Improved phenomenological nuclear charge radius formulae with kernel ridge regression

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 $Z\ge 8$ and neutron number $N\ge 8$ 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.

9 pages, 5 figures, 2 tables

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Cited by in corpus (6)

• Nuclear charge radius predictions by kernel ridge regression with odd-even effects
• Global prediction of nuclear charge density distributions using deep neural network
• Local variations of charge radii for nuclei with even $Z$ from 84 to 120
• Nuclear shape evolution of neutron-deficient Au and kink structure of Pb isotopes
• Implication of shell quenching in scandium isotopes around N=20
• Predictions of charge density distributions for nuclei with $Z\ge 8$