We present a study of the possible plasmon excitations that can occur in systems where strong superconductivity is present. In these systems the plasmon energy is comparable to, or smaller than the pairing gap. As a prototype of these systems we cons
ider the proton component of neutron star matter just below the crust when electron screening is not taken into account. For the realistic case we consider in detail the different aspects of the elementary excitations when the proton, electron components are considered within the Random Phase Approximation generalized to the superfluid case, while the influence of the neutron component is considered only at qualitative level. Electron screening plays a major role in modifying the proton spectrum and spectral function. At the same time the electron plasmon is strongly modified and damped by the indirect coupling with the superfluid proton component, even at moderately low values of the gap. The excitation spectrum shows the interplay of the different components and their relevance for each excitation mode. The results are relevant for neutrino physics and thermodynamical processes in neutron stars. If electron screening is neglected, the spectral properties of the proton component show some resemblance with the physical situation in high T$_c$ superconductors, and we briefly discuss similarities and differences in this connection. In a general prospect, the results of the study emphasize the role of Coulomb interaction in strong superconductors.
The thermal evolution of neuron stars depends on the elementary excitations affecting the stellar matter. In particular, the low-energy excitations, whose energy is proportional to the transfered momentum, can play a major role in the emission and pr
opagation of neutrinos. In this paper, we focus on the density modes associated with the proton component in the homogeneous matter of the outer core of neutron stars (at density between one and three times the nuclear saturation density, where the baryonic constituants are expected to be neutrons and protons). In this region, it is predicted that the protons are superconductor. We study the respective roles of the proton pairing and Coulomb interaction in determining the properties of the modes associated with the proton component. This study is performed in the framework of the Random Phase Approximation, generalized in order to describe the response of a superfluid system.The formalism we use ensures that the Generalized Wards Identities are satisfied. An important conclusion of this work is the presence of a pseudo-Goldstone mode associated with the proton superconductor in neutron-star matter. Indeed, the Goldstone mode, which characterizes a pure superfluid, is suppressed in usual superconductors due to the long-range Coulomb interaction, which only allows a plasmon mode. However, for the proton component of stellar matter, the Coulomb field is screened by the electrons and a pseudo-Goldstone mode occurs, with a velocity increased by the Coulomb interaction.
The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to
be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis we show that a) the transition density $rho_t$ is mainly correlated with the symmetry energy slope $L$, b) the proton fraction $Y_{p,t}$ with the symmetry energy and symmetry energy slope $(J,L)$ defined at saturation density, or, even better, with the same quantities defined at $rho=0.1$ fm$^{-3}$, and c) the transition pressure $P_t$ with the symmetry energy slope and curvature $(J,K_{rm sym})$ defined at $rho=0.1$ fm$^{-3}$.
The slope of the nuclear symmetry energy at saturation density $L$ is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between $L$ and the core-crust transition. We confirm t
hat the transition density is soundly correlated with $L$ despite differences between models, and we propose a clear understanding of this correlation based on a generalised liquid drop model. Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure $P_t$ and $L$. From a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. The correlation between the isovector coefficients $K_{rm sym}$ and $L$ plays a crucial role in this discussion.
We study the collective density modes which can affect neutron-star thermodynamics in the baryonic density range between nuclear saturation ($rho_0$) and $3rho_0$. In this region, the expected constituents of neutron-star matter are mainly neutrons,
protons and electrons ($npe$ matter), under the constraint of beta equilibrium. The elementary excitations of this $npe$ medium are studied in the RPA framework. We emphasize the effect of Coulomb interaction, in particular the electron screening of the proton plasmon mode. For the treatment of the nuclear interaction, we compare two modern Skyrme forces and a microscopic approach. The importance of the nucleon effective mass is observed.
We study the possible collective plasma modes which can affect neutron-star thermodynamics and different elementary processes in the baryonic density range between nuclear saturation ($rho_0$) and $3rho_0$. In this region, the expected constituents o
f neutron-star matter are mainly neutrons, protons, electrons and muons ($npemu$ matter), under the constraint of beta equilibrium. The elementary plasma excitations of the $pemu$ three-fluid medium are studied in the RPA framework. We emphasize the relevance of the Coulomb interaction among the three species, in particular the interplay of the electron and muon screening in suppressing the possible proton plasma mode, which is converted into a sound-like mode. The Coulomb interaction alone is able to produce a variety of excitation branches and the full spectral function shows a rich structure at different energy. The genuine plasmon mode is pushed at high energy and it contains mainly an electron component with a substantial muon component, which increases with density. The plasmon is undamped for not too large momentum and is expected to be hardly affected by the nuclear interaction. All the other branches, which fall below the plasmon, are damped or over-damped.
We present various properties of nuclear and compact-star matter, comparing the predictions from two kinds of phenomenological approaches: relativistic models (both with constant and density-dependent couplings) and non-relativistic Skyrme-type inter
actions. We mainly focus on the liquid-gas instabilities that occur at sub-saturation densities, leading to the decomposition of the homogeneous matter into a clusterized phase. Such study is related to the description of neutron-star crust (at zero temperature) and of supernova dynamics (at finite temperature).
