Bartha, Ferenc

Bartha, Ferenc A.

Bog\ue1r, Ferenc

March, Norman H.

Abstract: Independently, in the mid-1980s, several groups proposed to bosonize the density-functional theory (DFT) for fermions by writing a Schr\uf6dinger equation for the density amplitude \u3c1(r)1/2, with \u3c1(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, \u3c1 1e(r) say, calculated analytically by Heilmann and Lieb (HL), by summation over the entire hydrogenic bound-state spectrum. We show that VP 1e(r) has simple limits for both r tends to infinity and r approaching zero. In particular, at large r, VP 1e(r) precisely cancels the attractive Coulomb potential -Ze2/r, leaving V(r)+VP 1e(r) of O(r-2) as r tends to infinity. The HL density \u3c1 1e(r) is finally used numerically to display VP 1e(r) for all r values

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

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