Background: double-$\alpha$ decay is an exotic nuclear decay mode that offers a sensitive probe of quantum tunneling, nuclear clustering, and barrier penetration phenomena in medium-heavy and heavy nuclei. Despite being energetically allowed for a significant fraction of nuclei, this decay mode remains experimentally unexplored. An experimental proposal to search for double-$\alpha$ decay in ${}^{224}\mathrm{Ra}$ has been advanced at the ISOLDE facility of CERN, highlighting ongoing efforts to probe this rare decay channel.

Purpose: This work presents a systematic investigation of double-$\alpha$-decay half-lives and branching ratios across the nuclear chart, to identify energetically allowed and experimentally promising candidates, as well as evaluating the predictive performance of machine-learning approaches for such rare nuclear-decay modes.

Methods: A machine-learning framework based on the extreme gradient boosting regression algorithm is employed to predict double-$\alpha$-decay half-lives for nuclei with positive double-$\alpha$-decay energy in the atomic number range $Z=60–101$. The atomic mass table AME2016 is used to determine decay energetics, and the machine-learning predictions are compared with results from the modified generalized liquid drop model [Phys. Rev. C 104, 064604 (2021)] and the semiempirical formulation of Tretyak [Nucl. Phys. At. Energy 22, 121 (2021)]. In addition, a Geiger-Nuttall-type linear relation for double-α decay is extracted from the global systematics.

Results: The predicted double-$\alpha$-decay half-lives span many orders of magnitude and show good overall agreement with established theoretical models. The machine-learning approach successfully captures the dominant dependence of the decay probability on decay energy and Coulomb barrier penetration. At the same time, deviations are attributed to shell effects, deformation, and pairing correlations in specific nuclei. A simple empirical relation linking ${log}_{10}{T}_{1/2}^{2\alpha }$ to $Z_d/\sqrt{Q_{2\alpha }}$ is proposed for double-$\alpha$ decay. The calculated branching ratios confirm the rare nature of this decay mode and identify a subset of nuclei with enhanced probabilities that may be accessible to future experiments.

Conclusion: The present study demonstrates that machine-learning methods provide a reliable and efficient framework for exploring double-$\alpha$ decay across a wide region of the nuclear chart. The results offer quantitative guidance for experimental searches and establish machine learning as a powerful complementary tool for investigating rare and exotic nuclear-decay processes.

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• Alpha decay
• Lifetimes & widths
• Nuclear structure & decays
• Rare & new isotopes
• Machine learning