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Neutron star and supernova matter at densities just below the nuclear mattersaturation density is expected to form a lattice of exotic shapes. Theseso-called nuclear pasta phases are caused by Coulomb frustration. Their elasticand transport properties are believed to play an important role for thermal andmagnetic field evolution, rotation and oscillation of neutron stars.Furthermore, they can impact neutrino opacities in core-collapse supernovae. Inthis work, we present proof-of-principle 3D Skyrme Hartree-Fock (SHF)simulations of nuclear pasta with the Multi-resolution ADaptive NumericalEnvironment for Scientific Simulations (MADNESS). We perform benchmark studiesof $^{16} \mathrm{O}$, $^{208} \mathrm{Pb}$ and $^{238} \mathrm{U}$ nuclearground states and calculate binding energies via 3D SHF simulations. Resultsare compared with experimentally measured binding energies as well as withtheoretically predicted values from an established SHF code. The nuclear pastasimulation is initialized in the so-called waffle geometry as obtained by theIndiana University Molecular Dynamics (IUMD) code. The size of the unit cell is24\:fm 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. Our calculationsreproduce the binding energies and shapes of light and heavy nuclei withdifferent geometries. For the pasta simulation, we find that the final geometryis very similar to the initial waffle state. In the present pasta calculationsspin-orbit forces are not included but will be added in the future. Within theMADNESS framework, we can successfully perform calculations of inhomogeneousnuclear matter. By using pasta configurations from IUMD it is possible toexplore different geometries and test the impact of self-consistentcalculations on the latter.

Quantum Simulations of Nuclei and Nuclear Pasta with the Multi-resolution Adaptive Numerical Environment for Scientific Simulations