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

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.

Nuclear Structure at the Crossroads

“…A particular opportunity is the use of EFT to improve nuclear EDFs. A DME implementation of long-range chiral interactions has shown improvement over pure Skyrme functionals, but there are many open questions to address [66,67]. An alternative program for DFT from EFT is to apply field-theoretic background-field methods for dealing with symmetry breaking and restoration [68].…”

Complete solution to the inverse Kohn-Sham problem: From the density to the energy

“…In this respect, nonempirical EDFs, or even strategies to better constrain some terms of the EDFs, would be extremely welcome. Deriving the nuclear EDF from ab initio is a possible avenue and is the subject of intense investigations [29,37,38]. Solving the IKS problem with experimental or ab initio densities as an input is a complementary possibility.…”

Nuclear energy density functionals grounded in ab initio calculations

“…While there are already some attempts along this line [37,40,41], e.g. using the Density Matrix Expansion (DME) [42,43], or constraining specific terms of the EDFs on ab initio calculations [44][45][46][47][48][49], in this work we propose a novel and more systematic approach. This approach is well-established in electronic DFT, and known as the "reductionist", or non-empirical, research program [25,[50][51][52].…”