Collisions involving112 Sn and 124 Sn nuclei have been simulated with the Improved Quantum Molecular Dynamics transport model. The results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra. By comparing these data to calculations performed over a range of symmetry energies at saturation density and different representations of the density dependence of the symmetry energy, constraints on the density dependence of the symmetry energy at sub-normal density are obtained. Results from present work are compared to constraints put forward in other recent analyses.

A three parameter scaling relationship between isotopic distributions for elements with Z< or =8 has been observed. This allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed isoscaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation, and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.