Precise Determination of Electric Quadrupole Moments and Isotope Shift Constants of Yb$^+$ in Pursuance of Probing Fundamental Physics and Nuclear Radii

Contemplating to register signature of a new vector boson unambiguously from the measured non-linear isotope shift (IS) effects in three recent experiments [Phys. Rev. X {\bf 12}, 021033 (2022); Phys. Rev. Lett. {\bf 128}, 163201 (2022) and Phys. Rev. Lett. {\bf 134}, 063002 (2025)], very precise values of quadrupole moments and IS constants for the $6s ~ ^2S_{1/2} \rightarrow 5d ~ ^2D_{3/2}$ and $6s ~ ^2S_{1/2} \rightarrow 5d ~ ^2D_{5/2}$ clock transitions of $^{171}$Yb$^+$ are presented. This is accomplished by incorporating contributions from the computationally challenging triply excited configurations through the relativistic coupled-cluster (RCC) theory. Testament of quality atomic wave functions of states of the above transitions, obtained using the RCC theory, are gauged by comparing the calculated energies and magnetic dipole hyperfine structure constants with their measurements. The improved quadrupole moments from this work will be immensely useful to estimate quadrupole shifts of the clock transitions of Yb$^+$. Complementary approaches are employed to ascertain accuracy and comprehend roles of orbital relaxation and correlation effects in evaluating the IS constants. Combining these constants with the IS measurements from Phys. Rev. Lett. {\bf 128}, 163201 (2022), differential nuclear charge radii of the Yb isotopes are inferred that deviate by 6-7\% from the literature data.