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

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