Investigation of Nuclear Binding Energy and Charge Radius Based on Random Forest Algorithm

The random forest algorithm was applied to study the nuclear binding energy and charge radius. The regularized root-mean-square of error (RMSE) was proposed to avoid overfitting during the training of random forest. RMSE for nuclides with Z, N>7 is reduced to 0.816 MeV and 0.020 0 fm compared with the six-term liquid drop model and a three-term nuclear charge radius formula, respectively. Specific interest is in the possible (sub) shells among the superheavy region, which is important for searching for new elements and the island of stability. The significance of shell features estimated by the so-called shapely additive explanation method suggests (Z, N)=(92, 142) and (98, 156) as possible subshells indicated by the binding energy. Because the present observed data is far from the N=184 shell, which is suggested by mean-field investigations, its shell effect is not predicted based on present training. The significance analysis of the nuclear charge radius suggests Z=92 and N=136 as possible subshells. The effect is verified by the shell-corrected nuclear charge radius model.