Quantum nuclear pasta and nuclear symmetry energy

Complex and exotic nuclear geometries, collectively referred to as "nuclear pasta," are expected to appear naturally in dense nuclear matter found in the crusts of neutron stars and supernovae environments. The pasta geometries depend on the average baryon density, proton fraction, and temperature and are critically important in the determination of many transport properties of matter in supernovae and the crusts of neutron stars. Using a set of self-consistent microscopic nuclear energy density functionals, we present the first results of large scale quantum simulations of pasta phases at baryon densities 0.03≤ρ≤0.10fm-3, proton fractions 0.05≤Yp≤0.40, and zero temperature. The full quantum simulations, in particular, allow us to thoroughly investigate the role and impact of the nuclear symmetry energy on pasta configurations. We use the Sky3D code that solves the Skyrme Hartree-Fock equations on a three-dimensional Cartesian grid. For the nuclear interaction we use the state-of-the-art UNEDF1 parametrization, which was introduced to study largely deformed nuclei, hence is suitable for studies of the nuclear pasta. Density dependence of the nuclear symmetry energy is simulated by tuning two purely isovector observables that are insensitive to the current available experimental data. We find that a minimum total number of nucleons A=2000 is necessary to prevent the results from containing spurious shell effects and to minimize finite size effects. We find that a variety of nuclear pasta geometries are present in the neutron star crust, and the result strongly depends on the nuclear symmetry energy. The impact of the nuclear symmetry energy is less pronounced as the proton fractions increase. Quantum nuclear pasta calculations at T=0 MeV are shown to get easily trapped in metastable states, and possible remedies to avoid metastable solutions are discussed.