Stopping and Isospin Equilibration in Heavy Ion Collisions

We investigate the density behaviour of the symmetry energy with respect to isospin equilibration in the combined systems $Ru(Zr)+Zr(Ru)$ at relativistic energies of 0.4 and $1.528 AGeV$. The study is performed within a relativistic framework and the contribution of the iso-vector, scalar $\delta$ field to the symmetry energy and the isospin dynamics is particularly explored. We find that the isospin mixing depends on the symmetry energy and a stiff behaviour leads to more transparency. The results are also nicely sensitive to the "fine structure" of the symmetry energy, i.e. to the covariant properties of the isovector meson fields. The isospin tracing appears much less dependent on the in-medium neutron-proton cross-sections ($\sigma_{np}$) and this makes such observable very peculiar for the study of the isovector part of the nuclear equation of state. Within such a framework, comparisons with experiments support the introduction of the $\delta$ meson in the description of the iso-vector equation of state.