Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation

We extend a recent three-loop calculation of nuclear matter by including the effects from two-pion exchange with single and double virtual Δ(1232)-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, E¯0=−16 MeV, ρ0=0.16 fm−3, can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as K=304 MeV. The real single-particle potential U(p,kf0) is substantially improved by the inclusion of the chiral πNΔ-dynamics: it grows now monotonically with the nucleon momentum p. The effective nucleon mass at the Fermi surface takes on a realistic value of M∗(kf0)=0.88M. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value Tc≃15 MeV. In this work we continue the complex-valued single-particle potential U(p,kf)+iW(p,kf) into the region above the Fermi surface p>kf. The effects of 2π-exchange with virtual Δ-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is M˜∗(ρ0)=0.64M. Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral πNΔ-dynamics. Instead of bending downward above ρ0 as in previous calculations, the energy per particle of pure neutron matter E¯n(kn) and the asymmetry energy A(kf) now grow monotonically with density. In the density regime ρ=2ρn<0.2 fm−3 relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.