The Negele-Vautherin density matrix expansion applied to the Gogny force

TL;DR

This paper applies the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for fermionic systems with finite-range interactions, accurately reproducing Gogny-force properties.

Contribution

It extends the Negele-Vautherin approach by fixing angle averaging issues using gauge invariance, enabling derivation of Skyrme functional parameters from Gogny forces.

Findings

Reproduces Gogny-force binding energies within 1-2%.

Derives Skyrme functional parameters from finite-range Gogny interactions.

Provides a quasi-local density functional including spin-orbit and tensor terms.

Abstract

We use the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for the description of systems of fermions interacting with short-ranged interactions composed of arbitrary finite-range central, spin-orbit, and tensor components. Terms that are absent in the original Negele-Vautherin approach owing to the angle averaging of the density matrix are fixed by employing a gauge invariance condition. We obtain the Kohn-Sham interaction energies in all spin-isospin channels, including the exchange terms, expressed as functions of the local densities and their derivatives up to second (next to leading) order. We illustrate the method by determining the coupling constants of the Skyrme functional or Skyrme force that correspond to the finite-range Gogny central force. The resulting self-consistent solutions reproduce the Gogny-force binding energies and radii within the precision of 1-2%.