Ground State of the Helium Atom. II

Abstract

A further attempt is made to improve the theoretical prediction of the energy of the ground state of atomic helium. The nonrelativistic part is treated by the variational method of Stevenson and Crawford which is useful for improving the lower bound for the ground-state energy. Linear combinations of up to 80 terms of generalized Hylleraas type are employed in the numerical computation. The best trial function gives -2.9037237 atomic units as an upper bound and -2.9037467 atomic units as a lower bound for the ground-state energy. It is estimated from the calculated results that the exact nonrelativistic energy of He ground state will be found in the neighborhood of -2.9037247 atomic units. Rigorous formulas are derived which can be used for calculating the upper limits to the errors in the expectation values of mass polarization and relativistic corrections. Although these formulas give very broad limits of error, they are useful in estimating the order of magnitude of actual errors in a semiempirical manner. With mass polarization and relativistic corrections as well as electrodynamical corrections, the theoretical ionization potential becomes 198310.77 ${\mathrm{cm}}^{\ensuremath{-}1}$ which is in good agreement with the latest observed value ${198310.8}_{2}$\ifmmode\pm\else\textpm\fi{}0.15 ${\mathrm{cm}}^{\ensuremath{-}1}$.