Nuclear “pasta matter” for different proton fractions

Nuclear matter under astrophysical conditions is explored with time-dependent and static Hartree-Fock calculations. The focus is in a regime of densities where matter segregates into liquid and gaseous phases unfolding a rich scenario of geometries, often called nuclear pasta shapes (e.g., spaghetti, lasagna). Particularly the appearance of the different phases depending on the proton fraction and the transition to uniform matter are investigated. In this context the neutron background density is of special interest, because it plays a crucial role in the type of pasta shape that is built. The study is performed in two dynamical ranges, once for hot matter and once at temperature zero, to investigate the effect of cooling.

Figure 1

Binding energy per particle $E/A$ as function of total density for asymmetric nuclear matter at zero temperature for various proton fractions $X_p$ as indicated. The ground states are indicated by black boxes for those $X_p$ where a local minimum could be found. The curves have been computed for the Skyrme force SLy6.

Figure 2

Equilibrium density as function of proton fraction $X_p$ for different Skyrme interactions (for explanations see text). Each curve stops at some low $X_p$ because no equilibrium (minimum of energy as function of $\rho$) could be found for smaller $X_p$.

Figure 3

Upper panel: Map of pasta shapes achieved in TDHF calculations starting from a gas of $\alpha$ particles with neutron background for various proton fractions and mean densities. Starting from these final states, the map of pasta shapes achieved in Hartree-Fock calculations (cooled pasta) is shown in the lower panel. Two different colors in a cell mark different final states for two calculations with similar initial conditions. The structures are named as in [16] and examples and further properties can be found there.

Figure 4

Upper panel: Neutron background densities $\left({\rho }_{\mathrm{nbg}}\right)$ of the series of calculations of Fig. 3. Full symbols show results from dynamical calculations and open symbols from zero-temperature configurations, marked with the additional index C in the legend. The case $X_{p,C}=0.5$ is not shown because it did not produce a background. The shaded area indicates the region where ${\rho }_g$ is only vaguely defined. Lower panel: Neutron Fermi energies for the cooled Pasta shapes in dependence on the mean density for different proton fractions are shown.

Figure 5

Upper panel: Liquid phase densities for two representative values of $X_p$. The cooled calculations are marked with the additional index C. Lower panel: Liquid phase occupied volume fractions $u_l$ for two $X_p$. The color bars on the right indicate a pasta shape with the color code as explained in Fig. 3. The bars mark the intervals of $u_l$ for which the pasta shape associated with this color appears.