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

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 $$\hbox {WS}^*$$ , and (v) HFB25 $$^*$$ 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 $$Z \ge 8$$ 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.