We study the role of the effective Coulomb interaction strength and length on the dynamics of nucleons in conditions according to those in a neutron star's crust. Calculations were made with a semi-classical molecular dynamics model, studying isospin symmetric matter at sub-saturation densities and low temperatures. The electrostatic interaction between protons interaction is included in the form of a screened Coulomb potential in the spirit of the Thomas-Fermi approximation, but the screening length is artificially varied to explore its effect on the formation of the nonhomogeneous nuclear structures known as "nuclear pasta". As the screening length increases, we can see a transition from a one-per-cell pasta regime (due exclusively to finite size effects) to a more appealing multiple pasta per simulation box. This shows qualitative difference in the structure of neutron star matter at low temperatures, and therefore, special caution should be taken when the screening length is estimated for numerical simulations.

In this work, we focus on different length scales within the dynamics of nucleons in conditions according to the neutron star crust, with a semiclassical molecular dynamics model, studying isospin symmetric matter at subsaturation densities. While varying the temperature, we find that a solidliquid phase transition exists, that can be also characterized with a morphology transition. For higher temperatures, above this phase transition, we study the neutrino opacity, and find that in the liquid phase, the scattering of low momenta neutrinos remain high, even though the morphology of the structures differ significatively from those of the traditional nuclear pasta.

The study of neutron rich matter, present in neutron star, proto-neutron stars and core-collapse supernovae, can lead to further understanding of the behavior of nuclear matter in highly asymmetric nuclei. Heterogeneous structures are expected to exist in these systems, often referred to as nuclear pasta. We have carried out a systematic study of neutrino opacity for different thermodynamic conditions in order to assess the impact that the structure has on it. We studied the dynamics of the neutrino opacity of the heterogeneous matter at different thermodynamic conditions with semiclassical molecular dynamics model already used to study nuclear multifragmentation. For different densities, proton fractions and temperature, we calculate the very long range opacity and the cluster distribution. The neutrino opacity is of crucial importance for the evolution of the core-collapse supernovae and the neutrino scattering.

Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the longer range coulomb repulsion between protons, the system has structural inhomogeneities. Several interactions tailored to reproduce nuclear matter plus screened Coulomb term reproduce these inhomogeneities known as nuclear pasta. These structural inhomogeneities, located in the crust of neutron stars, can also arise in expanding systems depending on the thermodynamic conditions (temperature, proton fraction, . . . ) and the expansion velocity.Purpose: We aim to find the dynamics of the fragments formation for expanding systems simulated according to the little big bang model. This expansion resembles the evolution of neutron stars merger. Method:We study the dynamics of the nucleons with semiclassical molecular dynamics models. Starting with an equilibrium configuration, we expand the system homogeneously until we arrive to an asymptotic configuration (i. e. very low final densities). We study, with four different cluster recognition algorithms, the fragment distribution throughout this expansion and the dynamics of the cluster formation.Results: Studying the topology of the equilibrium states, before the expansion, we reproduced the known pasta phases plus a novel phase we called pregnocchi, consisting of proton aggregates embedded in a neutron sea. We have identified different fragmentation regimes, depending on the initial temperature and fragment velocity. In particular, for the already mentioned pregnocchi, a neutron cloud surrounds the clusters during the early stages of the expansion, resulting in systems that give rise to configurations compatibles with the emergence of r-proccess.Conclusions: These calculations pave the way to a comparision between Earth experiments and neutron star studies.

Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the long range coulomb repulsion between protons, the system has structural inhomogeneities. These structural inhomogeneities arise also in expanding systems, where the fragment distribution is highly dependent on the thermodynamic conditions (temperature, proton fraction, . . . ) and the expansion velocity.Purpose: We aim to find the different regimes of fragment distribution, and the existence of infinite clusters. Method:We study the dynamics of the nucleons with a semiclassical molecular dynamics model. Starting with an equilibrium configuration, we expand the system homogeneously until we arrive to an asymptotic configuration (i. e. very low final densities). We study the fragment distribution throughout this expansion. Results:We found the typical regimes of the asymptotic fragment distribution of an expansion: u-shaped, power law and exponential. Another key feature in our calculations is that, since the interaction between protons is long range repulsive, we do not have always an infinite fragment. We found that, as expected, the faster the expansion velocity is, the quicker the infinite fragment disappears. Conclusions:We have developed a novel graph-based tool for the identification of infinite fragments, and found a transition from U-shaped to exponential fragment mass distribution with increasing expansion rate.