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The electric quadrupole moment for the $5d^{2}D_{3/2}$ state of$\mathrm{^{171}Yb^{+}}$, has been calculated using the relativisticcoupled-cluster method. Earlier a similar calculation was performed for the 4d$^2D_{5/2}$ state of $\mathrm{^{88}Sr^{+}}$ which is the most accuratedetermination to date {[}PRL, \textbf{96}, 193001 (2006)]. The presentcalculation of the electric quadrupole moment of $\mathrm{^{171}Yb^{+}}$yielded a value $2.157 ea_{0}^{2}$ where the experimental value is$2.08(11)ea_{0}^{2}$; $a_{0}$ is the Bohr radius and $e$ the elementary charge.We discuss in this paper our results in detail for $^{171}{\rm Yb}^{+}$ andhighlight the dominant correlation effects present. We have presented theeffect of inner core excitations and their contribution to the electricquadrupole moment, which is a property sensitive to regions away from thenucleus.

Electric quadrupole moment of the $5d^2 D_{3/2}$ state in $^{171}Yb^+$ : A relativistic coupled-cluster analysis