The Theory of the Thomas-Fermi Electron Density

A new modification of the Thomas-Fermi formula is derived which is similar to Weizsäcker's; this provides what is claimed to be a more plausible proof than usual of the Thomas-Fermi method. The method is applied to give a non-divergent relativistic approximation for Z<137/2 and is used to demonstrate the incorrectness of the Thomas-Fermi-Dirac equation based on Foch's equations. Slater's approximation to Foch's equations is used to derive a Thomas-Fermi equation with exchange only differing from Dirac's by a change in Z. The solutions of this equation are re-interpreted and shown to be not unique, though always giving a positive electron density.