Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+

The electric quadrupole moments of the metastable nd(3/2) and nd(5/2) states of Ca+, Sr+, and Ba+ are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all nonlinear single and double terms are also calculated for the case of Ca+ for comparison of our approach with results of the coupled-cluster method with singles, doubles, and perturbative triples. Third-order many-body perturbation theory is used to evaluate the contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. An extensive study of the uncertainty of our calculations is carried out to establish the accuracy of our recommended values as 0.5-1% depending on the particular ion. A comprehensive comparison of our results with other theoretical values and experimental results is carried out. Our result for the quadrupole moment of the 3d(5/2) state of the Ca+ ion, 1.849(17)ea(0)(2), is in agreement with the most precise recent measurement 1.83(1)eao(0)(2) by Roos et al. [Nature (London) 443, 316 (2006)].