Quasi-particle interaction in nuclear matter from chiral pion–nucleon dynamics Original Research Article

Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface View the MathML source. The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f0(kf), View the MathML source, g0(kf) and View the MathML source. 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 View the MathML source, 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 View the MathML source) the spin-dependent Fermi-liquid parameters g0(kf0) and View the MathML source 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 View the MathML source. 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 View the MathML source 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 View the MathML source follow a similar pattern.