The determination of nuclear symmetry energy and, in particular, its density dependence is a long-standing problem for the nuclear physics community. Previous studies have found that the product of electric dipole polarizability ${\alpha }_D$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$, the slope parameter of symmetry energy. However, the current uncertainty of $J$ hinders the precise constraint on $L$. We investigate the correlations between electric dipole polarizability ${\alpha }_D$ (or times symmetry energy at saturation density $J$) in Sn isotopes and the slope parameter of symmetry energy $L$ using the quasiparticle random-phase approximation based on the Skyrme Hartree-Fock-Bogoliubov model. A strong linear correlation between ${\alpha }_D$ and $L$ is found in neutron-rich Sn isotopes where pygmy dipole resonance (PDR) gives a considerable contribution to ${\alpha }_D$, attributed to the pairing correlations playing important roles through PDR. This newly discovered linear correlation would help one to constrain $L$ and neutron-skin thickness $\mathrm{\Delta }{R}_{n}p$ stiffly if ${\alpha }_D$ is measured with high resolution in neutron-rich nuclei. Additionally, a linear correlation between ${\alpha }_{D}J$ in a nucleus around the $\beta$-stability line and ${\alpha }_D$ in a neutron-rich nucleus can be used to assess ${\alpha }_D$ in neutron-rich nuclei.

中文翻译：

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富中子 Sn 同位素的电偶极极化率作为核等矢量特性的探针

核对称能量的确定，特别是其密度依赖性是核物理学界长期存在的问题。以前的研究发现，电偶极子极化率的乘积${\alpha }_D$ 和饱和密度下的对称能 $J$ 有很强的线性相关性 $升$，对称能量的斜率参数。然而，目前的不确定性$J$ 阻碍精确约束 $升$. 我们研究了电偶极子极化率之间的相关性${\alpha }_D$ （或在饱和密度下乘以对称能量 $J$) 中的 Sn 同位素和对称能的斜率参数 $升$使用基于 Skyrme Hartree-Fock-Bogoliubov 模型的准粒子随机相位近似。之间的强线性相关性${\alpha }_D$ 和 $升$ 存在于富含中子的 Sn 同位素中，其中侏儒偶极子共振 (PDR) 对 ${\alpha }_D$，归因于配对相关性通过 PDR 发挥重要作用。这种新发现的线性相关性将有助于限制$升$ 和中子皮肤厚度 $\mathrm{\Delta }{\mathrm{电阻}}_n磷$ 生硬如果 ${\alpha }_D$在富含中子的原子核中以高分辨率测量。此外，之间的线性相关${\alpha }_{D}J$ 在周围的核中 $\beta$- 稳定线和 ${\alpha }_D$ 在富含中子的原子核中可用于评估 ${\alpha }_D$ 在富含中子的原子核中。