Nonrelativistic energy levels of helium atoms

The nonrelativistic ionization energy levels of a helium atom are calculated for S, P, D, and F states. The calculations are based on the variational method of "exponential" expansion. The convergence of the calculated energy levels is studied as a function of the number of basis functions N. This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate up to 28-35 significant digits. Calculations of the nonrelativistic ionization energy of the negative hydrogen ion H- are also presented. © 2018 American Physical Society.