Thomas-Fermi theory for atomic systems

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.