Investigating Roles of Triple Excitations for High-precision Determination of Clock Properties of Alkaline Earth Singly Charged Ions

Abstract: High-accuracy calculations of electric dipole polarizabilities and quadrupole moments ($\Theta$) of the clock states of the singly charged calcium (Ca$^+$), strontium (Sr$^+$) and barium (Ba$^+$) alkaline-earth ions are estimated by employing relativistic coupled-cluster (RCC) theory. It demonstrates importance of the triple excitations in the RCC method for precise determination of the above quantities. We also observe a different trend of correlations in the $\Theta$ values than an earlier study with respect to orbitals from higher angular momenta. Reliability of the results is verified by comparing the calculated energies, magnetic dipole hyperfine structure constants, and lifetimes of the atomic states with the experimental values of the $^{43}$Ca$^+$, $^{87}$Sr$^+$ and $^{137}$Ba$^+$ ions. Nuclear quadrupole moments of these isotopes are also estimated by combining calculations with the measured electric quadrupole hyperfine structure constants, showing large deviations from the literature values.