Nuclear mean field from chiral pion-nucleon dynamics

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 nonmonotonic and can be translated into a mean effective nucleon mass of M̄* ≃ 0.8M. 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.