Typical new spherical-like $\gamma$-soft spectra in $^{104,106,108}$Pd

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. $^{106}$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(E2) 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 $^{104,108}$Pd are also discussed. These results completely disprove the possibility of the phonon excitations of the spherical nucleus in the Cd-Pd nuclei region.