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

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) 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 m −1 π 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. PACS: 12.38.Bx, 21.30.Fe, 21.60.-n, 31.15.Ew Among the various phenomenological interactions that have been used extensively in the description of nuclei, the Skyrme force [1] has gained much popularity because of its analytical simplicity and its ability to reproduce nuclear properties over the whole periodic table within the self-consistent Hartree-Fock approximation. Several Skyrme parameterizations have been tailored to account for single-particle spectra [2], giant monopole resonances [3] or fission barriers of heavy nuclei [4]. Recently, a new Skyrme force which also reproduces the equation of state of pure neutron matter up to neutron star densities, ρn ≃ 1.5 fm, has been proposed in ref.[5] for the study of nuclei far from stability. A microscopic interpretation of the various parameters entering the effective Skyrme forces is generally put aside. Sometimes the energy density functional is just parameterized without reference to any effective (zero-range) NNinteraction [6]. Another widely and successfully used approach to nuclear structure calculations are relativistic mean-field models [7, 8]. In these models the nucleus is described as a collection of independent Dirac-particles moving in self-consistently generated scalar and vector mean-fields. The footprints of relativity become visible through the large nuclear spin-orbit interaction which emerges in that framework naturally from the interplay of the two strong and counteracting (scalar and vector) mean-fields. The corresponding many-body calculations are usually carried out in the Hartree approximation, ignoring the negative-energy Dirac-sea. For a recent review on self-consistent mean-field models for nuclear structure, see ref.[6]. In that article the relationship between the relativistic mean-field models and the Skyrme phenomenology is also discussed.