$α$ -衰变系统的修正经验公式和机器学习
Modified empirical formulas and machine learning for $α$-decay systematics
摘要：
最新实验和评价的$α$ -82 $\leq$ Z $\leq$ 118之间的衰变半衰期已用于修改两个经验公式：（i）Horoi标度定律[J. Phys. \textbf{30}，945（2004）]和Sobiczewski公式[Acta Phys. Pol. \textbf{36}，3095（2005）]通过添加不对称依赖项（$I$和$I^2$）并重新拟合系数。这些修正公式的计算结果与其它21个公式的计算结果相比有了显著的改进，因此可以用来更精确地预测未知超重区的$α$衰变半衰期. Bao \textit{et al.} [J. Phys. G \textbf{42}，085101（2015）]提出的自发裂变（SF）半衰期公式进一步修改，采用FRDM-2012中的基态壳层加配对修正，并使用最新实验和评估的82个$\leq$ Z $\leq$ 118之间的自发裂变半衰期。使用这些修改后的公式，$α$ -衰变和SF之间的竞争是探测范围内的112 $\leq$ Z $\leq$ 118的核，因此可能的半衰期和衰变模式估计。分析了$^{286-302}$ Og和$^{287-303}$ 119（168 $\leq$ N $\leq$ 184：稳定岛）的潜在衰变链，发现其与可用的实验数据非常一致。此外，四种不同的机器学习模型：XGBoost、随机森林（RF）、决策树（DT）和多层感知器（MLP）神经网络用于训练预测器，用于$α$ -衰减和SF半衰期预测。使用XGBoost和MLP的衰变模式的预测被发现与现有的实验衰变模式以及我们的预测由上述修改后的公式得到的非常好的协议。
英文摘要：
Latest experimental and evaluated $α$-decay half-lives between 82$\leq$Z$\leq$118 have been used to modify two empirical formulas: (i) Horoi scaling law [J. Phys. G \textbf{30}, 945 (2004)], and Sobiczewski formula [Acta Phys. Pol. B \textbf{36}, 3095 (2005)] by adding asymmetry dependent terms ($I$ and $I^2$) and refitting of the coefficients. The results of these modified formulas are found with significant improvement while compared with other 21 formulas, and, therefore, are used to predict $α$-decay half-lives with more precision in the unknown superheavy region. The formula of spontaneous fission (SF) half-life proposed by Bao \textit{et al.} [J. Phys. G \textbf{42}, 085101 (2015)] is further modified by using ground-state shell-plus-pairing correction taken from FRDM-2012 and using latest experimental and evaluated spontaneous fission half-lives between 82$\leq$Z$\leq$118. Using these modified formulas, contest between $α$-decay and SF is probed for the nuclei within the range 112$\leq$Z$\leq$118 and consequently probable half-lives and decay modes are estimated. Potential decay chains of $^{286-302}$Og and $^{287-303}$119 (168$\leq$N$\leq$184: island of stability) are analyzed which are found in excellent agreement with available experimental data. In addition, four different machine learning models: XGBoost, Random Forest (RF), Decision Trees (DTs), and Multilayer Perceptron (MLP) neural network are used to train a predictor for $α$-decay and SF half-lives prediction. The prediction of decay modes using XGBoost and MLP are found in excellent agreement with available experimental decay modes along with our predictions obtained by above mentioned modified formulas.
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