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.
Categories: nucl-th