Determination of nuclear quadrupole moments for ${}^{25}$Mg, ${}^{87}$Sr, and ${}^{135,137}$Ba via configuration-interaction combined with a coupled-cluster approach

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 $3s3p{}^3\text{\hspace{0.17em}⁣}{P}_{1,2}$ states of Mg; the $5s4d{}^1\text{\hspace{0.17em}⁣}{D}_2$ and $5s5p{}^3\text{\hspace{0.17em}⁣}{P}_{1,2}$ states of Sr; as well as the $6s5d{}^3\text{\hspace{0.17em}⁣}{D}_{1,2,3}$, $6s5d{}^1\text{\hspace{0.17em}⁣}{D}_2$, and $6s6p{}^1\text{\hspace{0.17em}⁣}{P}_1$ states of Ba. By combining the measured electric quadrupole hyperfine-structure constants of these states, we accurately determine the nuclear quadrupole moments of ${}^{25}$Mg, ${}^{87}$Sr, and ${}^{135,137}$Ba. These results are compared with the available data. The comparison shows that our nuclear quadrupole moment of ${}^{25}$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 [Pyykk$\ddot{\mathrm{o}}$, Mol. Phys. 116, 1328(2018)] for the nuclear quadrupole moments of ${}^{87}$Sr and ${}^{135,137}$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.