Empirical modeling of one-proton radioactivity using symbolic regression

Abstract Proton radioactivity is a rare form of nuclear decay occurring in nuclei beyond the proton drip line, where proton-rich nuclei emit a proton to become more stable. The process provides useful information on the nuclear structure and shell effects in exotic regions of the nuclear chart. In this work, we obtain compact and robust empirical models with few parameters for the prediction of logarithmic half-lives of one-proton radioactivity through symbolic regression. A set of 44 experimentally determined one-proton emitters with decay energy ( Q ), orbital angular momentum ( ℓ ), and charge number ( Z ) are used to train an interpretable symbolic regression model (PySR). The model uses evolutionary algorithms to search a vast space of mathematical expressions and identify brief, physically insightful formulas for the logarithmic half-lives of proton decay. Among the expressions generated, the best-performing model achieves a root mean square error (RMSE) of 0.394 and a mean absolute error (MAE) of 0.322, highlighting high predictive accuracy. The model further precisely predicts the logarithmic half-life of recently observed heaviest proton-emitting isotope, 188 At , which was excluded from the training set. The prediction exhibited an absolute error of 0.407 (on the logarithmic scale) compared to the experimental value, demonstrating strong generalization capability. These results confirm that physics-informed symbolic regression is an effective and interpretable tool for modeling proton radioactivity and can be useful to explore the uncharted regions of the nuclear landscape.