Non-locality in the nucleon-nucleon interaction and nuclear matter saturation

We study the possible relationship between the saturation properties of nuclear matter and the inclusion of non-locality in the nucleon-nucleon interaction. To this purpose we compute the saturation curve of nuclear matter within the Bethe-Brueckner-Goldstone theory using a recently proposed realistic non-local potential, and compare it with the corresponding curves obtained with a purely local realistic interaction (Argonne v$_{18}$) and the most recent version of the one-boson exchange potential (CD Bonn). We find that the inclusion of non-locality in the two-nucleon bare interaction strongly affects saturation, but it is unable to provide a consistent description of few-body nuclear systems and nuclear matter.Comment: 9 pages, 8 figures; v2: introduction extended, references added, discussion of fig.8 reformulated; to be published in Phys. Rev.

The Equation of State of Dense Matter : from Nuclear Collisions to Neutron Stars

The Equation of State (EoS) of dense matter represents a central issue in the study of compact astrophysical objects and heavy ion reactions at intermediate and relativistic energies. We have derived a nuclear EoS with nucleons and hyperons within the Brueckner-Hartree-Fock approach, and joined it with quark matter EoS. For that, we have employed the MIT bag model, as well as the Nambu--Jona-Lasinio (NJL) and the Color Dielectric (CD) models, and found that the NS maximum masses are not larger than 1.7 solar masses. A comparison with available data supports the idea that dense matter EoS should be soft at low density and quite stiff at high density.Comment: 8 pages, 5 figures, invited talk given at NPA3, Dresden, March 200

Computation of Neutron Star Structure Using Modern Equation of State

Using the modern equations of state derived from microscopic calculations, we have calculated the neutron star structure. For the neutron star, we have obtained a minimum mass about $0.1 {\rm M_{\odot}}$ which is nearly independent of the equation of state, and a maximum mass between $1.47 {\rm M_{\odot}}$ and $1.98 {\rm M_{\odot}}$ which is strongly dependent on the equation of state. It is shown that among the equations of state of neutron star matter which we have used, the stiffest one leads to higher maximum mass and radius and lower central density. It is seen that the given maximum mass for the Reid-93 equation of state shows a good consistency with the accurate observations of radio pulsars. We have indicated that the thickness of neutron star crust is very small compared to the predicted neutron star radius.Comment: 16 pages, 6 figure

Temperature dependence of single-particle properties in nuclear matter

The single-nucleon potential in hot nuclear matter is investigated in the framework of the Brueckner theory by adopting the realistic Argonne V18 or Nijmegen 93 two-body nucleon-nucleon interaction supplemented by a microscopic three-body force. The rearrangement contribution to the single-particle potential induced by the ground state correlations is calculated in terms of the hole-line expansion of the mass operator and provides a significant repulsive contribution in the low-momentum region around and below the Fermi surface. Increasing temperature leads to a reduction of the effect, while increasing density makes it become stronger. The three-body force suppresses somewhat the ground state correlations due to its strong short-range repulsion, increasing with density. Inclusion of the three-body force contribution results in a quite different temperature dependence of the single-particle potential at high enough densities as compared to that adopting the pure two-body force. The effects of three-body force and ground state correlations on the nucleon effective mass are also discussed.Comment: 14 pages, 5 figure

Convergence of Ginzburg-Landau functionals in 3-d superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.Comment: 45 page

Elementary excitations in homogeneous superfluid neutron star matter: Role of the proton component

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 propagation 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 Ward's 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.Comment: Submitted for publicatio

Hybrid stars with the Dyson-Schwinger quark model

We study the hadron-quark phase transition in the interior of neutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the Brueckner-Hartree-Fock many-body theory with realistic two-body and three-body forces. For the description of quark matter, we employ the Dyson-Schwinger approach and compare with the MIT bag model. We calculate the structure of neutron star interiors comprising both phases and find that with the Dyson-Schwinger model, the hadron-quark phase transition takes place only when hyperons are excluded, and that a two-solar-mass hybrid star is possible only if the nucleonic equation of state is stiff enough.Comment: 10 pages, 8 figure

Chaotic Scattering in Heavy--Ion Reactions

We discuss the relevance of chaotic scattering in heavy--ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum-mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behaviour of several experimental data.Comment: 35 pages in RevTex (version 3.0) plus 27 PostScript figures obtainable by anonymous ftp from VAXFCT.CT.INFN.IT in directory kaos. Fig. 1 upon request to the authors. To be published in the October Focus issue on chaotic scattering of CHAO

Four-particle condensate in strongly coupled fermion systems

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of quartetting. Within a model calculation for symmetric nuclear matter, we find that below a critical density, the four-particle condensation (alpha-like quartetting) is favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the excition-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.Comment: LaTeX, 11 pages, 2 figures, uses psfig.sty (included), to be published in Phys. Rev. Lett., tentatively scheduled for 13 April 1998 (Volume 80, Number 15

Equation of State of Nuclear Matter at high baryon density

A central issue in the theory of astrophysical compact objects and heavy ion reactions at intermediate and relativistic energies is the Nuclear Equation of State (EoS). On one hand, the large and expanding set of experimental and observational data is expected to constrain the behaviour of the nuclear EoS, especially at density above saturation, where it is directly linked to fundamental processes which can occur in dense matter. On the other hand, theoretical predictions for the EoS at high density can be challenged by the phenomenological findings. In this topical review paper we present the many-body theory of nuclear matter as developed along different years and with different methods. Only nucleonic degrees of freedom are considered. We compare the different methods at formal level, as well as the final EoS calculated within each one of the considered many-body schemes. The outcome of this analysis should help in restricting the uncertainty of the theoretical predictions for the nuclear EoS.Comment: 51 pages, to appear in J. Phys. G as Topical Revie