Quasi-particle interaction in nuclear matter from chiral pion-nucleon dynamics

Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface |~ p1,2| = kf . The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f0(kf ), f ′ 0(kf ), g0(kf ) and g ′ 0(kf ). In the approximation to 1π-exchange and iterated 1π-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin-isospin interaction strength of g 0(2mπ) = 1.14 fm 2, compatible with existing empirical values. The consistency relations to the nuclear matter compressibility K and the spin/isospin asymmetry energies serve as a check on our perturbative calculation. In the next step we include systematically the contributions from 2π-exchange with virtual ∆(1232)-isobar excitation which have been found important for good single-particle properties and spin-stability of nuclear matter. Without any additional short-distance terms (contributing proportional to k2 f ) the spin-dependent Fermi-liquid parameters g0(kf0) and g 0(kf0) come out far too large. Estimates of these short-distance parameters from realistic NN-potentials go in the right direction, but sizeable enhancement factors are still needed to reproduce the empirical values of g0(kf0) and g ′ 0(kf0). This points towards the importance of higher order iterations subsumed in the induced interaction. We consider also the tensor part of the quasi-nucleon interaction at the Fermi surface. In comparison to the leading 1π-exchange tensor interaction we find from the 2π-exchange corrections almost a doubling of the isoscalar tensor strength h0(kf ), whereas the isovector tensor strength h′0(kf ) is much less affected. These features are not changed by the inclusion of the chiral πN∆-dynamics. The l = 1 tensor Fermi-liquid parameters h1(kf ) and h ′ 1(kf ) follow a similar pattern. PACS: 12.38.Bx, 21.30.Fe, 21.65.+f, 24.10.Cn Keyword: Quasi-particle interaction in nuclear matter; Isotropic Fermi-liquid parameters; Tensor interaction; Oneand two-pion exchange with medium modifications