Improved phenomenological nuclear charge radius formulae with kernel ridge regression *

Abstract The kernel ridge regression (KRR) method with a Gaussian is used to improve the description of nuclear charge radius by several phenomenological formulae. widely , N^{1/3} and Z^{1/3} formulae, their improved versions including isospin dependence, are adopted as examples. parameters in these six formulae refitted using Levenberg–Marquardt method, which give better results than previous versions. for each nucleus predicted KRR network, trained deviations between experimental calculated radii. For formula, resultant root-mean-square 884 nuclei proton number Z \geq 8 neutron N can be reduced about 0.017 fm after considering modification method. extrapolation ability neutron-rich region examined carefully compared radial basis function It found that avoid risk overfitting, have good ability. influence penalty term on also discussed. Finally, radii recently observed K Ca isotopes analyzed.