Chiral dynamics and nuclear matter

Abstract

We calculate the equation of state of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The contributions to the energy per particle E ̄ (k f ) from one- and two-pion exchange diagrams are ordered in powers of the Fermi momentum k f (modulo functions of k f/ m π ). It is demonstrated that, already at order O(k f 4) , two-pion exchange produces realistic nuclear binding. The underlying saturation mechanism is surprisingly simple (in the chiral limit), namely the combination of an attractive k f 3-term and a repulsive k f 4-term. The empirical saturation point and the nuclear compressibility K≃250 MeV are well reproduced at order O(k f 5) with a momentum cut-off of Λ≃0.65 GeV which parameterizes short-range dynamics. No further short-distance terms are required in our calculation of nuclear matter. In the same framework we calculate the density-dependent asymmetry energy and find A 0≃34 MeV at the saturation point, in good agreement with the empirical value. The pure neutron matter equation of state is also in fair qualitative agreement with sophisticated many-body calculations and a resummation result of effective field theory, but only for low neutron densities ρ n<0.25 fm −3.