AI 中文总结
该研究建立了α衰变半衰期的普适标度律，以Z^{2/3}/√Q_α为变量统一了跨越二十个数量级的数据，并成功应用于中子星并合千新星AT2017gfo的建模。
AI 中文摘要
我们基于变量 $X_a = Z^a/\sqrt{Q_\alpha}$ 建立了 $\alpha$ 衰变半衰期的普适标度律，该变量将跨越二十多个数量级的实验和理论数据压缩到单一线性关联上。对全部偶偶 $\alpha$ 发射体的全局优化揭示了在 $a \simeq 2/3$ 处存在唯一尖锐的最优值。该指数在理论上由重核的领先几何标度所驱动，并定量地源于相关核系统学，即由核素图中相关的 $(Z, Q_\alpha)$ 流形所决定。引人注目的是，五个结构不同的半经验模型和一个独立的微观 WKB 计算，在分别对指数 $a$ 进行独立优化时，所得值均聚集在 $2/3$ 附近，而相应的 $a=2/3$ 关联在无需重新拟合原始模型参数的情况下仍保持高度线性。这一涌现标度律意味着沿重 $r$-过程路径的衰变时间平滑变化。我们解析地证明，在该变量近似均匀分布的条件下，标度律自然支持准幂律放射性加热率（$\dot{\epsilon} \propto t^{-1.24}$），与完整网络计算一致。此外，将这些标度预测直接整合到辐射扩散模型的核源项中，所得多信使观测量准确再现了与引力波事件 GW170817 相关联的千新星 AT2017gfo，表明 $Z^{2/3}/\sqrt{Q_\alpha}$ 标度坐标可为中子星并合的放射性引擎建模提供稳健工具。
英文摘要
We establish a universal scaling law for $α$-decay half-lives based on the variable $X_a = Z^a/\sqrt{Q_α}$, which collapses experimental and theoretical data spanning over twenty orders of magnitude onto a single linear correlation. Global optimization over the complete set of even-even $α$ emitters reveals a uniquely sharp optimum at $a \simeq 2/3$. This exponent is theoretically motivated by the leading geometric scaling of heavy nuclei and emerges quantitatively from the correlated nuclear systematics, driven by the correlated $(Z, Q_α)$ manifold of the nuclear chart. Strikingly, five structurally distinct semi-empirical models and an independent microscopic WKB calculation, when independently optimized with respect to the exponent $a$, yield values clustered around $2/3$, while the corresponding $a=2/3$ correlations remain highly linear without refitting the original model parameters. This emergent scaling law implies smooth variations of decay times along the heavy $r$-process path. We demonstrate analytically that, given a roughly uniform distribution of this variable, the scaling law naturally supports a quasi-power-law radioactive heating rate ($\dotε \propto t^{-1.24}$), consistent with full network calculations. Furthermore, integrating these scaling predictions directly into nuclear source terms for radiative-diffusion models yields multimessenger observables that accurately reproduce the kilonova AT2017gfo associated with the gravitational-wave event GW170817, demonstrating that the $Z^{2/3}/\sqrt{Q_α}$ scaling coordinate provides a robust tool for modeling the radioactive engines of neutron-star mergers.
Comments8 pages, 7 Figures
