Electric quadrupole moments of the d states of alkaline-earth-metal ions

The electric quadrupole moment for the 4d D-2(5/2) state of Sr-88(+); one of the most important candidates for an optical clock, has been calculated using the relativistic coupled-cluster theory. This is the first application of this theory to determine atomic electric quadrupole moments. The result of the calculation is presented and the important many-body contributions are highlighted. The calculated electric quadrupole moment is (2.94 +/- 0.07)ea(0)(2), where a(0) is the Bohr radius and e the electronic charge while the measured value is (2.6 +/- 0.3)ea(0)(2). This is so far the most accurate determination of the electric quadrupole moment for the above mentioned state. We have also calculated the electric quadrupole moments for the metastable 4d D-2(3/2) state of Sr-88(+) and for the 3d D-2(3/2,5/2) and 5d D-2(3/2,5/2) states of Ca-43(+) and Ba-138(+), respectively.