We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton–neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and γ or β bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton–neutron shapes with solvable symmetric ground and γ bands and mixed-symmetry scissors and γ bands.

中文翻译：

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SU（3）局部动力学对称和核形状

我们考虑SU（3）部分动态对称性的几个变体，它们与原子核中的四极形状有关。具有相互作用性质的哈密顿量的显式构造在相互作用的玻色子模型（IBM）的框架中（包括高阶项）及其质子-中子扩展（IBM-2）被提出。所考虑的案例包括具有可溶的地面和γ或β谱带的单个扁长形变形形状，具有可溶的地面带的并存的扁长扁圆形形状，具有可溶的对称的地面和γ谱带的轴向变形的质子-中子形状对齐以及混合对称剪刀和γ波段。