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

The relativistic mean-field plus random phase and quasiparticle random phase approximation 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 response of ⁹⁰Zr, ¹¹⁶Sn, ¹⁴⁴Sm, the isoscalar monopole and isovector dipoles response of ²⁰⁸Pb, and also the differences between the neutron and proton radii for ²⁰⁸Pb and several Sn isotopes. The comparison of the calculated excitation energies with the experimental data on the giant monopole resonances restricts the nuclear matter compression modulus of structure models based on the relativistic mean-field approximation to Kₙₘ≈250--270MeV. The isovector giant dipole resonance in ²⁰⁸Pb and the available data on differences between the neutron and proton radii limit the range of the nuclear matter symmetry energy at saturation (volume asymmetry) of these effective interactions to 32MeV<~a₄<~36MeV.