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 . The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f0(kf), , g0(kf) and . 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 , 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 Δ(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 ) the spin-dependent Fermi-liquid parameters g0(kf0) and 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 . 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 is much less affected. These features are not changed by the inclusion of the chiral πNΔ-dynamics. The l=1 tensor Fermi-liquid parameters h1(kf) and follow a similar pattern.