Pauli potential from Heilmann-Lieb electron density obtained by summing hydrogenic closed-shell densities over the entire bound-state spectrumPauli potential from Heilmann-Lieb electron density obtained by summing hydrogenic closed-shell densities over the entire bound-state spectrum
Faculty of Sciences. Physics

Department of Physics

article

2011Lancaster, Pa, 2011

Physics

Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015

83(2011):1, p. 014502,1-014502,3

1094-1622

1050-2947

014502

E-only publicatie

English (eng)

University of Antwerp

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 VP∞(r) has simple limits for both r tends to infinity and r approaching zero. In particular, at large r, VP∞(r) precisely cancels the attractive Coulomb potential -Ze2/r, leaving V(r)+VP∞(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.

https://repository.uantwerpen.be/docman/irua/738a74/84066e55.pdf

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