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: [Formula Presented] 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 parameter-free results for the (density-dependent) strength functions [Formula Presented] and [Formula Presented] agree fairly well with that of phenomenological Skyrme forces for densities [Formula Presented] At very low densities, a strong variation of the strength functions [Formula Presented] and [Formula Presented] with density sets in. This has to do with chiral singularities [Formula Presented] and the presence of two competing small mass scales [Formula Presented] and [Formula Presented] The novel density dependencies of [Formula Presented] and [Formula Presented] as predicted by our parameter-free (leading order) calculation, should be examined in nuclear structure calculations.