We determine the phase diagram for dense carbon-oxygen mixtures in white dwarf (WD) star interiors using molecular dynamics simulations involving liquid and solid phases. Our phase diagram agrees well with predictions from Ogata et al. and from Medin and Cumming and gives lower melting temperatures than Segretain et al. Observations of WD crystallization in the globular cluster NGC 6397 by Winget et al. suggest that the melting temperature of WD cores is close to that for pure carbon. If this is true, our phase diagram implies that the central oxygen abundance in these stars is less than about 60%. This constraint, along with assumptions about convection in stellar evolution models, limits the effective S factor for the 12C(α,γ)16O reaction to S(300)≤170  keV b.

Nonuniform neutron-rich matter present in both core-collapse supernovae and neutron-star crusts is described in terms of a semiclassical model that reproduces nuclear-matter properties and includes long-range Coulomb interactions. The neutron-neutron correlation function and the corresponding static structure factor are calculated from molecular dynamics simulations involving 40,000 to 100,000 nucleons. The static structure factor describes coherent neutrino scattering which is expected to dominate the neutrino opacity. At low momentum transfers the static structure factor is found to be small because of ion screening. In contrast, at intermediate momentum transfers the static structure factor displays a large peak due to coherent scattering from all the neutrons in a cluster. This peak moves to higher momentum transfers and decreases in amplitude as the density increases. A large static structure factor at zero momentum transfer, indicative of large density fluctuations during a first-order phase transition, may increase the neutrino opacity. However, no evidence of such an increase has been found. Therefore, it is unlikely that the system undergoes a simple first-order phase transition. Further, to compare our results to more conventional approaches, a cluster algorithm is introduced to determine the composition of the clusters in our simulations. Neutrino opacities are then calculated within a single heavy nucleus approximation as is done in most current supernova simulations. It is found that corrections to the single heavy nucleus approximation first appear at a density of the order of 10 13 g/cm 3 and increase rapidly with increasing density. Thus, neutrino opacities are overestimated in the single heavy nucleus approximation relative to the complete molecular dynamics simulations.

Neutrinos in core collapse supernovae are likely trapped by neutrino-nucleus elastic scattering. Using molecular dynamics simulations, we calculate neutrino mean free paths and ion-ion correlation functions for heterogeneous plasmas. Mean free paths are systematically shorter in plasmas containing a mixture of ions compared to a plasma composed of a single ion species. This is because neutrinos can scatter from concentration fluctuations. The dynamical response function of a heterogeneous plasma is found to have an extra peak at low energies describing the diffusion of concentration fluctuations. Our exact molecular dynamics results for the static structure factor reduce to the Debye Huckel approximation, but only in the limit of very low momentum transfers.

Nucleosynthesis, on the surface of accreting neutron stars, produces a range of chemical elements. We perform molecular dynamics simulations of crystallization to see how this complex composition forms new neutron star crust. We find chemical separation, with the liquid ocean phase greatly enriched in low atomic number elements compared to the solid crust. This phase separation should change many crust properties such as the thermal conductivity and shear modulus.

The nuclear pasta-a novel state of matter having nucleons arranged in a variety of complex shapes-is expected to be found in the crust of neutron stars and in core-collapse supernovae at subnuclear densities of about 10 14 g/cm 3 . Owing to frustration, a phenomenon that emerges from the competition between short-range nuclear attraction and long-range Coulomb repulsion, the nuclear pasta displays a preponderance of unique low-energy excitations. These excitations could have a strong impact on many transport properties, such as neutrino propagation through stellar environments. The excitation spectrum of the nuclear pasta is computed via a molecular-dynamics simulation involving up to 100,000 nucleons. The dynamic response of the pasta displays a classical plasma oscillation in the 1-to 2-MeV region. In addition, substantial strength is found at low energies. Yet this low-energy strength is missing from a simple ion model containing a single-representative heavy nucleus. The low-energy strength observed in the dynamic response of the pasta is likely to be a density wave involving the internal degrees of freedom of the clusters. PACS number(s): 26.60.+c, 24.10. Lx, 25.30.Pt Baryonic matter is organized as a result of short-range nuclear attraction and long-range Coulomb repulsion. Often the corresponding nuclear and atomic length scales are well separated, so nucleons bind into atomic nuclei that are themselves segregated into a crystal lattice. However, at the enormous densities present in astrophysical objects-densities that exceed that of ordinary matter by 14 orders of magnitudethese length scales become comparable and complex new phenomena emerge. Complexity arises because it is impossible for the constituents to be simultaneously correlated from nuclear attraction and anticorrelated from Coulomb repulsion. Competition among these interactions plays a fundamental role in the organization of matter and results in Coulomb frustration. Frustration-a ubiquitous behavior in complex systems ranging from magnetism to protein folding to neural networks-develops from the inability of a system to simultaneously satisfy all of its elementary interactions. For example, the Ising antiferromagnet on a triangular lattice is frustrated because not all of the nearest neighbor spins can be antiparallel to each other. Frustrated systems have unusual dynamics owing to the preponderance of low-energy excitations [1].At subnuclear densities of about 10 14 g/cm 3 (normal nuclear matter saturation density is 2.5 × 10 14 g/cm 3 ) Coulomb frustration is expected to promote the development of complex shapes. These shapes follow from the competition between surface tension and Coulomb energies. Whereas surface tension favors spherical shapes, Coulomb interactions often * favor nonspherical configurations. Therefore, a variety of complex structures with a diversity of shapes-such as spheres, cylinders, and plates-have been predicted. The many phases of nuclear matter displaying this variety of shapes are known collectively as nuclear ...