Spherical-like spectra for the description of the normal states of ¹⁰⁸⁻¹²⁰Cd in the SU3-IBM and the Q2₁ ⁺ anomaly

The Cd puzzle implies that the phonon excitation of a spherical nucleus should be questioned and refuted. To understand the newly and experimentally discovered spherical-like γ -soft mode, the SU3-IBM was recently proposed. In this study, the evolutions of the normal states in Cd are investigated and compared with the experimental results. To better explain the nearly zero B ( E 2) values between the and 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 Cd, and the electric quadrupole moments of the state are predicted. The anomaly in Cd is also discussed.