Effective 3-Body Interaction for Mean-Field and Density-Functional Theory

TL;DR

This paper introduces a novel nonlocal 3-body interaction functional for density functional theory, inspired by many-body theory of Fermi gases, improving ground state energy predictions in weak-coupling regimes.

Contribution

It proposes a unique nonlocal generalization of the 3-body interaction that aligns with many-body theory and enhances energy calculations without free parameters.

Findings

Nonlocal interaction improves weak-coupling regime accuracy

Comparison with Green's Function Monte Carlo validates the approach

No free parameters needed for the nonlocal functional

Abstract

Density functionals for nuclei usually include an effective 3-body interaction that depends on a fractional power of the density. Using insights from the many-body theory of the low-density two-component Fermi gas, we consider a new, nonlocal, form for the energy functional that is consistent with the Fock space representation of interaction operators. In particular, there is a unique spatially nonlocal generalization of the contact form of the interaction that preserves the density-to-the-seven-thirds dependence required by the many-body theory. We calculate the ground state energies for particles in a harmonic trap using the nonlocal induced 3-body interaction, and compare them to numerically accurate Green's Function Monte Carlo calculations. Using no free parameters, we find that a nonlocality in the space domain provides a better description of the weak-coupling regime than the local-density approximation.