The low-charged ${\mathrm{Sn}}^{2+}$ ion has emerged as an ideal candidate for developing Coulomb-crystal optical clocks capable of achieving precision below ${10}^{-19}$ [Leibrandt et al., Nat. Commun. 15, 5663 (2024)]. To systematically investigate the structure properties of the ${\mathrm{Sn}}^{2+}$ ion, we employ the $B$-spline-based many-body perturbation theory combined with the configuration-interaction method. We conducted comprehensive calculations of energies, matrix elements, and electric and magnetic dipole polarizabilities. Furthermore, we determined the magic wavelengths and the sensitivity factor $K$ for variations in the fine-structure constant $\alpha$. Detailed comparisons with existing results demonstrate good agreement, validating the reliability of our method. Additionally, we derive a general formula to incorporate the contribution of negative-energy states to the magnetic dipole tensor polarizability, thereby elucidating their non-negligible impact on the calculation of high-accuracy magnetic polarizability.

Close

PrevNext

View figure in article

• Atomic & molecular structure
• Atomic, optical & lattice clocks
• Electronic structure of atoms & molecules
• Electronic transitions
• Hartree-Fock methods
• Perturbative methods