and $6s6p{}^{1}P_1$ states of Ba. By combining the measured electric quadrupole hyperfine-structure constants of these states, we accurately determine the nuclear quadrupole moments of ${}^{25}\mathrm{Mg}, {}^{87}\mathrm{Sr}$, and ${}^{135,137}\mathrm{Ba}$. These results are compared with the available data. The comparison shows that our nuclear quadrupole moment of ${}^{25}\mathrm{Mg}$ is in perfect agreement with the result from the mesonic x-ray experiment. However, there are approximately 10% and 4% differences between our results and the currently adopted values [Pyykkö, Mol. Phys. 116, 1328 (2018)] for the nuclear quadrupole moments of ${}^{87}\mathrm{Sr}$ and ${}^{135,137}\mathrm{Ba}$, respectively. Moreover, we also calculate the magnetic dipole hyperfine-structure constants of these states, and the calculated results exhibit good agreement with the measured data.

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• Atomic & molecular structure
• Atomic spectra
• Fine & hyperfine structure