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

Abstract

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: $(vec nabla rho_p- vec nabla rho_n)^2 G_d(rho)_s16 (vec nabla rho_p- vec nabla rho_n)cdot(vec J_p-vec J_n) G_{so(rho)_s16(vec J_p-vec J_n)^2 G_J(rho)$ pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1pi$-exchange, iterated $1pi$-exchange, and irreducible $2pi$-exchange with intermediate $Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(rho)$, $G_{so}(rho)$ and $G_J(rho)$ 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.