Exotic States of Nuclear Matter

PREFACE.

ORGANIZING COMMITTEES.

CONTENTS.

The quest for the nuclear equation of state (EoS) at high densities and/or extreme isospin is one of the longstanding problems of nuclear physics. In the last years substantial progress has been made to constrain the EoS both, from the astrophysical side and from accelerator based experiments. Heavy ion experiments support a soft EoS at moderate densities while recent neutron star observations require a "stiff" high density behavior. Ab initio calculations for the nuclear many-body problem make predictions for the density and isospin dependence of the EoS far away from the saturation point. Both, the constraints from astrophysics and accelerator based experiments are shown to be in agreement with the predictions from many-body theory.

Microscopic studies of nuclear matter under diverse conditions of density and asymmetry are of great contemporary interest. Concerning terrestrial applications, they relate to future experimental facilities that will make it possible to study systems with extreme neutron-to-proton ratio. In this talk, I will review recent efforts of my group aimed at exploring nuclear interactions in the medium through the nuclear equation of state. The approach we take is microscopic and relativistic, with the predicted EoS properties derived from realistic nucleon-nucleon potentials. I will also discuss work in progress. Most recently, we completed a DBHF calculation of the Λ hyperon binding energy in nuclear matter.

We investigate the equation of state (EOS) and single-particle (s.p.) properties of asymmetric nuclear matter (including the neutron and proton s.p. potentials and effective masses, symmetry potential, neutron/proton effective mass splitting) by using the Brueckner approach extended to include microscopic three-body forces. We have concentrated on the isospin-dependence of the properties of asymmetric nuclear matter and the TBF effects. We have discussed especially the TBF-induced rearrangement effect on the s.p. properties and their isospin behavior in neutron-rich nuclear medium.

The Self-Consistent Green's Function's (SCGF) method at the level of the ladder approximation is used to calculate the free-energy of symmetric nuclear matter. The ladder approximation considers the propagation of particles and holes which translates into the incorporation of significant correlations in the wave function. These correlations are reflected in the shape of the single-particle spectral functions. An essential ingredient of the free energy is the entropy, which is calculated with the Luttinger-Ward formalism. In this approach, the finite width of the quasi-particle states is explicitly taken into account. It turns out that the entropy measures thermal effects and the effect of dynamical correlations, already present at zero temperature, is not so relevant for the calculation of the entropy. Preliminary results for the liquid-gas phase transition are also presented.

We develop a method to make a very good estimate of the three-body cluster energy by using the state dependent correlation functions which have been produced by the lowest order constraint variational (LOCV) method. It is shown that the LOCV normalization constraint plays a major role in the convergence of the cluster expansion. Finally using the equation of state derived from LOCV formalism for neutron star matter, we calculate the neutron star properties such as its mass-radius relation and minimum mass.

The magnetic susceptibility of spin-polarized neutron matter is calculated at both zero and finite temperature within (i) the microscopic framework of the Brueckner-Hartree-Fock formalism, and (ii) using the Skyrme and Gogny phenomenological forces. The microscopic results show no indication of a ferromagnetic transition at any density and temperature. In the case of the Skyrme interaction, it is shown that the critical density at which ferromagnetism takes place decreases with temperature. This unexpected feature is associated to an anomalous behavior of the entropy that becomes larger for the polarized phase than for the unpolarized one above a certain critical density. For the Gogny force, the results show two different behaviors: whereas the D1P parametrization exhibits a ferromagnetic transition at a density of ρ ~ 1.31 fm^-3 whose onset increases with temperature, no sign of such a transition is found for D1 at any density and temperature, in agreement with the microscopic calculations.

We have found that it is possible to understand all the saturation observables of symmetric nuclear matter by incorporating in-medium modification of the parameters of sigma meson alone. In the framework of Brueckner-Bethe-Goldstone formalism with Bonn-B potential as two-body interaction, in-medium modification (density independent reduction) of σ-meson-nucleon coupling constant by about 3.5% and σ-meson mass by about 6.8% is enough to understand nuclear matter saturation observables.

