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 isoscaling parameter $\alpha$, from the fragments produced in the multifragmentation of $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at 30, 40 and 47 MeV/nucleon, was compared with that predicted by the antisymmetrized molecular dynamic (AMD) calculation based on two different nucleon-nucleon effective forces, namely the Gogny and Gogny-AS interaction. The results show that the data agrees better with the choice of Gogny-AS effective interaction, resulting in a symmetry energy of $\sim$ 18-20 MeV. The observed value indicate that the fragments are formed at a reduced density of $\sim$ 0.08 fm$^{-3}$.Comment: 5 pages, 5 figures, Accepted for publication in Phys. Rev. C (Rapid Communication

The density dependence of the symmetry energy in the equation of state of isospin asymmetric nuclear matter is of significant importance for studying the structure of systems as diverse as the neutron-rich nuclei and the neutron stars. A number of reactions using the dynamical and the statistical models of multifragmentation, and the experimental isoscaling observable, is studied to extract information on the density dependence of the symmetry energy. It is observed that the dynamical and the statistical model calculations give consistent results assuming the sequential decay effect in dynamical model to be small. A comparison with several other independent studies is also made to obtain important constraint on the form of the density dependence of the symmetry energy. The comparison rules out an extremely " stiff " and " soft " form of the density dependence of the symmetry energy with important implications for astrophysical and nuclear physics studies.

The evolution of the symmetry energy coefficient of the binding energy of hot fragments with increasing excitation is explored in multifragmentation processes following heavy-ion collisions below the Fermi energy. In this work, high-resolution mass spectrometric data on isotopic distributions of projectile-like fragments are systematically compared to calculations involving the Statistical Multifragmentation Model (SMM). Within the SMM picture, the present study suggests a gradual decrease of the symmetry energy coefficient of the hot primary fragments from 25 MeV at the compound nucleus regime towards 15 MeV in the multifragmentation regime. The isotopic distributions of the hot primary fragments are found to be very wide and extend towards the neutron drip-line. These findings are expected to have important implications to the modeling of the composition and the evolution of hot and dense astrophysical environments, such as those of core-collapse supernova.PACS numbers: 25.70.Hi,25.70.Lm,26.30.+k Nuclear multifragmentation is one of the most interesting phenomena in nuclear physics as it holds promise for understanding nuclear matter properties at the extreme conditions of high excitation energy and large isospin (N/Z) asymmetry [1,2,3,4,5]. The latter, in particular, plays a profound role in the dynamics of various astrophysical environments [6,7,8,9]. It is well established (e.g. [4]) that nuclear systems with relatively low excitation energy (E * /A ≤ 2 MeV) form the traditional compound nucleus, whereas at higher excitation energy, the hot nuclear system expands and, subsequently, disassembles into an ensemble of hot primary fragments. This extremely complicated process, namely the multifragmentation, occurs on a timescale of 100 fm/c (3.3×10 −22 sec) during which the system can sample a large number of configurations. For this reason, statistical calculations (e.g., [10,11]) have been very successful in describing this process.Recently, a remarkable similarity has been pointed out between the thermodynamic conditions (temperature, density, isospin asymmetry N/Z) reached in nuclear multifragmentation and the collapse/explosion of massive stars [12,13,14]. This observation opens up the possibility of applying well-established models of nuclear reactions to describe matter distribution and evolution during supernova explosions [12]. In addition, statistical calculations suggest that in multifragmentation [12,15] and in hot astrophysical environments (e.g. supernova) [12,16], the ensemble of primary fragments includes neutron-rich nuclei towards or beyond the neutron drip-line.The primary fragments are expected to be hot (with excitation energies approaching 2-3 MeV/nucleon [17]) and, initially, in close proximity to neighboring fragments or nucleons. These conditions render their properties, e.g. binding energy, different from those of cold (ground state) isolated nuclei. In particular, recent studies [18,19,20,21] give evidence for a significant decrease of the symmetry energy of hot primary fragments. ...