Background : Neutron star and supernova matter at densities just below the nuclear matter saturation density is expected to form a lattice of exotic shapes .
These so-called nuclear pasta phases are caused by Coulomb frustration .
Their elastic and transport properties are believed to play an important role for thermal and magnetic field evolution , rotation and oscillation of neutron stars .
Furthermore , they can impact neutrino opacities in core-collapse supernovae . Purpose : In this work , we present proof-of-principle 3D Skyrme Hartree-Fock ( SHF ) simulations of nuclear pasta with the Multi-resolution ADaptive Numerical Environment for Scientific Simulations ( MADNESS ) . Methods : We perform benchmark studies of ^ { 16 } \mathrm { O } , ^ { 208 } \mathrm { Pb } and ^ { 238 } \mathrm { U } nuclear ground states and calculate binding energies via 3D SHF simulations .
Results are compared with experimentally measured binding energies as well as with theoretically predicted values from an established SHF code .
The nuclear pasta simulation is initialized in the so-called waffle geometry as obtained by the Indiana University Molecular Dynamics ( IUMD ) code .
The size of the unit cell is 24fm with an average density of about \rho = 0.05 \ > \mathrm { fm } ^ { -3 } , proton fraction of Y _ { p } = 0.3 and temperature of T = 0 MeV . Results : Our calculations reproduce the binding energies and shapes of light and heavy nuclei with different geometries .
For the pasta simulation , we find that the final geometry is very similar to the initial waffle state .
We compare calculations with and without spin-orbit forces .
We find that while subtle differences are present , the pasta phase remains in the waffle geometry . Conclusions : Within the MADNESS framework , we can successfully perform calculations of inhomogeneous nuclear matter .
By using pasta configurations from IUMD it is possible to explore different geometries and test the impact of self-consistent calculations on the latter .