The pervasive role of the nuclear symmetry energy in establishing some nuclear static and dynamical properties, and in governing some attributes of neutron star properties is highlighted.

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The present approach is based upon a generalized Weizsäcker formula for ground-state energies. In particular effects from the Wigner energy and shell structure on the symmetry energy are investigated. Data on the neutron skin is used as an additional source of information.

We show that the phenomenology of isospin effects on heavy ion reactions at intermediate energies (few AGeV range) is extremely rich and can allow a "direct" study of the covariant structure of the isovector interaction in a high density hadron medium. We work within a relativistic transport frame, beyond a cascade picture, consistently derived from effective Lagrangians, where isospin effects are accounted for in the mean field and collision terms. Rather sensitive observables are proposed from collective flows ("differential" flows) and from pion/kaon production (π^-/π⁺, K⁰/K⁺ yields). For the latter point relevant non-equilibrium effects are stressed. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected "neutron trapping" effect.

With stochastic transport simulations we study in detail central and peripheral collisions at Fermi energies and suggest new observables, sensitive to the symmetry energy below normal density.

We address nuclear liquid-gas instablitities in the mean-field framework, using a Skyrme-like density functional. These instabilities lead to the clusterization of nuclear and compact-star matter at sub-saturation density. In this contribution, we study the extension of the spinodal region, how it affects star matter at β-equilibrium and how it is affected by the choice of different Skyrme forces. The dynamics of cluster formation is also characterized, comparing a semi-classical approach to a quantal one.

The relativistic microscopic optical potential (RMOP) in the nucleon-nucleus scattering is studied in the framework of the Dirac Brueckner Hartree-Fock (DBHF) approach. The real part of the nucleon self-energy in asymmetric nuclear matter is calculated with the G-matrix, while the imaginary part is obtained from the polarization diagram. Nuclear optical potentials in finite nuclei are derived from the nucleon self-energies in asymmetric nuclear matter through a local density approximation. The RMOP is applied to study the nucleon scattering off stable nuclei and nucleon effective mass. A satisfactory agreement with the experimental data is found. The complex nucleon-nucleus optical potential is extended to microscopic optical potentials of nucleus-nucleus interaction by a folding method. The elastic scattering data of ⁶He at 229.8 MeV on ¹²C target are analyzed.

For more than three decades, the inner crust of neutron stars, formed of a solid lattice of nuclear clusters coexisting with a gas of electrons and neutrons, has been traditionally studied in the Wigner-Seitz approximation. The validity of this approximation is discussed in the general framework of the band theory of solids, which has been recently applied to the nuclear context. Using this novel approach, it is shown that the unbound neutrons move in the crust as if their mass was increased.

Results of the semi-microscopic self-consistent approach to describe the ground state properties of the inner crust of a neutron star developed recently within the Wigner-Seitz method with pairing effects taken into account are briefly reviewed.

We discuss how the present uncertainty in the pairing properties of neutron matter affects the thermal response of the inner crust of neutron star in the case of a rapid cooling process. It is shown that the thermalisation time of the inner crust is changing by a factor of two if in the calculations one shifts between two posible pairing scenarios for neutron superfluidity, i.e., one corresponding to the BCS approximation and the other to many-body techniques which include polarisation effects.

Low-energy quadrupole excitations are analyzed in nuclear Fermi systems. The crust of neutron stars provides a unique framework for studying the evolution of low-lying modes from neutron-rich nuclei to a pure neutron gas. We modelize the crust with Wigner-Seitz cells and focus our attention on the Zr and Sn cells with baryon densities equal to 0.02 fm^-3 and 0.04 fm^-3, respectively. It is shown that the excitations with low multipolarities are concentrated almost entirely in one strongly collective mode which exhausts a very large fraction of the energy-weighted sum rule. Since these collective modes are located at very low energies compared to the giant resonances in standard nuclei, they may affect significantly the specific heat of baryonic inner crust matter of neutron stars.

