Complex and exotic nuclear geometries are expected to appear naturally in dense nuclear matter found in the crust of neutron stars and supernovae environment collectively referred to as “ nuclear pasta ” .
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 crust 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 \leq \rho \leq 0.10 fm ^ { -3 } , proton fractions 0.05 \leq Y _ { p } \leq 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 meta-stable states , and possible remedies to avoid meta-stable solutions are discussed .