Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

TL;DR

This paper introduces a new microscopically derived energy density functional for nuclei based on the Density Matrix Expansion, demonstrating its stability and potential for improved nuclear modeling over traditional Skyrme functionals.

Contribution

It presents the first implementation and assessment of a DME-based functional with richer density dependencies, showing its stability and systematic improvement over standard Skyrme functionals.

Findings

The DME functional yields stable and sensible nuclear results.

It shows a small but systematic reduction in the chi-squared fit metric.

The functional is suitable for future large-scale nuclear calculations.

Abstract

In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test $\chi^2$ function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.