Wave Functions for the Free Electron. II. The Inclusion of Polarization and Exchange

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Abstract
The effect of the polarization of the atomic core by the free electron on the free-electron wave function and the effect of the exchange of the free electron with the bound orbitals on this wave function are treated by perturbation theory. Polarization must be considered first. Its effect on the atomic charge cloud is introduced through an expansion over the bound wave functions for the atom in terms of the free-electron separation as a parameter. This parametric treatment of electron separation means we cannot accept the solution at small separations from the nucleus although this is not a serious restriction. From this wave function we obtain a polarized Coulomb potential from which a solution for the free-electron function may be obtained using our old programs. Having solved the free-electron wave equation with the exchange potential terms supposed zero, we use this solution to compute the exchange integrals. The equation including these integrals is then solved to obtain approximate wave functions for free electrons containing both exchange and polarization.