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 ${}^{90}\mathrm{Zr},$ ${}^{116}\mathrm{Sn},$ ${}^{144}\mathrm{Sm},$ the isoscalar monopole and isovector dipoles response of ${}^{208}\mathrm{Pb},$ and also the differences between the neutron and proton radii for ${}^{208}\mathrm{Pb}$ 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 ${K}_{\mathrm{nm}}\ensuremath{\approx}250--270\mathrm{MeV}.$ The isovector giant dipole resonance in ${}^{208}\mathrm{Pb}$ 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 $32\mathrm{MeV}<~{a}_{4}<~36\mathrm{MeV}.$

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