Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach

The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei. The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square (rms) deviations from data, i.e., 0.949 \begin{document}$ \mu_\mathrm{N} $\end{document} and 1.272 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and odd-proton nuclei, respectively. By including the dependence of the nuclear spin and Schmidt magnetic moment, the machine-learning approach precisely describes the magnetic moments of odd-A nuclei with rms deviations of 0.036 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and 0.061 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-proton nuclei. Furthermore, the evolution of magnetic moments along isotopic chains, including the staggering and sudden jump trend, which are difficult to describe using nuclear models, have been well reproduced by the Bayesian neural network (BNN) approach. The magnetic moments of doubly closed-shell \begin{document}$ \pm1 $\end{document} nuclei, for example, isoscalar and isovector magnetic moments, have been well studied and compared with the corresponding non-relativistic and relativistic calculations.