Curvature of the total electron density at critical coupling

Abstract

A structural property of the spherically averaged total charge density ρλ(r) of a degenerate electron gas distorted by the action of an attractive, screened potential λV(r) is the subject of this study. The total charge density is described as a sum over occupied bound and scattering wave functions of independent electrons moving in the effective central field. It is shown that the second radial derivative ρλ″(0) is a differentiable function of λ for any λ≥0. The smooth behavior implies that this curvature ρλ″(0) does not provide a criterion for the bound-to-free transition in metallic environments. © 2005 The American Physical Society.