The role of Pauli potentials in the semiclassical simulation of Fermi gases at low temperatures is investigated. An alternative Pauli potential to the usual bivariate Gaussian form by Dorso et al⁵ is proposed. This new Pauli potential allows for a simultaneous good reproduction of not only the kinetic energy per particle but also the momentum distribution and the two-body correlation function. The reproduction of the binding energies in finite nuclei in the low and medium mass range is also analyzed. What is found is that given a reasonable short-range atractive nuclear interaction one can include correlation effects in a suitable chosen density dependent Pauli potential.

Dynamical instability modes and thermodynamical instabilities of low-density asymmetric nuclear matter (ANM) neutralised by electrons as found in supernova core and neutron star crust are studied in the framework of relativistic mean-field hadron models with the inclusion of electron and photon fields. Both models with constant and density dependent coupling constants are considered. It is shown that the Coulomb field quenches large structure formation but has little effect on medium and small-size fluctuations. Implications on the crust of compact stars are discussed.

Alternatively to pairing, four-particle correlations may become of importance for the formation of quantum condensates in nuclear matter. With increasing density, four-particle correlations are suppressed because of Pauli blocking. Signatures of α-like clusters are expected to occur in low-density nuclear systems. The famous Hoyle state (0_2⁺ at 7.654 MeV in ¹²C) is identified as being an almost ideal condensate of three α-particles, hold together only by the Coulomb barrier. It, therefore, has a ⁸Be-α structure of low density. Transition probability and inelastic form factor together with position and other physical quantities are correctly reproduced without any adjustable parameter from our two parameter wave function of α-particle condensate type. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

The calculation of transport properties of Fermi liquids, based on the formalism developed by Abrikosov and Khalatnikov, requires the knowledge of the probability of collisions between quasiparticles in the vicinity of the Fermi surface. We have carried out a study of the shear viscosity of pure neutron matter, whose value plays a pivotal role in determining the stability of rotating neutron stars, in which these processes are described using a state-of-the-art nucleon-nucleon potential. Medium modifications of the scattering cross section have been consistently taken into account, through an effective interaction obtained from the matrix elements of the bare interaction between correlated states. Medium effects produce a large increase of the viscosity at densities ρ ≳ 0.1 fm^-3.

We briefly review the turbulent mean-field dynamo action in protoneutron stars that are subject to convective and neutron finger instabilities during the early evolutionary phase. By solving the mean-field induction equation with the simplest model of α-quenching we estimate the strength of the generated magnetic field. If the initial period of the protoneutron star is short, then the generated large-scale field is very strong (> 3 × 10¹³G) and exceeds the small-scale field at the neutron star surface, while if the rotation is moderate, then the pulsars are formed with more or less standard dipole fields (< 3 × 10¹³G) but with surface small-scale magnetic fields stronger than the dipole field. If rotation is very slow, then the mean-field dynamo does not operate, and the neutron star has no global field.

We present the first long term simulations¹ of the nonlinear magnetic field evolution in realistic neutron star crusts with a stratified electron number density and temperature dependent conductivity. We show that Hall drift influenced Ohmic dissipation takes place in neutron star crusts on a timescale of 10⁶ years. When the initial magnetic field has magnetar strength, the fast Hall drift results in an initial rapid dissipation stage that lasts ~ 10⁴ years. The interplay of the Hall drift with the temporal variation and spatial gradient of conductivity tends to favor the displacement of toroidal fields toward the inner crust, where stable configurations can last for ~ 10⁶ years. The decay of magnetic fields in young neutron stars is also supported by the existence of a strong trend between neutron star surface temperature and the magnetic field strength.² This trend can be explained by the decay of currents in the crust over a time scale of ~ 10⁶ yr. The implication of these results on the interpretation of cooling curves and previous constraints on the existence of exotic phases in neutron star interiors will be outlined.

