Pauli potential from Heilmann-Lieb electron density obtained by summing hydrogenic closed-shell densities over the entire bound-state spectrum

Ferenc Bogár, Ferenc Bartha, Ferenc A. Bartha, Norman H. March

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number014502
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume83
Issue number1
DOIs
Publication statusPublished - Jan 28 2011

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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