The symmetry energy contribution to the nuclear equation of state impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics, with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and on its density dependence at and somewhat below normal nuclear matter density. Even though some of these constraints have been derived from properties of nuclei while others have been derived from the nuclear response to electroweak and hadronic probes, within experimental uncertainties-they are consistent with each other. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope parameter. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how contributions of three-body forces, which are essential ingredients in neutron matter models, can be determined.

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 disappearance of collective flow in nucleus-nucleus collisions occurs at an incident energy (^bai) where the attraxitive scattering dominant at low energies balances the repulsive scattering dominant at high energies. We have performed the first systematic study of the entrance-channel mass dependence of the disappearance of flow and hence -Ebai-The new data presented for the C-j-C, Ne-hAl, Ar+Sc, and Kr+Nb systems show that JE^bai scales as A~^^^ where A is the mass of the combined system. Boltzmann-Uehling-Uehlenbeck model calculations show trends which are in qualitative agreement with these new results.

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...