论文标题
Bohr-Mottelson模型的微观壳模型对应物
Microscopic shell-model counterpart of the Bohr-Mottelson model
论文作者
论文摘要
在本文中,我们证明了Bohr-Mottelson模型的完全显微镜壳模型,通过将后者嵌入原子核的微观壳模型理论中,原子核的框架中的框架中,在最近提出的完全显微镜的质子质子 - 底发质子 - 质子 - 质子 - 质子 - 质子 - 模型模型(PNSM)中。为此,考虑了PNSM的另一个Shell模型耦合方案,其中基础状态由代数结构$ su(1,1)\ otimes so(6)$对基础状态进行分类。结果表明,PNSM的配置空间包含一个六维子空间,该子空间与广义四极杆 - 单位bohr-Mottelson模型及其动力学分解为径向和轨道运动密切相关。相比之下,该组$ so(6)$在这个领域中作用于流行的IBM,其中包含一个$ su(3)$子组,该组允许引入微观壳模型的bohr-mottelson模型的可溶解限制的显微镜壳模型对应物,这些模型与原始Wilets-Jean-Jean-Jean-Jean-Jean-Jean-Jean-Jean和转子模型的关系紧密相似。与原始的集体模型配方相比,本方法中的Willets-Jean-type动力学由Symphectic Bandhead的微观壳模型固有结构支配,该结构定义了相关的Pauli允许$ SO(6)$,以及$ SU(3)$,suberprementations。对于封闭壳核的情况,恢复了广义的Bohr-Mottelson模型的原始Willets-Jean动力学,为此,Symbletectic Bandhead结构可微不足道地降低到标量或等效于其不可约形表示。
In the present paper we demonstrate that there exists a fully microscopic shell-model counterpart of the Bohr-Mottelson model by embedding the latter in the microscopic shell-model theory of atomic nucleus within the framework of the recently proposed fully microscopic proton-neutron symplectic model (PNSM). For this purpose, another shell-model coupling scheme of the PNSM is considered in which the basis states are classified by the algebraic structure $SU(1,1) \otimes SO(6)$. It is shown that the configuration space of the PNSM contains a six-dimensional subspace that is closely related to the configuration space of the generalized quadrupole-monopole Bohr-Mottelson model and its dynamics splits into radial and orbital motions. The group $SO(6)$ acting in this space, in contrast, e.g., to popular IBM, contains an $SU(3)$ subgroup which allows to introduce microscopic shell-model counterparts of the exactly solvable limits of the Bohr-Mottelson model that closely parallel the relationship of the original Wilets-Jean and rotor models. The Wilets-Jean-type dynamics in the present approach, in contrast to the original collective model formulation, is governed by the microscopic shell-model intrinsic structure of the symplectic bandhead which defines the relevant Pauli allowed $SO(6)$, and hence $SU(3)$, subrepresentations. The original Wilets-Jean dynamics of the generalized Bohr-Mottelson model is recovered for the case of closed-shell nuclei, for which the symplectic bandhead structure is trivially reduced to the scalar or equivalent to it irreducible representation.