Nuclear charge radius predictions by kernel ridge regression with odd–even effects

• DOI: 10.1007/s41365-024-01379-4
• Publication Date: 2024-02-05T09:02:18Z
• Authors: Lu Tang; Zhen-Hua Zhang
• Keywords: Nuclear Theory (nucl-th); Nuclear Theory; FOS: Physical sciences; Nuclear Experiment (nucl-ex); Nuclear Experiment

The extended kernel ridge regression (EKRR) method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models. These are: (i) the isospin dependent $A^{1/3}$ formula, (ii) relativistic continuum Hartree-Bogoliubov (RCHB) theory, (iii) Hartree-Fock-Bogoliubov (HFB) model HFB25, (iv) the Weizsäcker-Skyrme (WS) model WS$^\ast$, and (v) HFB25$^\ast$ model. In the last two models, the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models, respectively. For each model, the resultant root-mean-square deviation for the 1014 nuclei with proton number $Z \geq 8$ can be significantly reduced to 0.009-0.013~fm after considering the modification with the EKRR method. The best among them was the RCHB model, with a root-mean-square deviation of 0.0092~fm. The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined and it was found that after considering the odd-even effects, the extrapolation power was improved compared with that of the original KRR method. The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron $N=126$ and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.<br/>8 pages, 5 figures, 1 table<br/>