Spin-isospin stability of nuclear matter

We calculate the density-dependent spin-isospin asymmetry energy J(kf) of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to J(kf) originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual Δ-isobar excitation. We find that the approximation to 1π-exchange and iterated 1π-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contact term) is spin-isospin stable, since J(kf0) 24MeV>0. The inclusion of the chiral πNΔ dynamics, necessary in order to guarantee the spin stability of nuclear matter, keeps this property intact. The corresponding spin-isospin asymmetry energy J(kf) stays positive even for extreme values of an undetermined short-distance parameter J5 (whose possible range we estimate from realistic NN potentials). The largest positive contribution to J(kf) (a term linear in density) comes from a two-body contact term with its strength fitted to the empirical nuclear matter saturation point.