Transport of Isospin Degree of Freedom in Heavy Ion Reactions and the Constraint of Symmetry Energy

Heavy ion reactions provide an effective tool to study the nuclear equation of state (EOS) in terristial laborartory. When the number of neutrons differs largely with the number of protons in a nuclear system or nuclei, the main contribution to the nuclear EOS comes from the symmetry energy term. The nuclear symmetry energy, reflecting the isovector sector of the nucleon-nucleon potential, is closely relevant to the structural properties of dense object and the merging process in stellar environments, as well as to the exotic properties of nuclei and the location of the board of nuclear chart. However, the density dependence of the nuclear symmetry energy is the most unknown ingredient in the properties of nuclear matter so far. Thus the investigation of nuclear symmetry energy in wide density range becomes the main frontiers in many world-level nuclear laboratories and astrophyics observatories. In this article, we review briefly the experimental progress in this field. Particularly the experimental studies on the transport of the isospin degree of freedom in heavy ion reactions and the constraint of nuclear symmetry energy based on the Heavy Ion Research Facity at Lanzhou (HIRFL) are introduced. It has been shown that the isospin drift process persists to the late stage of the reaction, indicating that the isospin transport time scale may depend on the physics process under investigation. Due to the long-time accumulation of isospin effects, the angular distribution of the isospin concentration of the light particles in a wide range of angle is a sensitive probe of nuclear symmetry energy. With ${S}\!=\!28.3\,\mathrm{M}\mathrm{e}\mathrm{V}$ fixed at saturation point, the slope of the symmetry energy depending on density is contrained in the range of $L\!=\!33\!\sim\!61\,\mathrm{M}\mathrm{e}\mathrm{V}$ at $\mathrm{C}\mathrm{L}\!=\!95$%. Using a Compact Spectrometer for Havy Ion Experiment (CSHINE) with ability to achieve isotopic particle identification and fission event reconstruction, the small angle correlation function of the isotope-resolved light charged particles can be measured to derive the time scale of isospin relaxation in heavy ion reactions at Fermi energies. In the last section of the article, the isovector orientation effect of the polarized deuteron beam scattering off heavy target is introduced, which offers a novel means to constrain the nuclear symmetry energy below saturation density.