Symmetry energy and the isospin dependent equation of state

The isoscaling parameter $\alpha$, from the fragments produced in the multifragmentation of ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, ${}^{58}\mathrm{Fe}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Fe}+{}^{58}\mathrm{Fe}$ reactions at 30, 40 and $47\mathrm{MeV}∕\text{nucleon}$, was compared with that predicted by the antisymmetrized molecular dynamic calculation based on two different nucleon-nucleon effective forces, namely the Gogny and Gogny-AS interaction. The results show that the data agree better with the choice of Gogny-AS effective interaction, resulting in a symmetry energy of $\sim 18–20\mathrm{MeV}$. The observed value indicates that the fragments are formed at a reduced density of $\sim 0.08{\mathrm{fm}}^{-3}$.

Figure 1

Yield ratios of the fragments from $\mathrm{Fe}+\mathrm{Fe}$ and $\mathrm{Ni}+\mathrm{Ni}$ reactions (top), and $\mathrm{Fe}+\mathrm{Ni}$ and $\mathrm{Ni}+\mathrm{Ni}$ reactions (bottom), as a function of neutron number $N$ for the $30\mathrm{MeV}∕\text{nucleon}$ beam energy. The solid lines are the exponential fits to the data. The fit parameter $\alpha$, is shown in the top left corner of each panel.

Figure 2

Scaling parameter $\alpha$, obtained from a fit similar to those shown in Fig. 1, as a function of bombarding energy. The solid lines are exponential fit to the data.

Figure 3

AMD calculations of the asymmetry ${(Z∕A)}^2$, of the fragments at $t=300\mathrm{fm}∕c$ for the Gogny (solid line and closed squares) and Gogny-As (dotted line and open squares) interactions at $35\mathrm{MeV}∕\text{nucleon}$. The calculations are taken from Ref. 15 for the systems shown by squares. The lines are linear fit to the square. Circles are the interpolated values for the systems studied in this work.

Figure 4

Scaling parameter $\alpha$, as a function of the asymmetry of the fragments. The solid and the dotted lines are the AMD calculations for the Gogny and Gogny-AS interactions at $35\mathrm{MeV}∕\text{nucleon}$, respectively [15]. Circles are the interpolated values of the parameter from the present work for $35\mathrm{MeV}∕\text{nucleon}$. The triangles are the observed values for the $30\mathrm{MeV}∕\text{nucleon}$. The error bars are of the size of symbols.

Figure 5

Scaling parameter $\alpha$, as a function of the asymmetry of the fragments. The solid and the dotted lines are the AMD calculations for the Gogny and Gogny-AS interactions at $35\mathrm{MeV}∕\text{nucleon}$, respectively [15]. The closed and open circles are the extracted values from the present work for $35\mathrm{MeV}∕\text{nucleon}$. The various symbols are as explained in the text.