Nuclear energy density functional from chiral pion-nucleon dynamics revisited

Abstract

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. 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. We find that the effective nucleon mass $M^*(rho)$ entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength $F_nabla(rho)$ of the $(vecnabla rho)^2$ surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region $rho_0/2