Spin-asymmetry energy of nuclear matter

Abstract

We calculate the density-dependent spin-asymmetry energy $S(k_f)$ of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $S(k_f)$ 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 truncation to $1π$-exchange and iterated $1π$-exchange terms (which leads already to a good nuclear matter equation of state) is spin-unstable, since $S(k_{f0})<0$. The inclusion of the chiral $πNΔ$-dynamics guarantees the spin-stability of nuclear matter. The corresponding spin-asymmetry energy $S(k_f)$ stays positive within a wide range of an undetermined short-range parameter $S_5$ (which we also estimate from realistic NN-potentials). Our results reemphasize the important role played by two-pion exchange with virtual $Δ$-isobar excitation for the nuclear matter many-body problem. Its explicit inclusion is essential in order to obtain good bulk and single-particle properties.