Core-collapse supernovae have been supposed to be one of the most plausible sources of gravitational waves. Based on a series of our magnetohydrodynamic core-collapse simulations, we found that the gravitational amplitudes at core bounce can be within the detection limits for the currently running laser-interferometers for a galactic supernova if the central core rotates sufficiently rapidly. This is regardless of the difference of the realistic equations of state and the possible occurence of the QCD phase transition near core bounce. Even if the core rotates slowly, we point out that the gravitational waves generated from anisotropic neutrino radiation in the postbounce phase due to the standing accretion shock instability (SASI) could be within the detection limits of the detectors in the next generation such as LCGT and the advanced LIGO for the galactic source. Since the waveforms significanly depend on the exploding scenarios, our results suggest that we can obtain the information about the long-veiled explosion mechanism from the gravitational wave signals when the supernova occurs near to us.

We present 2D simulations of the cooling of neutron stars with strong magnetic fields (B ≥ 10¹³ G). We solve the diffusion equation in axial symmetry including the state of the art microphysics that controls the cooling such as slow/fast neutrino processes, superfluidity, as well as possible heating mechanisms. We study how the cooling curves depend on the the magnetic field strength and geometry. Special attention is given to discuss the influence of magnetic field decay. We show that Joule heating effects are very large and in some cases control the thermal evolution. We characterize the temperature anisotropy induced by the magnetic field for the early and late stages of the evolution of isolated neutron stars.

We demonstrate that the Fermi surface of dense neutron matter experiences a rearrangement near the onset of pion condensation, due to strong momentum dependence of the effective interaction induced by spin-isospin fluctuations. We show that new filling n(p) has a hole adjacent to the center of the Fermi sphere, and its appearance activates the normally forbidden Urca cooling mechanism.

The conditions under which nuclear collective modes couple to plasmon modes in asymmetric nuclear matter (ANM) neutralized by electrons, which is of interest for the study of neutron stars and supernovae, are investigated. We take a mean-field approach to nuclear matter, and the Coulomb field is included. We show that the coupling may be so strong that it affects the onset of the nuclear mode and it may also change its isovector/isoscalar character.

Based on the density-dependent relativistic Hartree-Fock theory (DDRHF) for hadronic matter, the properties of neutron stars have been studied and compared with the results from the density-dependent relativistic mean field theory (DDRMF). Though similar equations of state are obtained, DDRHF calculations give larger fractions of proton, electron and muon at high baryon density for neutron star matter than the ones from DDRMF. The maximum masses of neutron stars lie between 2.3 M_⊙ and 2.5 M_⊙, and the corresponding radii between 11.7 km and 12.5 km. In addition, the phase transition from hadronic matter to quark matter in neutron stars is studied by using the MIT bag model for the quark phase. The transition is studied in both Gibbs and Maxwell constructions.

Current data (by September 2007) on masses of neutron stars in binary systems (X-ray binaries, double neutron star binaries, pulsar–white dwarf binaries, and pulsar–nondegenerate star binaries) are reviewed.

Neutron stars are a natural laboratory for the exploration of dense nuclear matter. Analytic constraints from general relativity, causality and stability provide a general framework into which specific constraints concerning dense matter properties can be made from measurements of masses, spin rates, thermal emissions, and quasi-periodic oscillations observed in accreting and bursting sources. Focus is placed upon recent mass and spin rate measurements and their implications for theory.

Recent astrophysical observations of neutron stars and heavy-ion data are confronted with our present understanding of the equation of state of dense hadronic matter. Emphasis is put on the possible role of the presence of hyperons in the interior of compact stars. We argue that data from low-mass pulsars provide an important cross-check between high-density astrophysics and heavy-ion physics.

