Symmetry energy and density

The nuclear equation-of-state is a topic of highest current interest in nuclear structure and reactions as well as in astrophysics. In particular, the equation-of-state of asymmetric matter and the symmetry energy representing the difference between the energy densities of neutron matter and of symmetric nuclear matter are not sufficiently well constrained at present. The density dependence of the symmetry energy is conventionally expressed in the form of the slope parameter L describing the derivative with respect to density of the symmetry energy at saturation. Results deduced from nuclear structure and heavy-ion reaction data are distributed around a mean value L = 60 MeV. Recent studies have more thoroughly investigated the density range that a particular observable is predominantly sensitive to. Two thirds of the saturation density is a value typical for the Information contained in nuclear-structure data. Higher values exceeding saturation have been shown to be probed with meson production and collective flows at incident energies in the range of up to about 1 GeV/nucleon. From the measurement of the elliptic-flow ratio of neutrons with respect to light charged particles in recent experiments at the GSI laboratory, a new more stringent constraint for the symmetry energy at suprasaturation density has been deduced. It confirms, with a considerably smaller uncertainty, the moderately soft to linear density dependence of the symmetry energy previously deduced from the FOPI-LAND data. Future opportunities offered by FAIR will be discussed.