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

Abstract

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 , ρ 0 = 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 , k f 0 ) is substantially improved by the inclusion of the chiral π N Δ -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 ∗ ( k f 0 ) = 0.88 M . As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value T c ≃ 15 MeV . In this work we continue the complex-valued single-particle potential U ( p , k f ) + i W ( p , k f ) into the region above the Fermi surface p > k f . The effects of 2 π-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 ˜ ∗ ( ρ 0 ) = 0.64 M . Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral π N Δ -dynamics. Instead of bending downward above ρ 0 as in previous calculations, the energy per particle of pure neutron matter E ¯ n ( k n ) and the asymmetry energy A ( k f ) now grow monotonically with density. In the density regime ρ = 2 ρ n < 0.2 fm −3 relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.