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

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.

16 pages, 12 figures, submitted to Eur. Phys. J. A

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• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• The Skyrme Interaction in finite nuclei and nuclear matter
• Subleading contributions to the chiral three-nucleon force I: long-range terms
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• Low Momentum Nucleon-Nucleon Interactions and Shell-Model Calculations
• Density Matrix Expansion for Low-Momentum Interactions

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