Alpha-Clustering in Nuclei and Its Impact on Nuclear Symmetry Energy

Nuclear symmetry energy is a fundamental quantity currently under intense investigation in both nuclear physics and astrophysics. The {\it softness} or {\it stiffness} of symmetry energy is still under debate and the extraction of symmetry energy from neutron skin thickness $R_{\rm skin}$ remains a challenge. Parity-violating measurements PREX and CREX provide important opportunities for constraining $R_{\rm skin}$ in $^{208}$Pb and $^{48}$Ca. We investigate the occurrence of $\alpha$-cluster at the surface of nuclei and its impact on the extraction of symmetry energy from $R_{\rm skin}$. Our result indicates that the $\alpha$-clustering probability in $^{208}$Pb is small and the extracted density slope of symmetry energy $L$ is almost unaffected. In contrast, the $\alpha$-clustering probability in $^{48}$Ca is sizeable and the corresponding correction to $L$ should be taken into account. This correction progressively increases with the $\alpha$-clustering probability, leading to a modification of the $L$-$R_{\rm skin}$ correlation, a fact may have important implications in constraining nuclear symmetry energy.