### 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 |
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Article number | 014502 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 83 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 28 2011 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

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