Nuclear energy density functional from chiral pion-nucleon dynamics

We calculate the nuclear energy density functional relevant for N=Z even-even nuclei in the systematic framework of chiral perturbation theory. The calculation includes the onepion 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 very good equation of state of isospin symmetric nuclear matter. We find that in the region below nuclear matter saturation density the effective nucleon mass M̃(ρ) deviates by at most 15% from its free space value M , with 0.89M < M̃(ρ) < M for ρ < 0.11 fm and M̃(ρ) > M for higher densities. The parameterfree strength of the (~ ∇ρ)2-term, F∇(kf ), is at saturation density comparable to that of phenomenological Skyrme forces. The magnitude of FJ (kf ) accompanying the squared spin-orbit density ~ J 2 comes out somewhat larger. The strength of the nuclear spin-orbit interaction, Fso(kf ), as given by iterated one-pion exchange is about half as large as the corresponding empirical value, however, with the wrong negative sign. The novel density dependencies of M̃(ρ) and F∇,so,J(kf ) as predicted by our parameterfree calculation should be examined in nuclear structure calculations (after introducing an additional short range spin-orbit contribution constant in density). PACS: 12.38.Bx, 21.30.Fe, 21.60.-n, 31.15.Ew