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 (12)

• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Superfluid Fermi Gases with Large Scattering Length
• Low-density neutron matter
• 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
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Effective Field Theory for Dilute Fermi Systems
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Energy density functional on a microscopic basis
• Density-Dependence of Two-Body Interactions Beyond the Mean-Field Approximation. Part 1: Generalized Brueckner G-Matrix in the Local Approximation
• Exploration of a modified density dependence in the Skyrme functional
• Density Dependence of Two-Body Interactions for Beyond Mean-Field Calculations

Cited by in corpus (12)

• Resonantly Interacting Fermions In a Box
• Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter
• Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms
• New parameterization of Skyrme's interaction for regularized multi-reference energy density functional calculations
• Effective density functionals beyond mean field
• Nonlocal energy density functionals for low-energy nuclear structure
• From dilute matter to the equilibrium point in the energy--density--functional theory
• Extension and parameterization of high-order density dependence in Skyrme forces
• Spin constraints on nuclear energy density functionals
• Kohn-Sham Density Functional Theory of Abelian Anyons
• Semi-contact 3-body interaction for nuclear density functional theory
• Energy spectrum and effective mass using a non-local 3-body interaction