Empirical relations using symbolic regression models for cluster decay half-lives

Background: Cluster radioactivity is a rare nuclear decay phenomenon that emits clusters heavier than the alpha particle but lighter than the smallest fission fragment observed. The experimentally observed clusters, as well as other possible cluster emitters, are theoretically studied based on preformed cluster models, fission-like models, and empirical models.Purpose: The purpose of this paper is to establish reliable empirical models with fewer parameters for predicting half-lives of cluster decay using symbolic regression.Methods: The experimentally measured half-lives of the 22 cluster decay of various parents and different clusters in the trans-lead region, along with their mass number, proton number, neutron number, and decay energy (Q) are used to train the interpretable symbolic regression model (pysr). The trained model extracts empirical formulas for intricate physical phenomena from the experimental data. The model traverses an immense mathematical expression space using an evolutionary search strategy to discover the most interpretable and precise formulas to be used to predict logarithmic half-lives of cluster decay. The obtained empirical equations are tested with statistical metrics such as root-mean-square error (RMSE) and mean absolute error (MAE) with respect to the experimental data.Results: Within the model limits, several empirical equations are obtained with varying score and loss values. The half-lives calculated using the empirical relations are compared with available experimental data and with the results of other empirical formulas available in the literature. Further, the obtained empirical formula is used to predict the half-lives for 51 energetically possible nuclei in the trans-actinide region.Conclusions: The generated expressions for half-lives are found to have strong correlations between Q values, barrier penetration probabilities, and charge numbers of the decay fragments. The consistency of pysr-derived predictions with known decay systematics suggests that symbolic regression can be a valuable tool for predicting half-lives of exotic cluster decay modes in the unexplored regions of the nuclear chart.