A feed-forward neural network model is trained to calculate the nuclear charge radii. The model trained with input data set of proton and neutron number $Z,N$, the electric quadrupole transition strength $B(E2)$ from the first excited 2$^+$ state to the ground state, together with the symmetry energy. The model reproduces well not only the isotope dependence of charge radii, but also the kinks of charge radii at the neutron magic numbers $N=82$ for Sn and Sm isotopes, and also $N=126$ for Pb isotopes. The important role of $B(E2)$ value is pointed out to reproduce the kink of the isotope dependence of charge radii in these nuclei. Moreover, with the inclusion of the symmetry energy term in the inputs, the charge radii of Ca isotopes are well reproduced. This result suggests a new correlation between the symmetry energy and charge radii of Ca isotopes. The Skyrme HFB calculation is performed to confirm the existence of this correlation in a microscopic model.

中文翻译：

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使用经过训练的前馈神经网络计算核电荷半径

训练前馈神经网络模型来计算核电荷半径。该模型使用质子和中子数 $Z,N$ 的输入数据集、从第一激发 2$^+$ 态到基态的电四极跃迁强度 $B(E2)$ 以及对称能进行训练。该模型不仅很好地再现了电荷半径的同位素依赖性，而且再现了 Sn 和 Sm 同位素的中子幻数 $N=82$ 以及 Pb 同位素的 $N=126$ 处的电荷半径扭结。指出$B(E2)$ 值的重要作用是重现这些原子核中电荷半径的同位素依赖性的扭结。此外，通过在输入中包含对称能量项，可以很好地再现 Ca 同位素的电荷半径。该结果表明对称能与 Ca 同位素的电荷半径之间存在新的相关性。Skyrme HFB 计算用于确认微观模型中这种相关性的存在。