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arXiv 2406.14730nucl-th
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原子核聚类的辛对称方法:$^{24}$Mg 的情形

Symplectic symmetry approach to clustering in atomic nuclei: The case of $^{24}$Mg

H. G. Ganev

AI总结:

本文改进并应用 SSAC 方法,以 $^{20}$Ne+$α$ 图像和代数 Hamiltonian 描述 $^{24}$Mg 的低能转动带及无有效电荷的 $B(E2)$ 跃迁。

摘要:

本文对近期提出的原子核聚类辛对称方法(SSAC)进行了修改和更详细的进一步发展。该方法首次应用于 $^{24}$Mg 的轻双聚类 $^{20}$Ne + $α$ 系统,后者在其能谱中展现出发育良好的低能 $K^π = 0^{+}_{1}$、$K^π = 2^{+}_{1}$ 和 $K^π = 0^{-}_{1}$ 转动带。文中使用一个由动力学对称、剩余混合和垂直混合部分组成的简单代数 Hamiltonian,来描述 $^{24}$Mg 中这三个最低的正宇称和负宇称转动带。通过仅考虑局限于拉伸多粒子 Hilbert 子空间中的 $SU(3)$ 聚类态,可以获得对激发能的良好描述;这些态分别建立在正宇称态和负宇称态的主导 Pauli 允许 $SU(3)$ 多重态之上。与更高聚类模型组态的耦合,使得无需使用有效电荷即可描述已知的、实验观测到的低能 $B(E2)$ 跃迁概率,包括所考察三个转动带的聚类态内部及彼此之间的跃迁。

英文摘要:

Symplectic symmetry approach to clustering (SSAC) in atomic nuclei, recently proposed, is modified and further developed in more detail. It is firstly applied to the light two-cluster $^{20}$Ne + $α$ system of $^{24}$Mg, the latter exhibiting well developed low-energy $K^π = 0^{+}_{1}$, $K^π = 2^{+}_{1}$ and $K^π = 0^{-}_{1}$ rotational bands in its spectrum. A simple algebraic Hamiltonian, consisting of dynamical symmetry, residual and vertical mixing parts is used to describe these three lowest rotational bands of positive and negative parity in $^{24}$Mg. A good description of the excitation energies is obtain by considering only the $SU(3)$ cluster states restricted to the stretched many-particle Hilbert subspace, built on the leading Pauli allowed $SU(3)$ multiplet for the positive- and negative-parity states, respectively. The coupling to the higher cluster-model configurations allows to describe the known low-lying experimentally observed $B(E2)$ transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge.

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