Exploring the role of high- j configurations in collective observables through the Coulomb excitation of Cd106

The shape and collectivity of $^{106}\mathrm{Cd}$ was investigated via a sub-barrier-energy Coulomb excitation experiment performed at the National Superconducting Cyclotron Laboratory Re-accelerator facility using the JANUS setup. Transition matrix elements between low-lying states were found to agree with adopted values, and information on the shape and collectivity of higher-lying states was extracted for the first time. Locally optimized large-scale shell-model calculations were found to describe well the $B(E2)$ transition strengths but failed to reproduce the spectroscopic quadrupole moments ${Q}_{s}$. An analysis of the $E2$ rotational invariants and the normalized quadrupole moment ${q}_{s}$ indicates that this may be due to a significant degree of triaxiality in $^{106}\mathrm{Cd}$ which is not captured by the present shell-model calculations. Analogous calculations for the Fe isotopes (two protons below the $Z=28$ magic number) reveal the critical role of high-$j$ neutron configurations for the description of quadrupole moments in the heavy Fe and Cd isotopes (two protons below magic $Z=50$), but this effect is insufficient to explain the shape of $^{106}\mathrm{Cd}$, posing a puzzle for the understanding of nuclear structure towards $N=50$.