Hartree–Fock Approximation to the (ns2)1S Autoionizing States of Helium

As a first step in estimating the utility of the Hartree–Fock method for calculating positions and widths of autoionizing levels of atoms and molecules, an investigation of the helium problem has been initiated and is reported here. Wavefunctions and energies for the ten lowest (ns2)1S states are calculated by numerically integrating the Hartree–Fock equation for solutions corresponding to energy levels above the ground state. Except for n = 1 all these states are autoionizing, and each is probably the lowest bound state for each closed channel for n = 2(1)10. The energies of the ns2 states are found to be between the nth and (n − 1)th thresholds for n = 2(1)6 but for n > 6 the calculated levels fall below the (n − 1)th threshold. The method of numerical integration used is described, and the wavefunctions are reported in terms of an expansion in a basis determined by a least-squares curve-fitting method.