Novel technique to extract experimental symmetry free energy information for nuclear matter

A new method of accessing information on the symmetry free energy from yields of fragments produced in Fermi-energy heavy-ion collisions is proposed. Furthermore, by means of quantum fluctuation analysis techniques, correlations between extracted symmetry free energy coefficients with temperature and density were studied. The obtained results are consistent with those of commonly used isoscaling techniques.

Figure 1

$F/T$ values as a function of fragment's neutron-proton asymmetry $m$ for an excitation energy of 5.5 MeV/A of the QP. The solid line (Landau Fit1) is a fit to the data with all Landau's equation parameters as free parameters while the dashed line (Landau Fit2) represents a fit to data fixing $c=115$. Error bars corresponding to statistical errors are smaller than the symbols.

Figure 2

(a) Symmetry free energy vs temperature. (b) Symmetry free energy vs density. The symmetry free energy coefficients ($F_{\mathrm{sym}}$) are extracted from Landau's free energy approach. Temperatures and densities are derived from the quantum-fluctuation method with protons as the probe particle. Full circles and squares correspond respectively to results without and with Coulomb correction. For comparison, $F_{\mathrm{sym}}$ values obtained from isoscaling techniques along with $T$ and $\rho$ from Albergo [17] and coalescence [18] methods are also plotted. Statistical errors are indicated by the bars and are not shown when smaller than the symbols.

Figure 3

Symmetry free energy density (${\mathfrak{J}}_{\mathrm{sym}}=F_{\mathrm{sym}}\times \rho$) as a function of the system temperature $T$. Error bars represent statistical errors and are not shown when smaller than the symbols.