• Comparison of different kernel functions in nuclear charge radius predictions by the kernel ridge regression method

    分类: 物理学 >> 核物理学 提交时间: 2024-04-01

    摘要: Using two nuclear models, i) the relativistic continuum Hartree-Bogoliubov (RCHB) theoryand ii) the Weizs acker-Skyrme (WS) model WS$^ ast$,the performances of nine kinds of kernel functions in the kernel ridge regression (KRR) methodare investigated by comparing the accuracies of describing the experimental nuclear chargeradii and the extrapolation abilities.It is found that, except the inverse power kernel, other kernels can reach the same levelaround 0.015-0.016~fm for these two models with KRR method.The extrapolation ability for the neutron rich region of each kernel depends on the trainning data.Our investigation shows that the performances of the power kernel and Multiquadric kernel arebetter in the RCHB+KRR calculation, and the Gaussian kernel is better in the WS$^ ast$+KRR calculation.In addition, the performance of different basis functions inthe radial basis function method is also investigated for comparison.The results are similar to the KRR method.The influence of different kernels on the KRR reconstruct function is discussedby investigating the whole nuclear chart.At last, the charge radii of some specific isotopic chains have been investigatedby the RCHB+KRR with power kernel and the WS$^ ast$+KRR with Gaussian kernel.The charge radii and most of the specific features in these isotopic chainscan be reproduced after considering the KRR method.

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

    分类: 物理学 >> 核物理学 提交时间: 2023-12-13

    摘要: The extended kernel ridge regression (EKRR) method with odd-even effects was adopted to improve the de 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 Weizs acker-Skyrme (WS) model WS$^ ast$,(v) HFB25$^ ast$ model.In the last two models, the charge radii were calculated using a five-parameter formulawith 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 nucleiwith proton number $Z geq 8$ can be significantly reducedto 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 afterconsidering 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 isotopesand the abrupt kinks across the neutron $N=126$ and 82 shell closures were alsocalculated and could be reproduced quite well by calculations using the EKRR method.