Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions

TL;DR

This paper applies the density matrix expansion to coordinate-space chiral interactions at the Hartree-Fock level, introducing a new organization scheme to handle three-nucleon forces and local regulators to improve functional optimization.

Contribution

It presents a novel organization scheme for applying the DME to three-nucleon forces and incorporates local regulators, advancing the use of chiral effective field theory in nuclear density functionals.

Findings

Successful application of DME to chiral interactions up to N2LO

Introduction of a new scheme for three-nucleon force algebra

Mitigation of singular potential effects with local regulators

Abstract

We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit Delta isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.