Mapping low-lying states and B(E2;01+→21+) in even-even nuclei with machine learning

A machine-learning algorithm, Light Gradient Boosting Machine, was applied for the first time to investigate the fundamental experimental observables in even-even nuclei over the Segrè chart. Specifically, we focused on the excitation energies of the $2_1^{+}$ and $4_1^{+}$ states, and the reduced electric quadrupole transition probability $B(E2;0_1^{+}\to 2_1^{+})$. Present obtained results well reproduced experimental data within an accuracy of 1.07, 1.05, and 1.14 times for the $2_1^{+}$ and $4_1^{+}$ states as well as $B(E2;0_1^{+}\to 2_1^{+})$, respectively, being significantly precise than the results from any state-of-the-art nuclear models and from any machine-learning-based approaches. The predictive capability of our machine learning methodology was further validated using 17 newly measured data points which were not used in the training set. Taking O, Ca, Sn, and Pb isotopes as examples, it has been found that our methodology precisely captures both the isotopic trend and absolute values, surpassing all theoretical models hitherto. Our findings reveal the double-magic nature of ¹⁰⁰Sn and the disappearance of the $N=20$ shell in ²⁸O.