Quadrupole moments and hyperfine constants of metastable states of Ca$^+$, Sr$^+$, Ba$^+$, Yb$^+$, Hg$^+$, and Au

Abstract

Atomic quadrupole moments and hyperfine constants of the metastable $^2 D_{3/2, 5/2}$ states of Ca$^+$, Sr$^+$, Ba$^+$, Yb$^+$, and Hg$^+$ are calculated by the multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods. For Hg$^+$, the configuration is $5d^9 6s^2$. For the other ions, the configuration consists of a single $d$-electron outside a set of closed shells. Current interest in the quadrupole moments of these states is due to the fact that optical transitions of these ions may be useful as references for frequency standards. Energy shifts of the metastable states due to the interactions of the quadrupole moments with external electric field gradients are among the largest sources of error in these frequency standards. For the quadrupole moments, agreement is obtained to within about 10~% with the available measurements. For the hyperfine constants, good agreement is obtained with measurements and with other calculations, except for the $A$ factors of the $^2D_{5/2}$ states of Sr$^+$, Ba$^+$, and Yb$^+$, where the correlation effects are so large that they reverse the sign of the constant relative to the Dirac-Hartree-Fock value. As a test of the Hg$^+$ calculational methods, quadrupole moments and hyperfine constants are calculated for the $5d^9 6s^2 ^2 D_{3/2, 5/2}$ states in isoelectronic neutral Au. This yields a new value of the nuclear quadrupole moment $Q$($^{197}$Au) = +0.587(29) b.