XDINSs (X-ray dim isolated neutron stars) are a group of seven soft X-ray sources originally discovered by ROSAT and characterized by purely thermal spectra (kT ∼ 40 – 100 eV), lack of radio emission and rather long spin periods (P ∼ 3 – 11 s). The absence of contamination from magnetospheric activity, a surrounding supernova remnant or a binary companion makes XDINSs the only sources in which we can have a clean view of the neutron star surface. As such they offer an unprecedented opportunity to confront theoretical models of surface emission with observations. This may ultimately lead to a direct measure of the star radius and thus probe the equation of state. XDINSs were long believed to be steady blackbody emitters. In the last few years new XMM and Chandra observations revelaled a much more faceted picture. The brightest source, RX J1856.5-3754, is the only one which indeed exhibits a purely blackbody spectrum. In all the other members of the class broad absorption features (E ∼ 200 – 700 eV) have been discovered. The second brightest object, RX J0720.4-3125 was recently found to undergo (cyclic ?) spectral variations most probably produced by the star nutation. The increasing number of optical identifications confirms that the optical continuum lies above the Rayleigh-Jeans tail of the X-ray spectrum. All these facts challenge the standard picture of XDINSs as cooling neutron stars covered by an atmosphere and endowed with a dipolar magnetic field. In this talk I will review the current status of theoretical efforts in the modeling of XDINS surface emission, discuss the many still unsolved problems and address briefly the possible relationship between XDINSs and other isolated neutron star classes, like the recently discovered rotating radio transients (RRATs).

Neutrinos are very promising probes for high energy astrophysics. Indeed, many indications suggest that cosmic objects where acceleration of charged particles can takes place, e.g. GRBs and AGNs, are the sources of the detected UHECRs. Accelerated hadrons, interacting with ambient gas or radiation, can produce HE neutrinos. Contrary wise to charged particles and TeV gamma rays, neutrinos can reach the Earth from far cosmic accelerators, traveling in straight line, therefore carrying direct information on the source. Theoretical models indicate that a detection area of ≃1 km² is required for the measurement of HE cosmic ν fluxes. The detection of Čerenkov light emitted by secondary leptons produced by neutrino interaction in large volume transparent natural media (water or ice) is today considered the most promising experimental approach to build high energy neutrino detectors. The experimental efforts towards the opening of the high energy neutrino astronomy are also reviewed.

Neutron stars emit gravitational waves essentially by two mechanisms: because they rotate or because they pulsate. We will illustrate both mechanisms and discuss to what extent the detection of gravitational waves will allow to constrain the equation of state of matter at supranuclear densities.

The analysis of SN1987A led Brown and Bethe^1,2 to conclude that the maximum mass of cold neutron stars is M_max ≈ 1.5M_⊙. On the other hand, recent evaluation of the mass of PSR J0751+1807 implies M_max > 1.5M_⊙. This contradicts the original Bethe-Brown model but can be reconciled within evolutionary scenarios proposed in this talk.³

Recent observations of XTE J1739-285 suggest that it contains a neutron star rotating at 1122 Hz.¹ Such rotational frequency would be the first for which the effects of rotation are significant. We study the consequences of very fast rotating neutron stars for the potentially observable quantities as stellar mass and pulsar period.

At sufficiently high density, quark matter is expected to be in a color superconducting state. One way to detect the presence of such matter in a compact star is via the bulk and shear viscosities, which damp r-modes, preventing the star from spinning down quickly via an r-mode instability. I discuss recent calculations of the bulk viscosity of color-superconducting quark matter, and their application to observations of compact stars.

We study the nuclear equation state at large densities and intermediate temperatures by means of a purely hadronic chirally symmetric model and, from another point of view, by considering a mixed phase of hadrons and clusters of quarks. In both models a significant softening of the equation of state takes place due to the appearance of new degrees of freedom. However, in the first case the bulk modulus is mainly dependent on the density, while in the mixed phase model it also strongly depends on the temperature. We also show that the bulk modulus is not vanishing in the mixed phase due to the presence of two conserved charges, the baryon and the isospin one. Only in a small region of densities and temperatures the incompressibility becomes extremely small. Finally we compare our results with recent analysis of heavy ion collisions at intermediate energies.

Recent indications for high neutron star masses (M ~ 2 M_⊙) and large radii (R > 12 km) could rule out soft equations of state and have provoked a debate whether the occurence of quark matter in compact stars can be excluded as well. We show that modern quantum field theoretical approaches to quark matter including color superconductivity and a vector meanfield allow a microscopic description of hybrid stars which fulfill the new, strong constraints. For these objects color superconductivity turns out to be essential for a successful description of the cooling phenomenology in accordance with recently developed tests. We discuss QCD phase diagrams for various conditions thus providing a basis for a synopsis for quark matter searches in astrophysics and in future generations of nucleus-nucleus collision experiments such as low-energy RHIC and CBM @ FAIR.

