Density dependence of the symmetry energy and the equation of state of isospin asymmetric nuclear matter

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, ${\mathrm{E}}_{\mathrm{sym}}\approx 31.6(\rho /{\rho }_{○}){}^{0.69}$, 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, ${\mathrm{E}}_{\mathrm{sym}}\approx 31.6(\rho /{\rho }_{○}){}^{\gamma }$, where $\gamma =0.6-1.05$. This constrains the form of the density dependence of the symmetry energy at higher densities, ruling out an extremely “stiff” and “soft” dependences.

Figure 1

Experimental isoscaling parameter α, as a function of the beam energy. The solid circles are from the Ar+Fe and Ca+Ni reactions. The open triangles are from Fe+Fe and Ni+Ni reactions. The solid stars are from Ar+Ni and Ca+Ni reactions. The open squares are from Fe+Ni and Ni+Ni reactions.

Figure 2

Scaling parameter α, as a function of the difference in fragment asymmetry for 35 MeV/nucleon. The solid and the dotted lines are the AMD calculations for the Gogny and Gogny-AS interactions, respectively [26]. The solid and the hollow, squares, stars, triangles, and circles are from the present work as described in the text. The other symbols corresponds to data taken from [30] (asterisks) and [31] (crosses, diamonds, inverted triangles).

Figure 3

Parametrization of the various forms of the density dependence of the nuclear symmetry energy used in the analysis of the present measurements on isoscaling data and the isospin diffusion measurements of NSCL-MSU [36]. The various curves are as described in the text.