The Effect of a Potential Gradient on the Density of a Degenerate Fermi Gas

By studying the properties of a degenerate gas in a linearly varying potential a modified relation is derived between density and potential which replaces the usual ρ = const. V3/2, takes into account explicitly the presence of potential gradients and can be used in regions of negative kinetic energy. When combined with Poisson's equation this gives a modified Thomas-Fermi differential equation. The resulting change in the density distribution of electrons in an atom is most marked in the outer regions, where the new equation leads to an r-2 exp (-r/a) decrease of density for a neutral atom. Applications to nuclear surface problems are mentioned.