Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective $S$, $D$, $G$,...pairs (i.e., with angular momentum zero, two, four,...) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for six protons and six neutrons in the $pf$ ($sdg$) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with $SDG$ ($SDGI$) pairs. The $SD$-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with $s$, $d$, $g$,... bosons provides insight into the existence of a decoupled collective subspace in terms of $S$, $D$, $G$,... pairs.

中文翻译：

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Elliott SU（3）模型中的核子对偶联方案

Elliott的SU（3）模型是原子核中旋转运动的壳模型描述的基础。我们证明，如果根据足够多的集合体构造，SU（3）对称性可以在截断的壳模型空间中实现$\mathrm{小号}$， $d$， $G$，...对（即角动量为零，两个，四个...），以及是否通过共轭梯度最小化方法或从Hartree-Fock本征态最佳确定了对的结构。我们说明了六种质子和六个中子的过程$pF$ （$sdG$）并精确地再现基态旋转带的能级和四极电性质 $\mathrm{小号}dG$ （$\mathrm{小号}dG\mathrm{一世}$）对。这$\mathrm{小号}d$另一方面，没有显着重新归一化的双对逼近不能描述完整的SU（3）集合。从Elliott的Fermionic SU（3）模型到具有$s$， $d$， $G$，...玻色子从以下方面提供了对解耦集合子空间的存在的见解 $\mathrm{小号}$， $d$， $G$，...对。