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 p^→1,2 = k f. The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f₀(k f), f′₀(k f), g₀(k f) and g′₀(k f). 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 (2m_π) = 1.14 fm², 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 k_f²) the spin-dependent Fermi-liquid parameters g₀(k f₀) and g′₀(k f₀) come out far too large. Estimates of these short-distance parameters from realistic N N-potentials go in the right direction, but sizeable enhancement factors are still needed to reproduce the empirical values of g₀(k f₀) 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(k f), whereas the isovector tensor strength h′₀(k f) is much less affected. These features are not changed by the inclusion of the chiral π N Δ-dynamics. The l = 1 tensor Fermi-liquid parameters h₁(k f) and h′₁(k f) follow a similar pattern.