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 ∆-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 contactterm) is spin-isospin stable, since J(kf0) ≃ 24MeV > 0. The inclusion of the chiral πN∆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. PACS: 12.38.Bx, 21.30.-x, 21.65.+f In recent years a novel approach to the nuclear matter problem has emerged. Its key element 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 threeloop order in Refs.[1, 2]. Both calculations are able to reproduce the empirical saturation point of nuclear matter by adjusting one single parameter (either a contact-coupling g0+g1 ≃ 3.23 [1] or a cutoff scale Λ ≃ 0.65GeV [2]) related to unresolved short-distance dynamics. The basic mechanism for saturation in this approach is a repulsive contribution to the energy per particle Ē(kf) generated by Pauli-blocking in second order (iterated) pion-exchange. As outlined in Sec. 2.5 of Ref.[2] this mechanism becomes particularly transparent by taking the chiral limitmπ = 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 2π-exchange with virtual ∆(1232)-isobar excitation. The physical motivation for such an extension is threefold. First, the spin-isospin-3/2 ∆(1232)-resonance Fitting a cutoff scale, as done in Ref.[2], must be viewed as a short-term intermediate step before an eventual full effective field theory calculation. Cutoff independence of physical observables is in fact a primary goal of effective field theory.