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

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