Low-density nuclear matter with quantum molecular dynamics: The role of the symmetry energy

We study the effect of isospin-dependent nuclear forces on the pasta phase in the inner crust of neutron stars. To this end we model the crust within the framework of quantum molecular dynamics. For maximizing the numerical performance, a newly developed code has been implemented on GPU processors. As a first application of the crust studies we investigate the dependence of the particular pasta phases on the isospin dependence of the interaction, including nonlinear terms in this sector of the interactions. Our results indicate that in contrast to earlier studies the phase diagram of the pasta phase is not very sensitive to isospin effects. We show that the extraction of the isospin parameters like asymmetry energy and slope from numerical data is affected by higher-order terms in the asymmetry dependence of the energies per particle. Furthermore, a rapid transition from the pasta to a homogeneous phase is observed even for proton-to-neutron ratios typical for a supernova environment.

Figure 1

Binding energies for nuclei obtained from simulation for three different parameter sets: (I) $C_s^{\left(1\right)}=30.0, C_s^{\left(2\right)}=-15.0$; (II) $C_s^{\left(1\right)}=25.0, C_s^{\left(2\right)}=0.0$; and (III) $C_s^{\left(1\right)}=18.0, C_s^{\left(2\right)}=22.5$. Experimental values are denoted by solid squares.

Figure 2

The nucleon distribution of phases with simple structures of cold matter at $Y_p=0.3$ and densities (left to right) $0.1{\rho }_0, 0.2{\rho }_0, 0.36{\rho }_0, 0.5{\rho }_0$, and $0.575{\rho }_0$, respectively. Green/gray (red/dark gray) spheres represent neutrons (protons).

Figure 3

Asymmetry energy per nucleon obtained from simulation as a function of density for three different parameter sets.

Figure 4

Fit of energy per nucleon using Eq. (17) for different parameter sets: (a) $C_s^{\left(1\right)}=30.0, C_s^{\left(2\right)}=-15.0$; (b) $C_s^{\left(1\right)}=25.0, C_s^{\left(2\right)}=0.0$; (c) $C_s^{\left(1\right)}=18.0, C_s^{\left(2\right)}=22.5$.

Figure 5

Normalized (a) mean curvatures and (b) Euler characteristics as functions of threshold density for various nucleon densities.

Figure 6

Comparison of normalized (a) mean curvatures and (b) Euler characteristics as functions of density for different $L$.

Figure 7

Two-point correlation function ${\xi }_{NN}$ of the density fluctuation of nucleons at densities around the transition region of pasta to uniform matter.

Figure 8

Fit of the energy per nucleon using Eq. (27) for different parameter sets.

Figure 9

Energy per particle as a function of normalized density for $Y_p=0.3$ without Coulomb interaction.