Study of Charge Radii with Neural Networks

TL;DR

This paper employs neural networks to accurately predict nuclear charge radii, capturing isotope trends and kinks at magic numbers, and reveals a new correlation between symmetry energy and charge radii, validated by microscopic calculations.

Contribution

The study introduces a neural network model incorporating $Z$, $N$, $B(E2)$, and symmetry energy to predict charge radii, highlighting the importance of $B(E2)$ and establishing a novel correlation with symmetry energy.

Findings

Neural network reproduces isotope dependence and kinks in charge radii.

Including symmetry energy improves Ca isotope radius predictions.

Microscopic Skyrme HFB confirms the correlation between symmetry energy and charge radii.

Abstract

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.