Modified empirical formulas and machine learning for $\alpha$-decay systematics

TL;DR

This paper improves empirical formulas for alpha-decay and spontaneous fission half-lives using experimental data and machine learning, enhancing prediction accuracy for superheavy nuclei and decay modes.

Contribution

It introduces modified empirical formulas with asymmetry terms and applies machine learning models to predict decay properties with high accuracy.

Findings

Modified formulas outperform previous models in predicting half-lives.

Machine learning models achieve excellent agreement with experimental decay modes.

Predictions for superheavy nuclei decay chains are consistent with observed data.

Abstract

Latest experimental and evaluated $\alpha$-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 $\alpha$-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 $\alpha$-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 $\alpha$-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.