Nuclear mean field from chiral pion-nucleon dynamics

Abstract

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent single particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of $U(0,k_{f0}) = -53.2 $MeV at saturation density. The momentum dependence of the real part of the single particle potential $U(p,k_{f0})$ is non-monotonic and can be translated into a mean effective nucleon mass of $\bar M^* \simeq 0.8 M$. The imaginary part of the single particle potential $W(p,k_f)$ is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as $W(0,k_{f0})=29.7 $MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.