Some observations on atomic independent-particle models

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The two principal ways of determining the pair of parameters characterizing the atomic independent-particle-model potential of Green, Sellin, and Zachor (GSZ) are described. The first method based upon fitting ionization and excitation energies should provide an accurate description of the IPM potential in the outer region. A second ab-initio variational method, which gives total energies which are usually within 50 ppm of true Hartree-Fock energies, should provide an accurate description of the IPM potential in the inner region. The differences of the two potentials obtained by these two approaches are discussed as well as the possibility of giving a physical interpretation to the differences. Three-parameter variations of the GSZ potential are also proposed which make it possible to fuse the good inner potential with the good outer potential in a reasonable way. Finally, several possible explanations of the differences are discussed from a fundamental point of view.