The essence of the quasi-SU(3) coupling scheme suggested by Zuker et al. is that the high-$j$ intruder orbit alone is insufficient to induce required large collectivity, and it is necessary for the high-$j$ orbit to correlate through the quadrupole interaction with another higher-lying orbit with $\mathrm{\Delta }j=2$. To extend this idea to the medium-heavy mass region, we investigate the systematics of energy levels and $B\left(E2\right)$ values for Sn, Te, Xe, Ba, Ce, Nd, and Sm isotopes by applying the recently proposed realistic PMMU shell model. The calculations are performed by using the projected Hartree-Fock-Bogolyubov plus generator coordinate method in the model space of ($1g_{9/2},1g_{7/2},2d_{5/2},2d_{3/2},3s_{1/2},1h_{11/2}$). The calculations describe well the experimental data over a wide range of nuclei. However, it is found that, in some nuclei close to the neutron midshell, ${}^{124,126}\mathrm{Ce}$, ${}^{130,132}\mathrm{Nd}$, and ${}^{134}\mathrm{Sm}$, the calculated $B(E2;2_1^{+}\to 0_1^{+})$ values underestimate the data considerably. This problem can be resolved by inclusion of the $2f_{7/2}$ orbit into the model space, which, with $1h_{11/2}$, forms a quasi-SU(3) coupling scheme. It is shown that the $QQ$ interaction between the SU(3)-partner $1h_{11/2}\text{−}2f_{7/2}$ is a driving force for enhanced $E2$ collectivity in the above nuclei and is responsible for the shape evolution in Nd isotopes. In addition, the participation of the $2f_{7/2}$ orbit in the model space favors prolate shape in the ground state of $N\le 76$ isotopes, thus subverting the oblate result from the same calculation but without $2f_{7/2}$.

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• Collective levels
• Electromagnetic transitions
• 90 ≤ A ≤ 149
• Nuclear many-body theory
• Nuclear structure & decays