Heavy-ion reactions induced by neutron-rich nuclei provide a unique means toinvestigate the equation of state of isospin-asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy. Inparticular, recent analyses of the isospin diffusion data in heavy-ionreactions have already put a stringent constraint on the nuclear symmetryenergy around the nuclear matter saturation density. We review this excitingresult and discuss its implications on nuclear effective interactions and theneutron skin thickness of heavy nuclei. In addition, we also review thetheoretical progress on probing the high density behaviors of the nuclearsymmetry energy in heavy-ion reactions induced by high energy radioactivebeams.
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