THE DENSITY DEPENDENCE OF THE NUCLEAR SYMMETRY ENERGY IN HEAVY-ION COLLISIONS

The density dependence of the nuclear symmetry energy is of great interest over a broad range of densities from very dilute matter in supernovae up to very dense neutron stars. However, more information and stronger constraints on the symmetry energy below and above saturation density are needed. An important way to investigate the symmetry energy is to perform heavy-ion collisions. In this contribution, we give an overview of the methods to extract the symmetry energy with transport theories. We discuss the role of fluctuations in transport approaches to describe the production of light clusters and intermediate mass fragments. We discuss, in more detail, three representative examples: the equilibration of the isospin in peripheral collisions between nuclei of different asymmetry, the pre-equilibrium emission of light clusters in the compression stage of a collision, and the isospin flow at high density. We summarize with the discussion of presently known constraints and open questions about the symmetry energy with emphasizing the need of more data from heavy-ion collisions and from astrophysical observations.