Nonrelativistic energy levels of helium atoms

Abstract

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 ${\mathrm{H}}^{\ensuremath{-}}$ are also presented.