Neutron Skin Thickness Dependence of Astrophysical $S$-factor

TL;DR

This study investigates how the neutron skin thickness influences the astrophysical S-factor and sub-barrier fusion cross-sections in asymmetric nuclei, highlighting the significant impact of symmetry energy on nuclear reaction rates relevant to astrophysics.

Contribution

It demonstrates the strong dependence of fusion cross-sections and S-factors on neutron skin thickness using double folding model calculations across various nuclear models.

Findings

Neutron skin thickness significantly affects the fusion barrier height and width.

Increased skin thickness enhances the astrophysical S-factor by over an order of magnitude.

Results vary with different nuclear models and interactions.

Abstract

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.