The long journey from the giant-monopole resonance to the nuclear-matter incompressibility

Differences in the density dependence of the symmetry energy predicted by nonrelativistic and relativistic models are suggested, at least in part, as the culprit for the discrepancy in the values of the compression modulus of symmetric nuclear matter extracted from the energy of the giant monopole resonance in 208Pb. ``Best-fit'' relativistic models, with stiffer symmetry energies than Skyrme interactions, consistently predict higher compression moduli than nonrelativistic approaches. Relativistic models with compression moduli in the physically acceptable range of K=200-300 MeV are used to compute the distribution of isoscalar monopole strength in 208Pb. When the symmetry energy is artificially softened in one of these models, in an attempt to simulate the symmetry energy of Skyrme interactions, a lower value for the compression modulus is indeed obtained. It is concluded that the proposed measurement of the neutron skin in 208Pb, aimed at constraining the density dependence of the symmetry energy and recently correlated to the structure of neutron stars, will also become instrumental in the determination of the compression modulus of nuclear matter.Comment: 9 pages with 2 (eps) figure

Relativistic Mean Field Model with Generalized Derivative Nucleon-Meson Couplings

The quantum hadrodynamics (QHD) model with minimal nucleon-meson couplings is generalized by introducing couplings of mesons to derivatives of the nucleon field in the Lagrangian density. This approach allows an effective description of a state-dependent in-medium interaction in the mean-field approximation. Various parametrizations for the generalized couplings are developed and applied to infinite nuclear matter. In this approach, scalar and vector self-energies depend on both density and momentum similarly as in the Dirac-Brueckner theory. The Schr\"{o}diger-equivalent optical potential is much less repulsive at high nucleon energies as compared to standard relativistic mean field models and thus agrees better with experimental findings. The derivative couplings in the extended model have significant effects on properties of symmetric nuclear matter and neutron matter.Comment: 35 pages, 1 table, 10 figure