Symmetry energy effects on fusion cross sections

We investigate the reaction path followed by heavy ion collisions with exotic nuclear beams at low energies. We focus on the interplay between reaction mechanisms, fusion vs. breakup (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, 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, nicely allows us to extract the fusion probability at relatively early times, when the transport results are reliable. Fusion probabilities for reactions induced by Sn-132 on Ni-64,Ni-58 targets at 10 A MeV 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 breakup events, depending on the stiffnsess of the symmetry term just below saturation.