A microscopic estimate of the nuclear matter compressibility and symmetry energy in relativistic mean-field models

The relativistic mean-field plus RPA calculations, based on effective Lagrangians with density-dependent meson-nucleon vertex functions, are employed in a microscopic analysis of the nuclear matter compressibility and symmetry energy. We compute the isoscalar monopole and the isovector dipole response of $^{208}$Pb, as well as the differences between the neutron and proton radii for $^{208}$Pb and several Sn isotopes. The comparison of the calculated excitation energies with the experimental data on the giant monopole resonance in $^{208}$Pb, restricts the nuclear matter compression modulus of structure models based on the relativistic mean-field approximation to $K_{\rm nm}\approx 250 - 270$ MeV. The isovector giant dipole resonance in $^{208}$Pb, and the available data on differences between neutron and proton radii, limit the range of the nuclear matter symmetry energy at saturation (volume asymmetry) to 32 MeV $\leq a_4 \leq$ 36 MeV.