AI 中文总结
本文针对十六极形变是否影响α衰变的争议，在Royer公式中加入逆Casten因子与母核形变项，使192个偶-偶核的均方根偏差降低，证实正十六极形变可缩短半衰期，还改进了UDL并预测了1060个偶-偶核的情况。
AI 中文摘要
十六极形变（β₄）是否影响α衰变仍存在争议：机器学习分析表明其与集团预形成存在强关联，而经验公式仅发现微弱效应。本文指出该差异源于壳效应的处理方式——若无明确的壳修正，幻数附近的残差会被纳入形变系数，掩盖了真实的β₄依赖关系。在Royer公式中加入编码价质子-中子相对于最近闭壳相关性的逆Casten因子Cₚₙ，以及母核形变β₄⁽ᵖ⁾，可使192个偶-偶核的均方根偏差从0.309降至0.184。拟合得到的负β₄⁽ᵖ⁾系数表明，正十六极形变会系统性缩短半衰期，与局域凸表面区域α集团预形成增强的结论一致。对于Z=94的钚（Pu）同位素链，其存在显著的β₄⁽ᵖ⁾>0，原始Royer公式对半衰期的高估可达约0.5 dex，为该表面预形成效应提供了清晰可检验的特征。相同修正还改进了UDL，并对1060个偶-偶核作出预测。
英文摘要
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.
Comments19 pages,7 figures
