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

Abstract

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. The equation of state of pure neutron matter, ${\bar{E}}_n(k_n)$, can be reproduced very well up to quite high neutron densities of ${\rho }_n=0.5\text{fmd}$ 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 $-\bar{E}(k_{f0})=15.3$MeV we find that any possible equilibrium density ${\rho }_0$ lies below ${\rho }_0^{\max }=0.191\text{fmd}$. The additional constraint from the neutron matter equation of state leads however to a somewhat too low saturation density of ${\rho }_0=0.134\text{fmd}$. We also investigate the effects of the NN-contact interaction on the complex single-particle potential $U(p,k_f)+iW(p,k_f)$. We find that the effective nucleon mass at the Fermi-surface is bounded from below by $M^{\ast }(k_{f0})\ge 1.4M$. This property keeps the critical temperature of the liquid-gas phase transition at somewhat too high values $T_c\ge 21$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. 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.

Comments: 24 pages, 12 figures, accepted for publication in: Eur. Phys. J. A