Isospin properties of the pasta phase with an extended statistical model from microscopic energy functionals

In this work, we have developed an extended statistical model to study nuclear multifragmentation reactions at intermediate energies, and we link the associated observables to the properties of supernova matter. The canonical thermodynamical model, used for this study, is modified by including inputs from the relativistic mean-field energy functionals. Even though the length scale of the supernova matter is very large compared to that of the multifragmentation reaction, we find an isospin observable, the average $\langle Z/N\rangle$ of the fragments, which is almost independent of the size of system, and can be directly compared to the estimation of fractionation in infinite nuclear matter. The isospin ratio $\langle Z/N\rangle$ of the heaviest cluster produced in nuclear fragmentation and of the corresponding pasta structure occurring in supernova matter are significantly lower than the spinodal estimation in uncharged nuclear matter, due to the presence of lighter isospin symmetric clusters that dominate the mass fraction in full equilibrium at finite temperature. The screening effect of electrons is also studied.

Figure 1

Bulk symmetry energy per particle (left part) and ground-state surface tension (right part) as a function of the $Z/N$ ratio of the clusters for NL3 (solid blue) and $\mathrm{NL}3\omega \rho 6$ (dashed red) models.

Figure 2

Neutron and proton dripline for NL3 (solid blue) and $\mathrm{NL}3\omega \rho 6$ (dashed red) models.

Figure 3

Difference between theoretical and experimental energy per particle of some selected symmetric nuclei as a function of their mass number.

Figure 4

Difference between theoretical and experimental energy per particle vs. proton to neutron ratio $Z/N$ for different Z values (a) 20, (b) 28, (c) 50, and (d) 82, for the for NL3 and $\mathrm{NL}3\omega \rho 6$ models.

Figure 5

$\langle Z/N\rangle$ of the clusters as a function of their size, with (lower panels) and without (upper panels) the Coulomb screening effect from the electron background. Left (right) panels: NL3 ($\mathrm{NL}3\omega \rho 6$). In all panels, T = 4 MeV, $Y_p=0.3$, and $\rho /{\rho }_0=0.25$. The horizontal lines give the global $Z/N$ of the system. The total number of nucleons considered in each simulation is also given.

Figure 6

Cluster multiplicity as a function of their size, with (lower panels) and without (upper panels) the Coulomb screening effect from the electron background. Left (right) panels: NL3 ($\mathrm{NL}3\omega \rho 6$). In all panels, $T$ = 4 MeV, $Y_p=0.3$, and $\rho /{\rho }_0=0.25$. The total number of nucleons considered in each simulation is also given.

Figure 7

$\langle \mathrm{Z}$/${\mathrm{N}\rangle }_{\text{max}}$ of the clusters as a function of density $\rho /{\rho }_0$ of the system for different cases. The temperature is fixed to $T=4$ MeV and $Y_p=0.3$ (upper panel) and $Y_p=0.4$ (lower panel). Results with the NL3 ($\mathrm{NL}3\omega \rho 6$) are given by full (dashed) lines. Results are also compared with the thermodynamic spinodal calculation.