Because of colour confinement, the physical vacuum forms an event horizon for quarks and gluons; this can be crossed only by quantum tunneling, i.e., through the QCD counterpart of Hawking radiation by black holes. Since such radiation cannot transmit information to the outside, it must be thermal, of a temperature determined by the strong force at the confinement surface, and it must maintain colour neutrality. The resulting process provides a common mechanism for thermal hadron production in high energy interactions, from e⁺e^- annihilation to heavy ion collisions. The analogy with black-hole event horizon suggests a dependence of the hadronization temperature on the baryon density.

A possibility and properties of spontaneous magnetization in quark matter are investigated. Magnetic susceptibility is evaluated within Fermi liquid theory, taking into account of screening effect of gluons. Spin wave in the polarized quark matter, as the Nambu-Goldstone mode, is formulated by way of the coherent-state path integral.

We derive conditions for an asymmetric neutrino emission of hot neutron stars with quark matter as a source for the observed large kick velocities of pulsars out of supernova remnants. We work out in detail the constraints for the initial temperature, the strength of the magnetic field and the electron chemical potential in the quark matter core. Also the neutrino mean free paths for quark matter and a possible hadronic mantle are considered for a successful kick mechanism. Heat capacities and neutrino emissivities in magnetised hot quark matter are investigated to delineate the maximum possible kick velocity. In addition, the influence of colour superconducting quark matter is taken into consideration as well. In a first study we find that ignoring neutrino quark scattering kick velocities of 1000 km/s can be reached very easily for quark phase radii smaller than 10 km and temperatures higher than 5 MeV. On the other hand, taking into account the small neutrino mean free paths it seems impossible to reach velocities higher than approximately 100 km/s, even when including effects from colour superconductivity where the neutrino quark interactions are suppressed.

We investigate the thermal evolution of isolated neutron stars, including the transition of nuclear matter into quark matter at some time during the cooling stage. We show cooling curves by changing the transition periods in parametric manner. If there would be observational data which fit to our results, it suggests the existence of quark stars.

We present the general relativistic calculation of the energy release associated with a first order phase transition (PT) at the center of a rotating neutron star (NS). The energy release, E_rel, is equal to the difference in mass-energies between the initial (normal) phase configuration and the final configuration containing a superdense matter core, assuming constant total baryon number and the angular momentum. The calculations are performed with the use of precise pseudo-spectral 2-D numerical code; the polytropic equations of state (EOS) as well as realistic EOSs (Skyrme interactions, Mean Field Theory kaon condensate) are used. The results are obtained for a broad range of metastability of initial configuration and size of the new superdense phase core in the final configuration. For a fixed "overpressure", , defined as the relative excess of central pressure of a collapsing metastable star over the pressure of the equilibrium first-order PT, the energy release up to numerical accuracy does not depend on the stellar angular momentum and coincides with that for nonrotating stars with the same . When the equatorial radius of the superdense phase core is much smaller than the equatorial radius of the star, analytical expressions for the E_rel can be obtained: E_rel is proportional to for small . At higher , the results of 1-D calculations of for non-rotating stars reproduce with very high precision exact 2-D results for fast-rotating stars. The energy release-angular momentum independence for a given overpressure holds also for the so-called "strong" PTs (that destabilise the star against the axi-symmetric perturbations), as well as for PTs with "jumping" over the energy barrier.

We investigate the properties of the hadron-quark mixed phase in compact stars using a Brueckner-Hartree-Fock framework for hadronic matter and the MIT bag model for quark matter. We find that the equation of state of the mixed phase is similar to that given by the Maxwell construction. The composition of the mixed phase, however, is very different from that of the Maxwell construction; in particular, hyperons are completely suppressed.

