Abstract
The core-collapse supernova (CCSN) phenomenon, one of the most explosive events in the Uni- verse, presents a challenge to theoretical astrophysics. Of the large variety of forms of matter present in CCSN, we focus on the transitional region between homogeneous and inhomogeneous phases. Traditionally, here the nuclear structures undergo a series of changes in shape from spher- ical to exotic deformed forms: rods, slabs, cylindrical holes and bubbles, termed “nuclear pasta”. A fully self-consistent three-dimensional, finite temperature Skyrme-Hartree-Fock + BCS (SHF) calculation yields, for the first time, the critical density and temperature of both the onset of the pasta in inhomogeneous matter, consisting of neutron heavy nuclei and a free neutron and electron gas, and its dissolution in to a homogeneous neutron, proton and electron liquid. As the nuclear matter properties depend on the effective nucleon-nucleon interaction in the SHF model, we employ four different forms of the Skyrme interaction, SkM∗, SLy4, NRAPR and SQMC700 and find subtle variations in the low density and high density transitions into and out of the pasta phase. Two new stable pasta shapes have been identified, in addition to the classic ones, on the grid of densities and temperatures used in this work. Detailed examination and clasification of the transitions found will form the content of a forthcoming publication.