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: f 0 ( k f ) , f 0 ′ ( k f ) , g 0 ( k f ) and g 0 ′ ( k f ) . In the approximation to 1 π-exchange and iterated 1 π-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin–isospin interaction strength of g 0 ′ ( 2 m π ) = 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 2 π-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 f 2 ) the spin-dependent Fermi-liquid parameters g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) 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 g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) . 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 1 π-exchange tensor interaction we find from the 2 π-exchange corrections almost a doubling of the isoscalar tensor strength h 0 ( 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 πNΔ-dynamics. The l = 1 tensor Fermi-liquid parameters h 1 ( k f ) and h 1 ′ ( k f ) follow a similar pattern.
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