Enhancement of $\alpha$ decay by positive hexadecapole deformation

摘要: Whether hexadecapole deformation ($\beta_4$) affects $\alpha$ decay remains controversial: machine-learning studies suggest a strong link to $\alpha$-cluster preformation, whereas empirical formulas find only a marginal effect. We show that this discrepancy originates in the treatment of shell effects. When shell effects are not included explicitly in empirical formulas, the residuals can be absorbed into fitted deformation coefficients, obscuring the genuine $\beta_4$ dependence. Including the inverse Casten factor $C_{pn}$, which accounts for valence proton--neutron correlations relative to the nearest closed shells, and the parent-nucleus deformation $\beta_4^{(p)}$ to the Royer formula reduces the root-mean-square deviation from 0.309 to 0.184 for 192 even--even nuclei. The fitted coefficient of $\beta_4^{(p)}$ is negative: positive deformation shortens the half-life, While negative deformation has the opposite effect. This trend is consistent with enhanced $\alpha$-cluster preformation at locally convex surface regions. In the Pu isotopic chain, where $\beta_4^{(p)}>0$ is pronounced, the original Royer formula overestimates half-lives by up to $\sim\!0.42$~dex, providing a testable signature of this surface-preformation effect. The same correction improves the UDL formula, and global predictions for 1060 even--even nuclei are provided in the Supplemental Material.