To solve the Cd puzzle (spherical nucleus puzzle), I have proposed a new spherical-like $\gamma$-soft nucleus. Since shape coexistence often occurs in such nuclei, explicit spherical-like $\gamma$-soft spectra are not easily identified. In this paper, I finally find the direct evidence for the existence of the new spherical-like $\gamma$-soft nucleus. ${}^{106}\mathrm{Pd}$ is in fact a typical spherical-like $\gamma$-soft nucleus. The low-lying parts, up to the ${10}_1^{+}$ state, under 4000 keV, of the spherical-like $\gamma$-soft spectra are verified. The $B$(2) values and the quadrupole moments of the low-lying levels are also studied. By comparison, the new spherical-like $\gamma$-soft mode is confirmed. Moreover ${}^{104,108}\mathrm{Pd}$ are also discussed. These results completely disprove the possibility of the phonon excitations of the spherical nucleus in the Cd-Pd nuclei region.

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• Collective models
• Models based on symmetries
• Nuclear astrophysics
• Nuclear shapes and moments
• Nuclear structure & decays
• 90 ≤ A ≤ 149