Fluctuations in the composition of nuclear pasta in symmetric nuclear matter at finite temperature

The equilibrium distributions of the different pasta geometries and their linear sizes are calculated from the mean field Gibbs energy functional in symmetric nuclear matter at finite temperature. The average sizes and shapes coincide approximately with the ones predicted by a standard pasta calculation in the coexisting phase approximation, but fluctuations are additionally calculated and seen to increase with temperature and baryonic density. The different pasta shapes are shown to coexist in a wide domain of density and temperature, in qualitative agreement with the findings of large scale molecular dynamics simulations, but with a much less expensive computational cost.

Figure 1

Free energy per nucleon as a function of the density for $Y_p=0.5$ and $T=1$ (left figure) and 5.5 MeV (right figure) for different geometries. The final (preferential) configuration curve coincides with the droplets at the bottom and the subsequent curves (from bottom to top) represent rods, slabs, bubbles, and tubes.

Figure 2

Denser phase single-nucleus grand canonical potential with (wR, thick lines) and without (nR, thin lines) the rearrangement term for $T=1$ MeV. 1D curves are on the left, 2D in the middle and 3D on the right.

Figure 3

Evolution with density of the linear size of the different geometries. Top curves stand for 3D, curves in the middle for 2D, and bottom curves for 1D. Solid lines represent $T=1$ MeV and dashed lines $T=4.5$ MeV for average distribution radius; dotted lines represent the pasta phase at 1 MeV and dot-dashed lines the pasta phase at $T=4.5$ MeV.

Figure 4

Probability distribution as a function of the pasta linear dimension with different geometries, for different temperatures and densities with $Y_p=0.5$. Solid lines represent $T=1$ MeV and dashed lines $T=5$ MeV.

Figure 5

Evolution with temperature of the probability of the different geometries. Solid lines represent $\rho =0.0119$ ${\mathrm{fm}}^{-3}$ and dashed lines represents $\rho =0.0278$ ${\mathrm{fm}}^{-3}$. From top to bottom the solid curves stand for 3D, 2D, and 1D (hardly noticed) and the dashed curves for 1D, 2D, and 3D.