The boson number hypothesis and the boson number odd-even effect in $^{196-204}$Hg

Abstract

In the SU3-IBM the oblate shape is described by the \textrm{SU(3)} third-order Casimir operator in the large-$N$ limit. However for finite $N$, this interaction can produce a boson number odd-even effect. In this Letter, we find that, the unique odd-even effect really exists in the nuclei $^{196-204}$Hg. This finding implies that realistic low-lying excitations are sensitive to certain boson number $N$. The boson number hypothesis is verified for the first time since the advent of the interacting boson model. This also proves the accuracy and validity of the SU3-IBM directly. The SU(3) symmetry and the higher-order interactions are both indispensable for understanding the nuclear quadrupole deformations.