Quasi-SU(3) coupling of (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>11</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mn>7</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>) across the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>82</mml:mn></mml:mrow></mml:math> shell gap: Enhanced <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:math> collectivity and shape evolution in Nd isotopes
Kazunari Kaneko, Noritaka Shimizu, T. Mizusaki, Yang Sun
Abstract
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 $\mathrm{\ensuremath{\Delta}}j=2$. To extend this idea to the medium-heavy mass region, we investigate the systematics of energy levels and $B(E2)$ 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 ($1{g}_{9/2},1{g}_{7/2},2{d}_{5/2},2{d}_{3/2},3{s}_{1/2},1{h}_{11/2}$). 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 $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ values underestimate the data considerably. This problem can be resolved by inclusion of the $2{f}_{7/2}$ orbit into the model space, which, with $1{h}_{11/2}$, forms a quasi-SU(3) coupling scheme. It is shown that the $QQ$ interaction between the SU(3)-partner $1{h}_{11/2}\text{\ensuremath{-}}2{f}_{7/2}$ 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 $2{f}_{7/2}$ orbit in the model space favors prolate shape in the ground state of $N\ensuremath{\le}76$ isotopes, thus subverting the oblate result from the same calculation but without $2{f}_{7/2}$.