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The classical Thomas-Fermi theory of the electrons in an atom is amended in a manner that produces continuity of the electron density ρ. This is done by imposing the constraint that ʃ e -2 kr unk 2 ρ d r should be finite, with k determined by the nuclear cusp condition, followed or preceded by an optimum coordinate scaling. Electron densities and total energies are shown to be vastly improved.
Parr et al. (Sun,) studied this question.