Title: Shell-model representations of the microscopic version of the Bohr-Mottelson collective model Show Chinese title

Title: 微观玻尔-莫特森集体模型的壳模型表示

Abstract: The structure of the irreducible collective spaces of the group $Sp(12,R)$, which many-particle nuclear states are classified according to the chain $Sp(12,R) \supset U(6) \supset SO(6) \supset SU_{pn}(3) \otimes SO(2) \supset SO(3)$ of the proton-neutron symplectic model (PNSM), is considered in detail. This chain of the PNSM was shown to correspond to a microscopic shell-model version of the Bohr-Mottelson collective model. The construction of the relevant shell-model representations of the $Sp(12,R)$ group along this chain is considered for three nuclei with varying collective properties and from different mass regions. It is shown that the $SU_{pn}(3)$ basis states of the $Sp(12,R)$ representations are always Pauli allowed for $\upsilon \geq \upsilon_{0}$, but organized in a different way into different $SO(6)$ shells. This is in contrast to the case of filling the levels of the standard three-dimensional harmonic oscillator and using the plethysm operation. Although the $SU_{pn}(3)$ multiplets with $\upsilon < \upsilon_{0}$ are not all Pauli forbidden, it is safe to discard them, as it was actually done in the practical applications. Show Chinese abstract

Abstract: 考虑了根据质子-中子辛模型（PNSM）链 $Sp(12,R) \supset U(6) \supset SO(6) \supset SU_{pn}(3) \otimes SO(2) \supset SO(3)$对多粒子核态进行分类的群 $Sp(12,R)$的不可约集体空间的结构。已显示 PNSM 的这一链对应于玻尔-莫特森集体模型的微观壳层模型版本。沿此链考虑了 $Sp(12,R)$群相关壳层模型表示的构建，涉及三个具有不同集体性质且来自不同质量区域的核。结果表明， $SU_{pn}(3)$基态的 $Sp(12,R)$表示对于 $\upsilon \geq \upsilon_{0}$总是泡利允许的，但以不同的方式组织到不同的 $SO(6)$壳层中。这与用标准三维谐振子填充能级和使用plethysm运算的情况相反。 尽管$SU_{pn}(3)$重数与$\upsilon < \upsilon_{0}$不全被泡利禁戒，但在实际应用中实际上已经舍弃它们，这样做是安全的。