Chiral approach to nuclear matter: Role of explicit short-range NN-terms

We extend a recent chiral approach to nuclear matter by including the most general (momentum-independent) NN-contact interaction. Iterating this two-parameter contact vertex with itself and with one-pion exchange the emerging energy per particle exhausts all terms possible up to and including fourth order in the small momentum expansion. Two (isospin-dependent) cut-offs Λ_0,1 are introduced to regularize the (linear) divergences of some three-loop in-medium diagrams. The equation of state of pure neutron matter, Ē_n(k_n), can be reproduced very well up to quite high neutron densities of ρ_n = 0.5 fm^-3 by adjusting the strength of a repulsive nn-contact interaction. Binding and saturation of isospin-symmetric nuclear matter is a generic feature of our perturbative calculation. Fixing the maximum binding energy per particle to -Ē(k_f0) = 15.3 MeV we find that any possible equilibrium density ρ₀ lies below ρ₀^max = 0.191 fm^-3. The additional constraint from the neutron matter equation of state leads however to a somewhat too low saturation density of ρ ₀ = 0.134 fm^-3. We also investigate the effects of the NN-contact interaction on the complex single-particle potential U(p, k _f) + i W(p, k_f). We find that the effective nucleon mass at the Fermi surface is bounded from below by M*(k_f0) ≥ 1.4M. This property keeps the critical temperature of the liquid-gas phase transition at somewhat too high values T_c ≥ 21 MeV. The downward bending of the asymmetry energy A(k_f) above nuclear-matter saturation density is a generic feature of the approximation to fourth order. We furthermore investigate the effects of the NN-contact interaction on the (∇^→ρ)²-term in the nuclear energy density functional Ε[ρ, τ]. Altogether, there is within this complete fourth-order calculation no "magic" set of adjustable short-range parameters with which one could reproduce simultaneously and accurately all semi-empirical properties of nuclear matter. In particular, the conditions for a good neutron matter equation of state and for good single-particle properties are mutually exclusive.