Modified empirical formulas and machine learning for α-decay systematics

Abstract

Latest experimental and evaluated α-decay half-lives between 82 ⩽ Z ⩽ 118 have been used to modify two empirical formulas: (i) Horoi scaling law (2004 J. Phys. G: Nucl. Part. Phys. 30 945), and Sobiczewski formula (2005 Acta Phys. Pol. B 36 3095) 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 et al (2015 J. Phys. G: Nucl. Part. Phys. 42 085101) is further modified by using ground-state shell-plus-pairing correction taken from FRDM-2012 and using the latest experimental and evaluated SF half-lives between 82 ⩽ Z ⩽ 118. Using these modified formulas, contest between α-decay and SF is probed for the nuclei within the range 112 ⩽ Z ⩽ 118 and consequently probable half-lives and decay modes are estimated. Potential decay chains of 286−302Og and 287−303119 (168 ⩽ N ⩽ 184: island of stability) are analyzed which are found to be in excellent agreement with available experimental data. In addition, four different machine learning models: XGBoost, random forest, decision trees, 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 to be in excellent agreement with available experimental decay modes along with our predictions obtained by the above-mentioned modified formulas.