Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

TL;DR

This paper develops a new approach to incorporate chiral effective field theory two-nucleon interactions into energy density functionals using an improved density matrix expansion, enabling more microscopic and accurate nuclear modeling.

Contribution

It introduces a microscopically-guided Skyrme functional with density-dependent couplings derived from chiral EFT, combining long-range pion exchanges with zero-range contact interactions.

Findings

Decomposition of couplings into cutoff-dependent and independent parts.

Implementation of the improved DME for non-local Fock energies.

Provision of a Mathematica notebook for the density-dependent couplings.

Abstract

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam {\it et al.} to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N$^2$LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a cutoff-dependent coupling {\it constant} arising from zero-range contact interactions and a cutoff-independent coupling {\it function} of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A Mathematica notebook containing the novel density-dependent couplings is provided.