This contribution reviews the present status on the available constraints to the nuclear equation of state (EoS) around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. It concentrates on predictions based on self-consistent mean-field calculations, which can be considered as an approximate realization of an exact energy density functional (EDF). EDFs are derived from effective interactions commonly fitted to nuclear masses, charge radii and, in many cases, also to pseudo-data such as nuclear matter properties. Although in a model dependent way, EDFs constitute nowadays a unique tool to reliably and consistently access bulk ground state and collective excited state properties of atomic nuclei along the nuclear chart as well as the EoS. For comparison, some emphasis is also given to the results obtained with the so called {\it ab initio} approaches that aim at describing the nuclear EoS based on interactions fitted to few-body data only. Bridging the existent gap between these two frameworks will be essential since it may allow to improve our understanding on the diverse phenomenology observed in nuclei. Examples on observations from astrophysical objects and processes sensitive to the nuclear EoS are also briefly discussed. As the main conclusion, the isospin dependence of the nuclear EoS around saturation density and, to a lesser extent, the nuclear matter incompressibility remain to be accurately determined. Experimental and theoretical efforts in finding and measuring observables specially sensitive to the EoS properties are of paramount importance, not only for low-energy nuclear physics but also for nuclear astrophysics applications.

Nuclear Equation of State from ground and collective excited state properties of nuclei

We have investigated the isoscalar giant resonances in the Sn isotopes using inelastic scattering of 386-MeV alpha particles at extremely forward angles, including 0 degrees. We have obtained completely "background-free" inelastic-scattering spectra for the Sn isotopes over the angular range 0 degrees-9 degrees and up to an excitation energy of 31.5 MeV. The strength distributions for various multipoles were extracted by a multipole decomposition analysis based on the expected angular distributions of the respective multipoles. We find that the centroid energies of the isoscalar giant monopole resonance (ISGMR) in the Sn isotopes are significantly lower than the theoretical predictions. In addition, based on the ISGMR results, a value of K(tau) = -550 +/- 100 MeV is obtained for the asymmetry term in the nuclear incompressibility. Constraints on interactions employed in nuclear structure calculations are discussed on the basis of the experimentally obtained values for K(infinity) and K(tau).

Isoscalar giant resonances in the Sn nuclei and implications for the asymmetry term in the nuclear-matter incompressibility

Nuclear equation of state from ground and collective excited state properties of nuclei

The isoscalar giant dipole resonance (ISGDR) has been investigated in 208Pb using inelastic scattering of 400 MeV alpha particles at forward angles, including 0deg. Using the superior capabilities of the Grand Raiden spectrometer, it has been possible to obtain spectra devoid of any "instrumental" background. The ISGDR strength distribution has been extracted from a multipole-composition of the observed spectra. The implication of these results on the experimental value of nuclear incompressibility are discussed.

The Isoscalar Giant Dipole Resonance in 208Pb and the Nuclear incompressibility

The isoscalar giant dipole resonance (ISGDR) has been investigated in 208Pb using inelastic scattering of 400 MeV α particles at extremely forward angles, including 0°. Using the superior capabilities of the Grand Raiden spectrometer, it has been possible to obtain inelastic spectra devoid of any “instrumental” background. The ISGDR strength distribution has been extracted from a multipole-decomposition of the observed spectra. The implications of these results on the experimental value of nuclear incompressibility are discussed.

The isoscalar giant dipole resonance in 208Pb and the nuclear incompressibility

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The Isoscalar Giant Dipole Resonance in 208Pb and the Nuclear incompressibility

The isoscalar giant dipole resonance in 208Pb and the nuclear incompressibility