Combined Use of the Methods of Superposition of Configurations and Correlation Factor on the Ground States of the Helium-Like Ions

The accurate solution of the Schrödinger equation by means of a combination of the method of correlation factor and the method using superposition of configurations is discussed. For a many-electron system, the total wave function divided by the nodeless function $g=g(r_{12}, r_{13}, r_{23}\cdots )$ may be expanded in a series of Slater determinants built up from a complete one-electron set. For a two-electron system, this expansion becomes very simple and, by going over to principal orbitals, it may be "diagonalized" and brought to a particularly rapidly convergent form.