Comparing different density-matrix expansions for long-range pion exchange

TL;DR

This paper evaluates different density-matrix expansion methods for incorporating long-range pion exchange into nuclear energy density functionals, finding that certain variants effectively approximate exchange energies and support their use in chiral pion contributions.

Contribution

It provides a systematic comparison of DME implementations for long-range pion interactions, highlighting the effectiveness of variants that avoid truncation at two derivatives.

Findings

All DME variants effectively approximate exchange energies with long-range one-pion contributions.

Variants not truncating at two derivatives are preferred for better approximation.

Separate treatment of neutrons and protons is important for scalar-isovector energies.

Abstract

Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. Here we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.