Determining the Density Dependence of the Nuclear Symmetry Energy and Its Impacts in Astrophysics with Heavy-Ion Reactions

The density dependence of the nuclear symmetry energy is important for both nuclear physics and astrophysics. Recent data on isospin transport in heavy-ion reactions have allowed us to constrain significantly the symmetry energy at sub-saturation densities. In this talk we discuss promising probes of the symmetry energy at supra-normal densities using heavy-ion reactions induced by high energy radioactive beams. Astrophysical impacts of the constrained symmetry energy on cooling mechanisms and mass-radius correlations of neutron stars as well as the changing rate of the gravitational ``constant G'' will also be discussed.