Reliable calculations of nuclear binding energies by the Gaussian process of machine learning

Reliable calculations of nuclear binding energies are crucial for advancing the research of nuclear physics. Machine learning provides an innovative approach to exploring complex physical problems. In this study, the nuclear binding energies are modeled directly using a machine-learning method called the Gaussian process. First, the binding energies for 2238 nuclei with \(Z > 20\) and \(N > 20\) are calculated using the Gaussian process in a physically motivated feature space, yielding an average deviation of 0.046 MeV and a standard deviation of 0.066 MeV. The results show the good learning ability of the Gaussian process in the studies of binding energies. Then, the predictive power of the Gaussian process is studied by calculating the binding energies for 108 nuclei newly included in AME2020. The theoretical results are in good agreement with the experimental data, reflecting the good predictive power of the Gaussian process. Moreover, the \(\alpha\)-decay energies for 1169 nuclei with \(50 \le Z \le 110\) are derived from the theoretical binding energies calculated using the Gaussian process. The average deviation and the standard deviation are, respectively, 0.047 MeV and 0.070 MeV. Noticeably, the calculated \(\alpha\)-decay energies for the two new isotopes \(^{204}\)Ac (Huang et al. Phys Lett B 834, 137484 (2022)) and \(^{207}\)Th (Yang et al. Phys Rev C 105, L051302 (2022)) agree well with the latest experimental data. These results demonstrate that the Gaussian process is reliable for the calculations of nuclear binding energies. Finally, the \(\alpha\)-decay properties of some unknown actinide nuclei are predicted using the Gaussian process. The predicted results can be useful guides for future research on binding energies and \(\alpha\)-decay properties.