Spin-asymmetry energy of nuclear matter

We calculate the density-dependent spin-asymmetry energy S(kf ) of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to S(kf ) originate from one-pion exchange, iterated one-pion exchange, and (irreducible) two-pion exchange with no, single, and double virtual ∆-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(kf0) < 0. The inclusion of the chiral πN∆-dynamics guarantees the spin-stability of nuclear matter. The corresponding spin-asymmetry energy S(kf ) stays positive within a wide range of an undetermined short-range parameter S5 (which we also estimate from realistic NN-potentials). Our results reemphasize the important role played by two-pion exchange with virtual ∆-isobar excitation for the nuclear matter many-body problem. Its explicit inclusion is essential in order to obtain good bulk and single-particle properties. PACS: 12.38.Bx, 21.30.-x, 21.65.+f In recent years a novel approach to the nuclear matter problem based on effective field theory (in particular chiral perturbation theory) has emerged. The key element there is a separation of longand short-distance dynamics and an ordering scheme in powers of small momenta. At nuclear matter saturation density ρ0 ≃ 0.16 fm the Fermi momentum kf0 and the pion mass mπ are comparable scales (kf0 ≃ 2mπ), and therefore pions must be included as explicit degrees of freedom in the description of the nuclear many-body dynamics. The contributions to the energy per particle Ē(kf) of isospin-symmetric (spin-saturated) nuclear matter as they originate from chiral pion-nucleon dynamics have been computed up to three-loop order in refs.[1, 2]. Both calculations are able to reproduce correctly the empirical saturation point of nuclear matter by adjusting one single parameter (either a coupling g0 + g1 ≃ 3.23 [1] or a cutoff Λ ≃ 0.65GeV [2]) related to unresolved short-distance dynamics. The novel mechanism for saturation in these approaches is a repulsive contribution to the energy per particle Ē(kf) generated by Pauli-blocking in second order (iterated) one-pion exchange. As outlined in section 2.5 of ref.[2] this mechanism becomes particularly transparent by taking the chiral limit mπ = 0. In that case the interaction contributions to Ē(kf) are completely summarized by an attractive k f -term and a repulsive k 4 f -term where the parameter-free prediction for the coefficient of the latter is very close to the one extracted from a realistic nuclear matter equation of state. In a recent work [3] we have extended the chiral approach to nuclear matter by including systematically the effects from two-pion exchange with single and double virtual ∆(1232)-isobar excitation. The physical motivation for such an extension is threefold. First, the spin-isospin3/2 ∆(1232)-resonance is the most prominent feature of low-energy πN -scattering. Secondly, it The cut-off scale Λ serves the purpose to tune the strength of an attractive zero-range NN-contact interaction.