论文标题
改进的现象学核电荷半径半径公式，内核脊回归
Improved phenomenological nuclear charge radius formulae with kernel ridge regression
论文作者
论文摘要
使用高斯内核的内核脊回归（KRR）方法用于通过几种现象学公式来改善核电荷半径的描述。广泛使用的$ a^{1/3} $，$ n^{1/3} $和$ z^{1/3} $公式，并考虑使用Isospin依赖性来改进版本。使用Levenberg-Marquardt方法对这六个公式中的参数进行了改装，该参数比以前的参数更好。用KRR网络预测每个核的半径，该网络经过实验和计算出的核电荷半径之间的偏差训练。对于每个公式，带有质子数$ z \ geq 8 $的884个核的根平方偏差和中子数$ n \ geq 8 $可以降低至约0.017〜 fm，在考虑了KRR方法的修改后。仔细检查了KRR方法对中子富含中子区域的外推能力，并将其与径向基函数方法进行比较。发现通过KRR方法改进的核电半径公式可以避免过度拟合的风险并具有良好的外推能力。还讨论了山脊惩罚项对KRR方法外推能力的影响。最后，已经分析了最近观察到的K和Ca同位素的几个核电荷半径。
The kernel ridge regression (KRR) method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$ formulae, and their improved versions by considering the isospin dependence are adopted as examples. The parameters in these six formulae are refitted using the Levenberg-Marquardt method, which give better results than the previous ones. The radius for each nucleus is predicted with the KRR network, which is trained with the deviations between experimental and calculated nuclear charge radii. For each formula, the resultant root-mean-square deviations of 884 nuclei with proton number $Z \geq 8$ and neutron number $N \geq 8$ can be reduced 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 is examined carefully and compared with the radial basis function method. It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability. The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed. At last, the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.
