Comment on atomic independent-particle models

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Abstract
The Hartree-Fock-Slater (HFS) independent-particle model in the form developed by Hermann and Skillman (HS) and the Green, Sellin, and Zachor (GSZ) analytic independent-particle model are being used for many types of applications of atomic theory to avoid cumbersome, albeit more rigorous, many-body calculations. We here examine the single-electron eigenvalues obtained with these models and find that the GSZ model is capable of yielding energy eigenvalues for valence electrons which are substantially closer to experimental values than are the results of HS-HFS calculations. With the aid of an analytic representation of the equivalent HS-HFS screening function, we identify the difficulty with this model as a weakness of the potential in the neighborhood of the valence shell. Accurate representations of valence states are important in most atomic applications of the independent-particle model.

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