Pure hadronic compact stars ("neutron stars") above a critical mass M_cr are metastable^1,2 for the conversion to quark stars (hybrid or strange stars). This conversion process liberates an enormous amount of energy (E_conv ~ 10⁵³ ergs), which could power some of the observed gamma ray bursts.^1–3 In cold deleptonized hadronic stars, the conversion process is triggered by the quantum nucleation of a quark matter drop in the stellar center. These drops can be made up of normal (i.e. unpaired) quark matter, or color superconducting quark matter, depending on the details of the equation of state of quark and hadronic matter.⁴ In this talk, we present the results of recent calculations⁵ of the effects of color superconductivity on the conversion of hadronic stars to quark stars. In particular, we study the dependence of the critical mass M_cr and conversion energy E_conv on the quark-quark pairing gap Δ, the bag constant B, and the surface tension σ of the quark-hadron interface.

Compact stars are generically unstable against gravitational radiation emission from r-mode instabilities, but dissipative phenomena such as bulk and shear viscosities tend to dampen these instabilities, thus creating a window of stability. This may provide an opportunity to identify the phase of matter in such objects.^1,2 Here, bulk viscosity and r-mode instabilities of strange stars will be discussed for both normal and color-superconducting phases. The effect of Urca processes³ will be emphasized.

We investigate the composition and the equation of state of the kaon condensed phase in neutrino-free and neutrino-trapped star matter within the framework of the Brueckner-Hartree-Fock approach with three-body forces. We find that neutrino trapping shifts the onset density of kaon condensation to a larger baryon density and reduces considerably the kaon abundance. As a consequence, when kaons are allowed, the equation of state of neutrino-trapped star matter becomes stiffer than the one of neutrino free matter. The effects of different three-body forces are compared and discussed. Neutrino trapping turns out to weaken the role played by the symmetry energy in determining the composition of stellar matter and thus reduces the difference between the results obtained by using different three-body forces.

The status of the P. Auger Observatory will be presented. The Fluorescence Detector has been completed and 1350 Cerenkov tanks have been already deployed and are currently taking data. The Observatory is expected to be completed by November 2007. Preliminary results on energy spectrum, small and large scale anisotropy search as well as photon flux and neutrino flux limits will be discussed.

The theory of nuclear forces has made great progress since the turn of the millenium using the framework of chiral effective field theory (ChEFT). The advantage of this approach, which was originally proposed by Weinberg, is that it has a firm basis in quantum-chromodynamics and allows for quantitative calculations. Moreover, this theory generates two-nucleon forces (2NF) and many-body forces on an equal footing and provides an explanation for the empirically known fact that 2NF ≫ 3NF ≫ 4NF. I will present the recent advances in more detail and put them into historical context. In addition, I will also provide a critical evaluation of the progress made including a discussion of the limitations of the ChEFT approach.

A non-relativisitic nuclear density functional theory is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin-orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces. For the pairing correlations, simply a density dependent zero range force is adopted from the literature. The ability of the proposed functional for describing deformed nuclei is also explored.

The structure and decay modes of the K^--condensed hypernucleus, which may be produced in the laboratory as the strangeness-conserving system, is investigated on the basis of the effective chiral Lagrangian for the kaon-baryon interaction, combined with the nonrelativistic baryon-baryon interaction model. It is shown that a large number of negative strangeness is needed for the formation of highly dense and self-bound state with K^- condensates and that part of the strangeness should be carried by hyperons. Such a self-bound object may decay only through weak processes.

The isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility and the isospin dependent term of the finite nucleus incompressibility is elucidated by using various different Skyrme Hamiltonians and RMF Lagrangians. Microscopic HF+random phase approximation (RPA) calculations are performed with Skyrme interactions for Sn isotopes to study the strength distributions of isoscalar giant monopole resonances (ISGMR). The symmetry term of nuclear incompressibility is extracted to be K_τ = -(500 ± 50) MeV from the recent experimental data of ISGMR in Sn isotopes.

In the present volume, several contributions are devoted to the study of the properties of exotic nuclear matter (nuclei at the drip lines or neutron stars) by using implementations of the Density Functional Theory (DFT) in atomic nuclei, either in the nonrelativistic or covariant formalism. In our contribution, we argue that tensor correlations are important to be included in the functionals; the necessity to include other kind of correlations, namely those associated with the particle-vibration coupling, is discussed by using the specific example of ¹³²Sn.

