Nuclear energy density functional from chiral two- and three-nucleon interactions

TL;DR

This paper derives a nuclear energy density functional from chiral two- and three-nucleon interactions using an improved density-matrix expansion, comparing the results with phenomenological models and identifying the need for higher-order treatments.

Contribution

It introduces a first-order derivation of the nuclear energy density functional from chiral interactions, highlighting the limitations of the Hartree-Fock approximation.

Findings

Surface and spin-orbit strength functions agree with Skyrme forces

First-order approximation shows deficiencies in nuclear matter equation of state

Second-order treatment is necessary for improved accuracy

Abstract

An improved density-matrix expansion is used to calculate the nuclear energy density functional from chiral two- and three-nucleon interactions. The two-body interaction comprises long-range one- and two-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition we employ the leading order chiral three-nucleon interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in calculations of nuclear few-body systems. With this input the nuclear energy density functional is derived to first order in the two- and three-nucleon interaction. We find that the strength functions $F_\nabla(\rho)$ and $F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant density range reasonably with results of phenomenological Skyrme forces. However, an improved description requires (at least) the treatment of the two-body interaction to second order. This observation is in line with the deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain in the Hartree-Fock approximation with low-momentum two- and three-nucleon interactions.