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

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We extend a recent calculation of the nuclear energy density functional in the systematic framework of chiral perturbation theory by computing the isovector spin-orbit terms: (∇ ρₚ- ∇ ρₙ)·(Jₚ- Jₙ) Gso(kf)+ (Jₚ- Jₙ)² Gⱼ(kf). The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a good equation of state of isospin-symmetric nuclear matter. We find that the parameterfree results for the (density-dependent) strength functions Gso(kf) and Gⱼ(kf) agree fairly well with that of phenomenological Skyrme forces for densities ρ> ρ₀/10. At very low densities a strong variation of the strength functions Gso(kf) and Gⱼ(kf) with density sets in. This has to do with chiral singularities mπ⁻¹ and the presence of two competing small mass scales kf and mπ. The novel density dependencies of Gso(kf) and Gⱼ(kf) as predicted by our parameterfree (leading order) calculation should be examined in nuclear structure calculations.