Results of the Hartree Theory

Here we consider the results of the Hartree theory of multi-electron atoms given in [2]. 

The Hartree eigenfunctions for the electron in the multi-electron atom can be written 

However, the radial dependence of the eigenfunctions for an electron in a multielectron atom is not the same as for an electron in an one-electron atom. The reason is that the net potential V(r), which enters the differential equation that determines the functions Rni r), does not have the same r dependence as the Coulomb potential. The innermost electron shells of an atom shield the outermost shells from parts of the nuclear charge + 2 e and reduce it. 

The characteristic radius of the outermost shell of argon (the principal quantum number n = 3) has the ratio r/ao which is equal to 1.5. 

Indeed, for argon we obtain —3500/ —14 = 250 (18 — if- = 256. Note that (3.33) is not applicable for atoms with high 2 because of relativistic effects. 

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