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Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: $(\vec \nabla ρ_p- \vec \nabla ρ_n)^2 G_d(ρ)+ (\vec \nabla ρ_p- \vec \nabla ρ_n)\cdot(\vec J_p-\vec J_n) G_{so(ρ)+(\vec J_p-\vec J_n)^2 G_J(ρ)$ pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(ρ)$, $G_{so}(ρ)$ and $G_J(ρ)$ which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.