The density dependence of the symmetry energy in the equation of state of isospin asymmetric nuclear matter is studied using the isoscaling of the fragment yields and the antisymmetrized molecular dynamic calculation. It is observed that the experimental data at low densities are consistent with the form of symmetry energy, Esym ≈ 31.6 (ρ/ρ•) 0.69 , in close agreement with those predicted by the results of variational many-body calculation. A comparison of the present result with those reported recently using the NSCL-MSU data suggests that the heavy ion studies favor a dependence of the form, Esym ≈ 31.6 (ρ/ρ•) γ , where γ = 0.6 -1.05. This constrains the form of the density dependence of the symmetry energy at higher densities, ruling out an extremely " stiff " and " soft " dependences. PACS numbers: 26.60.+c, 25.70.Pq, 25.70.Mn, The Equation Of State (EOS) of isospin asymmetric (N = Z) nuclear matter is a fundamental quantity that determines the properties of systems as small and light as an atomic nucleus, and as large and heavy as a neutron star [1,2,3]. The key ingredient in the EOS of asymmetric nuclear matter is the density dependence of the symmetry energy. Theoretical studies [4,5,6,7,8] based on microscopic many-body calculations and phenomenological approaches predict various different forms of the density dependence of the symmetry energy. In general, two different forms have been identified [9]. One, where the symmetry energy increases monotonically with increasing density (" stiff " dependence) and the other, where the symmetry energy increases initially up to normal nuclear density and then decreases at higher densities (" soft " dependence).Determining the exact form of the density dependence of the symmetry energy is important for studying the structure of neutron-rich nuclei [10,11,12,13], and studies relating to astrophysical origin, such as the structure of neutron stars and the dynamics of supernova collapse [14,15,16,17,18,19]. For example, a " stiff " density dependence of the symmetry energy is predicted to lead to a large neutron skin thickness compared to a " soft " dependence [11,13,20,21]. Similarly, a " stiff " dependence of the symmetry energy can result in rapid cooling of a neutron star, and a larger neutron star radius, compared to a soft density dependence [22,23].In a heavy ion reaction, the dynamics of the collision between two heavy nuclei is also sensitive to the density dependence of the symmetry energy [24,25]. One can therefore carry out laboratory-based experiments to constrain this dependence. Recently [26], the fragment yields from heavy ion collisions simulated within the Antisymmetrized Molecular Dynamics (AMD) calculation were reported to follow a scaling behavior of the type,where the parameters α and β are related to the neutronproton content of the fragmenting source, and Y 1 and Y 2 are the yields from two different reactions. A linear relation between the isoscaling parameter α, and the difference in the isospin asymmetry (Z/A) 2 of the fragments, with apprecia...

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The fragment yield ratios were investigated in the fission of 238,233 U targets induced by 14 MeV neutrons. The isoscaling behavior was typically observed for the isotopic chains of fragments ranging from the proton-rich to the most neutron-rich ones. The observed high sensitivity of neutronrich heavy fragments to the target neutron content suggests fission as a source of neutron-rich heavy nuclei for present and future rare ion beam facilities, allowing studies of nuclear properties towards the neutron drip-line and investigations of the conditions for nucleosynthesis of heavy nuclei. The breakdowns of the isoscaling behavior around N=62 and N=80 manifest the effect of two shell closures on the dynamics of scission. The shell closure around N=64 can be explained by the deformed shell. The investigation of isoscaling in the spontaneous fission of 248,244 Cm further supports such conclusion. The Z-dependence of the isoscaling parameter exhibits a structure which can be possibly related to details of scission dynamics. The fission isoscaling studies can be a suitable tool for the investigation of possible new pathways to synthesize still heavier nuclei.

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