### 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 V_{P}(r) where P denotes Pauli. To gain insight into the form of the Pauli potential V_{P}(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 V_{P}(r) for all r values.

Original language | English |
---|---|

Article number | 014502 |

Journal | Physical Review A |

Volume | 83 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 28 2011 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*83*(1), [014502]. https://doi.org/10.1103/PhysRevA.83.014502

**Pauli potential from Heilmann-Lieb electron density obtained by summing hydrogenic closed-shell densities over the entire bound-state spectrum.** / Bogár, F.; Bartha, Ferenc; Bartha, Ferenc A.; March, Norman H.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 83, no. 1, 014502. https://doi.org/10.1103/PhysRevA.83.014502

}

TY - JOUR

T1 - Pauli potential from Heilmann-Lieb electron density obtained by summing hydrogenic closed-shell densities over the entire bound-state spectrum

AU - Bogár, F.

AU - Bartha, Ferenc

AU - Bartha, Ferenc A.

AU - March, Norman H.

PY - 2011/1/28

Y1 - 2011/1/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79551592831&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551592831&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.83.014502

DO - 10.1103/PhysRevA.83.014502

M3 - Article

AN - SCOPUS:79551592831

VL - 83

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 014502

ER -