Improved phenomenological nuclear charge radius formulae with kernel ridge regression

TL;DR

This paper applies kernel ridge regression to enhance phenomenological nuclear charge radius formulae, significantly reducing deviations and improving extrapolation for neutron-rich nuclei, with implications for nuclear structure modeling.

Contribution

The study introduces a KRR-based approach to refine existing nuclear charge radius formulae, demonstrating improved accuracy and extrapolation capabilities over traditional methods.

Findings

Root-mean-square deviation reduced to ~0.017 fm for 884 nuclei.

KRR method shows strong extrapolation ability for neutron-rich nuclei.

Improved formulae avoid overfitting and enhance predictive accuracy.

Abstract

The kernel ridge regression (KRR) method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$ formulae, and their improved versions by considering the isospin dependence are adopted as examples. The parameters in these six formulae are refitted using the Levenberg-Marquardt method, which give better results than the previous ones. The radius for each nucleus is predicted with the KRR network, which is trained with the deviations between experimental and calculated nuclear charge radii. For each formula, the resultant root-mean-square deviations of 884 nuclei with proton number $Z \geq 8$ and neutron number $N \geq 8$ can be reduced to about 0.017~fm after considering the modification of the KRR method. The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method. It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability. The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed. At last, the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.