Independently, in the mid-1980s, several groups proposed to bosonize the density-functional theory (DFT) for fermions by writing a Schrödinger equation for the density amplitude ρ(r)1/2, with ρ(r) as the ground-state electron density, the central tool of DFT. The resulting differential equation has the DFT one-body potential V(r) modified by an additive term VP(r) where P denotes Pauli. To gain insight into the form of the Pauli potential VP(r), here, we invoke the known Coulombic density, ρ∞(r) say, calculated analytically by Heilmann and Lieb (HL), by summation over the entire hydrogenic bound-state spectrum. We show that V∞(r) has simple limits for both r tends to infinity and r approaching zero. In particular, at large r, V∞(r) precisely cancels the attractive Coulomb potential -Ze2/r, leaving V(r)+V∞(r) of O(r -2) as r tends to infinity. The HL density ρ∞(r) is finally used numerically to display VP(r) for all r values.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - Jan 28 2011|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics