Symmetry Energy Effects in Low Energy Heavy Ion Collisions with Exotic Beams

We investigate the reaction path followed by Heavy Ion Collisions with exotic nuclear beams at low energies. The evolution of the system is described by a Stochastic Mean Field transport equation (SMF), where two parameterizations for the density dependence of symmetry energy (Asysoft and Asystiff) are implemented, allowing one to explore the sensitivity of the results to this ingredient of the nuclear interaction. We report the properties of the prompt dipole radiation, produced via a collective bremsstrahlung mechanism, in fusion reactions with exotic beams. We show that the gamma yield is sensitive to the density dependence of the symmetry energy below/around saturation. Moreover we find that the angular distribution of the emitted photons from such fast collective mode can represent a sensitive probe of its excitation mechanism and of fusion dynamics in the entrance channel. We will focus on the interplay between reaction mechanisms, fusion vs. break-up, that in exotic systems is expected to be influenced by the symmetry energy term at densities around the normal value. The new method described here, based on the event by event evolution of phase space Quadrupole collective modes will nicely allow to extract the fusion probability at relatively early times, when the transport results are reliable. Fusion probabilities for reactions induced by 132Sn on 64,58Ni targets at 10 AMeV are evaluated. We obtain larger fusion cross sections for the more n-rich composite system, and, for a given reaction, in the Asysoft choice. A collective charge equilibration mechanism (the Dynamical Dipole) is revealed in both fusion and break-up events, depending on the stiffness of the symmetry term just below saturation. Finally we investigate the effect of the mass asymmetry in the entrance channel for systems with the same overall isospin content and similar initial charge asymmetry. As expected we find reduced fusion probabilities for the more mass symmetric case, while the DDR strength appears not much affected. This is a nice confirmation of the prompt nature of such collective isovector mode.