[论文解读] Revisiting the nuclear island of negative hexadecapole deformations in A$\approx$180 mass region: focusing on moments of inertia and quadrupole-hexadecapole coupling

R. B. Li, Hua-Lei Wang+3 more|arXiv (Cornell University)|Jan 15, 2026

Nuclear physics research studies被引用 0

一句话总结

本文在A≈180核的负十六极变形島上重新考察，采用宏观-微观和HFBC方法研究十六极自由度如何影响单粒子结构、势能曲面和转动惯量，并与刚体估计进行比较。

ABSTRACT

For even-even nuclei $^{180-184}$Yb, $^{182-186}$Hf and $^{184-188}$W located on an island of hexadecapole-deformation archipelago, the structure properties, especially under rotation, are reinvestigated by using the Hartree-Fock-Bogliubov-Cranking (HFBC) calculation with a fixed shape (e.g., the ground-state equilibrium shape). The equilibrium deformations, extracted from the potential energy surface, are calculated based on the phenomenological Woods-Saxon mean-field Hamiltonian within the framework of macroscopic-microscopic (MM) model. The impact of different deformation degrees of freedom on, e.g., single-particle levels, total energy, and moment of inertia, is revealed, especially concentrating on the hexadecapole-deformation effects and the quadrupole-hexadecapole coupling. Considering the axially hexadecapole deformation, the present calculations can well reproduce available experimental data, including the quadrupole deformations and moments of inertia. Interestingly, it is found that the impact of different deformation degrees of freedom on moment of inertia exhibits a similar trend in the HFBC and rigid-body calculations though the latter ignores the pairing effects. Before starting or constructing a complex theory-model, to some extent, such a similarity can provide an alternative way of understanding the effect of, e.g., exotic deformations, on moment of inertia by the calculation of a simple rigid-body approximation. The present findings could offer insights into the static and dynamic effects of hexadecapole deformations, contributing valuable information for the corresponding research in nuclear structure and reaction.

研究动机与目标

• 理解十六极变形及其在A≈180岛屿内核结构中的作用的 motivation
• 探索四极与十六极自由度如何影响单粒子能级、总能量与转动惯量
• 评估十六极耦合对静态（PES）和动态（转动）性质的影响，并与刚性体预期进行比较

提出的方法

• 使用带 Woods-Saxon 势的宏观-微观（MM）模型从势能曲面获得平衡形状
• 在一个轴对称的变形箱体基底中解 Woods-Saxon 哈密顿量，以计算单粒子能级
• 在 cranked HF-Bogoliubov 框架内应用 Strutinsky 壳修正和 Lipkin-Nogami 配对以获得旋转解（HFBC）
• 使用一维转动来模拟绕 x 轴的转动，并从 HFBC 解中计算转动惯量
• 用 beta2、gamma、beta4（及相应的 alpha4μ）参数化形状，分析四极-十六极自由度如何影响观测量
• 将 HFBC 结果与刚体计算进行比较，以评估配对与变形对转动惯量的影响

Figure 3: Projections of total energy on the ( $\beta_{2},\gamma$ ) (a), ( $\beta_{4},\gamma$ ) (b) and ( $\beta_{2},\beta_{4}$ ) (c) planes with contour-line separations of 0.5 MeV, minimized respectively at each deformation point over the remaining deformation, $\beta_{4}$ , $\beta_{2}$ and $\gamm

实验结果

研究问题

• RQ1 包含非轴对称分量在内的四极与十六极变形如何改变A≈180核在费米面附近的单粒子能级结构？
• RQ2 十六极变形与四极-十六极耦合对势能曲面与平衡形状有何影响？
• RQ3 十六极自由度在转动下如何影响转动惯量，HFBC结果与刚性体估计有何差异？
• RQ4 所观察的变形是否能再现研究岛屿中核的可用实验四极变形和转动惯量？

主要发现

• MM 模型得到的平衡变形能够再现研究核在轴向十六极变形下的可观测四极变形和转动惯量
• 在A≈180岛中，十六极变形（β4）非微不足道，轴向 α40 对能量极小化贡献显著（在 PES 投影中观察到较大能量降低）
• 尽管 HFBC 存在配对，但额外变形自由度对转动惯量的影响在 HFBC 与刚体计算之间呈现相似趋势
• 十六极耦合到四极形状显著影响费米面附近的单粒子能级结构，如β2 与 β4 相关的能级图所示
• 本研究为十六极变形的静态与动态效应提供了见解，并为理解奇异变形对转动惯量的影响提供了一个简单的刚性体视角

Figure 4: Similar to the preceding illustration in Fig. 3 , but projected on the $(\alpha_{20},\alpha_{4\mu=0,2,4})$ planes for 184 Hf.