Nonrelativistic energy levels of helium atom

TL;DR

This paper calculates highly precise nonrelativistic energy levels of helium atom and negative hydrogen ion using a variational exponential expansion method, achieving accuracy up to 35 significant digits.

Contribution

It introduces a variational method with exponential expansion for highly accurate energy level calculations of helium and H- ions.

Findings

Energy levels accurate to 28-35 significant digits.

Convergence studied as a function of basis functions.

Results include ionization energies of helium and H-.

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 H$^-$ are also presented.