English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The kernel ridge regression (KRR) method with Gaussian kernel is used toimprove the description of the nuclear charge radius by severalphenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$formulae, and their improved versions by considering the isospin dependence areadopted as examples. The parameters in these six formulae are refitted usingthe Levenberg-Marquardt method, which give better results than the previousones. The radius for each nucleus is predicted with the KRR network, which istrained with the deviations between experimental and calculated nuclear chargeradii. For each formula, the resultant root-mean-square deviations of 884nuclei with proton number $Z \geq 8$ and neutron number $N \geq 8$ can bereduced 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 isexamined carefully and compared with the radial basis function method. It isfound that the improved nuclear charge radius formulae by KRR method can avoidthe risk of overfitting and have a good extrapolation ability. The influence ofthe ridge penalty term on the extrapolation ability of the KRR method is alsodiscussed. At last, the nuclear charge radii of several recently observed K andCa isotopes have been analyzed.

Improved phenomenological nuclear charge radius formulae with kernel ridge regression