Chiral approach to nuclear matter: Role of explicit short-range NN-terms
Physik Department T39, Technische Universität München, D-85747, Garching, Germany
2 ECT*, I-38050, Villazzano (Trento), Italy
* e-mail: firstname.lastname@example.org
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 are introduced to regularize the (linear) divergences of some three-loop in-medium diagrams. The equation of state of pure neutron matter, , can be reproduced very well up to quite high neutron densities of 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 MeV we find that any possible equilibrium density lies below . The additional constraint from the neutron matter equation of state leads however to a somewhat too low saturation density of . 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 . This property keeps the critical temperature of the liquid-gas phase transition at somewhat too high values MeV. The downward bending of the asymmetry energy A(k f ) above nuclear-matter saturation density is a generic feature of theapproximation to fourth order. We furthermore investigate the effects of the NN-contact interaction on the -term in the nuclear energy density functional . 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.
© Società Italiana di Fisica and Springer-Verlag, 2004