Highly-accurate ground state energies of the He atom and the He-like ions by Hartree SCF calculation with Obrechkoff method

In this paper, we use the Obrechkoff one-step method to improve the performance of the Hartree SCF calculation and obtain the Hartree energies of the two-electron atom and ions for the nuclear charge up to 20 with 14 significant figures, which is more accurate than those reported in the literature by four figures. Our calculation demonstrates that the highly-accurate Obrechkoff one-step method for the SCF calculation has the obvious advantage in the accuracy and efficiency over the previous methods.