Enhancement of alpha-decay by positive hexadecapole deformation

Abstract

Whether hexadecapole deformation ($β_4$) influences $α$ decay remains controversial: machine-learning analyses suggest a strong link to cluster preformation, while empirical formulas find only marginal effects. We show that this discrepancy originates in the treatment of shell effects---without an explicit shell correction, residuals near magic numbers are absorbed into the deformation coefficients, obscuring the genuine $β_4$ dependence. Adding the inverse Casten factor $C_{pn}$, which encodes valence proton--neutron correlations relative to the nearest closed shells, and the parent-nucleus deformation $β_4^{(p)}$ to the Royer formula reduces the root-mean-square deviation from 0.309 to 0.184 for 192 even--even nuclei. The fitted negative $β_4^{(p)}$ coefficient shows that positive hexadecapole deformation systematically shortens half-lives, consistent with enhanced $α$-cluster preformation at locally convex surface regions. For the $Z=94$ isotopic chain (Pu), where pronounced $β_4^{(p)}>0$ occurs, the original Royer formula overestimates half-lives by up to $\sim\!0.5$~dex, providing a clear, testable signature of this surface-preformation effect. The same correction also improves the UDL and yields predictions for 1060 even--even nuclei.