Simple model for the spherically and system-averaged pair density: Results for two-electron atoms

As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this paper we explore the extension of this approach to nonuniform systems, and we discuss its potential for density functional theory. For the spherically- and system-averaged pair density of two-electron atoms we obtain very accurate short-range properties, including, for nuclear charge Z >= 2, "on-top" values (zero electron-electron distance) essentially indistinguishable from those coming from precise variational wave functions. By means of a nonlinear adiabatic connection that separates long- and short-range effects, we also obtain Kohn-Sham correlation energies whose error is less than 4 mhartree, again for Z >= 2, and short-range-only correlation energies whose accuracy is one order of magnitude better.