  We investigate the reaction path followed by Heavy Ion Collisions with exotic
nuclear beams at low energies. We will focus on the interplay between reaction
mechanisms, fusion vs. break-up (fast-fission, deep-inelastic), that in exotic
systems is expected to be influenced by the symmetry energy term at densities
around the normal value. The evolution of the system is described by a
Stochastic Mean Field transport equation (SMF), where two parametrizations 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. The 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. Finally 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.
