标题： 中子皮厚度对天体物理$S$-因子的影响 显示英文标题

标题： Neutron Skin Thickness Dependence of Astrophysical $S$-factor

摘要： 背景：核对称性能量的密度依赖性在确定有限核到中子星的质量特性方面起着关键作用，其中$\sim$ 1.4 $M_\odot$。不对称核中的中子皮厚度、矢量巨偶极共振能量以及各种核反应截面的值已被用于确定饱和密度处对称性能量的斜率 ($L_0$)。最近对$^{208}$铅和$^{48}$钙核中子皮厚度的 PREX-II 和 CREX 测量结果给出了非常不同的$L_0$值，在 90$\%$置信区间内仅略有重叠。 目的：我们的目标是展示对称能对非对称核的亚阈值融合截面和天体物理$S$-因子的作用。 方法：使用双折叠模型（DFM）生成三种不同的核子-核子相互作用的核核势。 这些 DFM 势用于计算亚阈值融合截面和天体物理$S$-因子。 生成 DFM 势所需的核子密度来自不同族的非相对论和相对论平均场模型，这些模型对应于广泛的中子皮厚度或$L_0$。 结果：我们计算了涉及 O、Ca、Ni 和 Sn 同位素的几个非对称核的亚阈值融合截面。 结果展示了屏障参数、截面以及天体物理$S$-因子对于$^{54}$Ca+$^{54}$Ca 和$^{124}$Sn+$^{124}$Sn 随中子皮厚度变化的情况。 结论：富含中子的核素的截面显示出对对称能量行为或中子皮厚度的强烈依赖。 皮肤厚度的增加降低了屏障的高度及其宽度，这使得$S$-因子的值提高了超过一个数量级。 显示英文摘要

摘要： Background: The density dependence of nuclear symmetry energy is crucial in determining several properties of finite nuclei to the neutron stars with mass $\sim$ 1.4 $M_\odot$. The values of neutron skin thickness, isovector giant dipole resonances energies and various nuclear reaction cross-sections in asymmetric nuclei have been utilized to determine the slope of symmetry energy ($L_0$) at the saturation density. Recent PREX-II and CREX measurements of neutron skin thickness in $^{208}$Pb and $^{48}$Ca nuclei yield very different values of $L_0$ which overlap marginally within 90$\%$ confidence interval. Purpose: Our objective is to demonstrate the role of symmetry energy on the sub-barrier fusion cross-section and the astrophysical $S$-factor for asymmetric nuclei. Method: The nucleus nucleus potentials are generated using the double folding model (DFM) for three different nucleon-nucleon interactions. These DFM potentials are used for the calculation of the sub-barrier fusion cross-section and the astrophysical $S$-factor. The nucleon densities required for DFM potentials are generated from different families of non-relativistic and relativistic mean-field models which correspond to a wide range of neutron skin thickness or $L_0$. Results: We have calculated the sub-barrier fusion cross-section for several asymmetric nuclei involving O, Ca, Ni, and Sn isotopes. The results are presented for the barrier parameters, cross-section, and astrophysical $S$-factor for $^{54}$Ca+$^{54}$Ca and $^{124}$Sn+$^{124}$Sn as a function of neutron skin thickness. Conclusions: The cross-section for the neutron-rich nuclei show a strong dependence on the behavior of symmetry energy or the neutron skin thickness. The increase in skin thickness lowers the height of the barrier as well as its width which enhances the values of the $S$-factor by more than an order of magnitude.