Fluctuations and Symmetry Energy in Nuclear Fragmentation Dynamics

Within a dynamical description of nuclear fragmentation, based on the liquid-gas phase transition scenario, we explore the relation between neutron-proton density fluctuations and nuclear symmetry energy. We show that, along the fragmentation path, isovector fluctuations follow the evolution of the local density and approach an equilibrium value connected to the local symmetry energy. Higher-density regions are characterized by smaller average asymmetry and narrower isotopic distributions. This dynamical analysis points out that fragment final state isospin fluctuations can probe the symmetry energy of the density domains from which fragments originate.

Figure 1

(a) The quantity $F_{\mathrm{eff}}^v$, extracted from stochastic mean-field simulations, for stable nuclear matter in several density conditions and at temperature $T=3\mathrm{MeV}$ (thick lines). Thin lines show the density dependence of the symmetry free energy ${\mathbf{F}}_{\mathrm{sym}}$. Full lines, asy-stiff EOS; dashed lines, asy-soft EOS. (b) The quantity $F_{\mathrm{uns}}^v$ as a function of the local density for unstable systems with initial density ${\rho }_1$ (full lines), ${\rho }_2$ (dashed lines), ${\rho }_3$ (dotted lines), asy-stiff EOS. (c) Same as in (b) for asy-soft EOS. In (b) and (c) thick gray (cyan) lines represent the same results shown in (a) as thick lines.

Figure 2

The quantity $4\Delta (\overline{Z/A}{)}^2)$ (see text) is plotted as a function of the local density, for systems having initial density ${\rho }_1$ (full lines), ${\rho }_2$ (dashed lines), ${\rho }_3$ (dot-dashed lines). Curves are shifted for a better visibility. Black, asy-stiff EOS; gray (red), asy-soft EOS.

Figure 3

The quantity $\ln (Y_2/Y_1)$ is plotted as a function of $N$, for the charges $Z=1–10$, in the case of the systems with initial density ${\rho }_1$. The stiff parametrization is considered. Lines are to guide the eye. The inset shows the product $\Delta =4\Delta (\overline{Z/A}{)}^2{F}_{\mathrm{eff}}^v$, as a function of the local density.