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

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.

4+ pages, 2 figures, 1 table; 3 references added; v2 corresponds to the published version

References in corpus (4)

• Strongly paired fermions: Cold atoms and neutron matter
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. IX: Constraint of pairing force to ${}^1{S}_0$ neutron-matter gap
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Exploration of a modified density dependence in the Skyrme functional

Cited by in corpus (1)

• Resonantly Interacting Fermions In a Box