在原子核物理中研究核物质对称能与巨共振观测量的关联

Investigation of the Correlation between Nuclear Matter Symmetry Energy and Giant Resonance Observables in Nuclear Physics

摘要: 在原子核物理相关课程中，巨共振现象是核结构部分的重要内容，其观测量是探究核物质性质的有效探针。本文利用BUU输运模型模拟了原子核²⁰⁸Pb的同位旋矢量巨偶极共振，并根据巨共振的强度函数提取了峰值能量E_x，其计算结果与实验值相符。然后选取了50种Skyrme有效相互作用，系统性地研究了峰值能量E_x与核物质对称能$J$ 之间的关系。通过研究发现E_x与$J$ 之间不存在直接的线性关联，但当引入与同位旋矢量单核子有效质量$m_{v,0}^{\ast }/m$ 有关的偶极增强因子k后，物理量$\sqrt{J\left(1+k\right)}$ 与E_x之间呈现出显著的线性关系，其拟合的Pearson系数为0.93。本文验证了利用输运模型研究原子核巨共振现象的合理性，同时为通过实验观测量E_x约束核物质的J和$m_{v,0}^{\ast }/m$ 提供了新思路，也为原子核物理教学中的科研拓展内容提供了新的素材。

Abstract: In nuclear physics courses, the phenomenon of giant resonance is a key topic of nuclear structure, and its observations serve as effective probes for exploring the properties of nuclear matter. In this work, we simulate the isovector giant dipole resonance of ²⁰⁸Pb using the BUU transport model and extract the peak energy E_x from the strength function of the resonance. The calculated E_x shows good agreement with experimental data. We then employ 50 Skyrme effective interactions to systematically study the relationship between the E_x and the nuclear symmetry energy $J$ . The results reveal that there is no direct linear correlation between E_x and $J$ . After introducing the dipole enhancement factor k, which is related to the isovector nucleon effective mass $m_{v,0}^{\ast }/m$ , a strong linear correlation emerges between E_x and the $\sqrt{J\left(1+k\right)}$ , with a fitted Pearson correlation coefficient of 0.93. This result demonstrates the effectiveness of using transport models to investigate nuclear structure phenomena and provides a new theoretical approach to constraining the J and the $m_{v,0}^{\ast }/m$ through experimental E_x. Furthermore, the findings provide new material for integrating frontier research into nuclear physics education.