\begin{document}$^{108-120}$\end{document}Cd are investigated and compared with the experimental results. To better explain the nearly zero B(E2) values between the \begin{document}$0_{2}^{+}$\end{document} and \begin{document}$2_{1}^{+}$\end{document} states, SU(3) higher-order interactions except for the SU(3) second-order and third-order Casimir operators are also considered in detail. We find that the results of theoretical fitting and experimental data agree well with simple parameter selection, and the spherical-like spectra truly exist. The deficiency may arise from the lack of configuration mixing. The realistic spectra characteristics of the spherical-like spectra are found for \begin{document}$^{118,120}$\end{document}Cd, and the electric quadrupole moments of the \begin{document}$2_{1}^{+}$\end{document} state are predicted. The \begin{document}$Q_{2_{1}^{+}}$\end{document} anomaly in \begin{document}$^{108-116}$\end{document}Cd is also discussed."> Spherical-like spectra for the description of the normal states of <sup>108-120</sup>Cd in the SU3-IBM and the <inline-formula><tex-math id="Z-20241107105545">\begin{document}$ {{\boldsymbol Q}_{\bf 2_{1}^{\bf +}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/05d7a2d2-b7ef-49cc-a569-99ffd3378cdd/CPC-2024-0509_Z-20241107105545.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/05d7a2d2-b7ef-49cc-a569-99ffd3378cdd/CPC-2024-0509_Z-20241107105545.png"/></alternatives></inline-formula> anomaly -
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