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 ρ(7/3) density dependence required by the many-body theory. We calculate the ground-state energies for particles in a harmonic trap by 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.