Nuclear symmetry energy is a fundamental quantity currently under intense investigation in both nuclear physics and astrophysics. The softness or stiffness of symmetry energy is still under debate and the extraction of symmetry energy from neutron skin thickness $R_{\mathrm{skin}}$ remains a challenge. Parity-violating measurements PREX and CREX provide important opportunities for constraining $R_{\mathrm{skin}}$ in ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$. We investigate the occurrence of an $\alpha$ cluster at the surface of nuclei and its impact on the extraction of symmetry energy from $R_{\mathrm{skin}}$. Our result indicates that the $\alpha$-clustering probability in ${}^{208}\mathrm{Pb}$ is small and the extracted density slope of symmetry energy $L$ is almost unaffected. In contrast, the $\alpha$-clustering probability in ${}^{48}\mathrm{Ca}$ is sizable 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 $L\text{−}{R}_{\mathrm{skin}}$ correlation, a fact that may have important implications in constraining nuclear symmetry energy.

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• Alpha decay
• Cluster models
• Neutron skin thickness
• Symmetry energy