Analysis of the Three Parameter Wave Function of Hylleraas for the He i Ground State in Terms of Central Field Wave Functions

Abstract

A study of configuration interaction in the ground state of He i has been carried through by expanding the various angular components of the three parameter wave function of Hylleraas in orthonormal sets of functions. The different sets have been constructed from symmetrized products of hydrogenic wave functions with different values of the parameter $Z$. The importance of the various configurations for $Z=2\mathrm{}$ is commented upon at some length. Configurations involving a free electron are shown to make surprisingly large contributions. The changing importance of the various components with changing $Z$ is illustrated. In particular, the minimum with respect to $Z$ of the contribution of configurations containing a free electron is pointed out. The implications of the results of these expansions for attempts to obtain wave functions for both normal and excited states of two-electron systems by the minimum principle from linear combinations of products of hydrogenic functions of the proper symmetry are discussed.