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

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.