After a brief introduction of general aspects on the spin-isospin responses of nuclei, the ICHOR project is introduced. The ICHOR Project aims to explore the unexplored spin-isospin responses of nuclei by using the exothermic heavy-Ion charge-exchange reactions employing radioactive beams.

Charge exchange spin-dipole (SD) excitations of ⁹⁰Zr are studied by the ⁹⁰Zr(p,n) and ⁹⁰Zr(n,p) reactions at 300 MeV. A multipole decomposition technique is employed to obtain the SD strength distributions in the cross section spectra. A model-independent SD sum rule value is obtained: 148 ± 12 fm². The neutron skin thickness of ⁹⁰Zr is determined to be 0.07 ± 0.04 fm from the SD sum rule.

Based on a modified di-nuclear system model in which the nucleon transfer is coupled with dissipation of energy and angular momentum, the evaporation residue cross sections of some cold and hot fusion reactions to synthesize super-heavy nuclei are calculated. The influences of deformation and relative orientation of projectile and target are discussed. Our results show that the waist to waist orientation is in favor of the formation of super-heavy compound nuclei. The isotopic dependence of the maximal evaporation residue cross section is also investigated. The calculated results show that the cross sections do not change much with increasing neutron number of the target.

The flow velocities in a rotating neutron star crust are low compared with the speed of light, so that a Newtonian description can be used without serious loss of accuracy at a local level. However, on a larger scale it will be necessary to take account of the curvature due to the very the strong gravitational field, so that for a global treatment it will be necessary to use a fully General Relativistic description.

In this paper, we calculate the stable Wigner-Seitz (W-S) cells in the inner crust of neutron stars and we discuss the nuclear shell effects. A distinction is done between the shell effects due to the bound states and those induced by the unbound states, which are shown to be spurious. We then estimate the effects of the spurious shells on the total energy and decompose it into a smooth and a residual part. We propose a correction to the Hartree-Fock binding energy in Wigner-Seitz cell (HF-WS).

We map out the temperature-density (T – n) phase diagram of an infinitely extended fermion system with pairwise interactions that support two-body (dimer) and three-body (trimer) bound states in free space. Adopting interactions representative of nuclear systems, we determine the critical temperature T_cs for the superfluid phase transition and the limiting temperature T_ce3 for the extinction of trimers. The phase diagram at subnuclear densities features a Cooper-pair condensate in the higher-density, low-temperature domain; with decreasing density there is a crossover to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers. The trimer binding energy decreases as the point (T,n) moves toward the domain occupied by the superfluid and vanishes at a critical temperature T_ce3 > T_cs. The ratio of the trimer and dimer binding energies is found to be a constant independent of temperature.

Medium effects on ¹S₀ pairing in neutron and nuclear matter are studied in a microscopic approach. The screening potential is calculated in the RPA limit, suitably renormalized to cure the low density mechanical instability of nuclear matter. The selfenergy corrections are consistently included resulting in a strong depletion of the Fermi surface. The selfenergy corrections always lead to a quenching of the gap, which is enhanced by the screening effect of the pairing potential in neutron matter, whereas it is almost completely compensated by the antiscreening effect in nuclear matter.

We investigate when the energy that pins a superfluid vortex to the lattice of nuclei in the inner crust of neutron stars can be approximated by the energy that binds the vortex to a single nucleus. Indeed, although the pinning energy is the quantity relevant to the theory of pulsar glitches, so far full quantum calculations have been possible only for the binding energy. Physically, the presence of nearby nuclei can be neglected if the lattice is dilute, namely with nuclei sufficiently distant from each other. We find that the dilute limit is reached only for quite large Wigner-Seitz cells, with radii R_WS ≳ 55 fm; these are found only in the outermost low-density regions of the inner crust. We conclude that present quantum calculations do not correspond to the pinning energies in almost the entire inner crust and thus their results are not predictive for the theory of glitches.

We study the vortex-nucleus interaction in the inner crust of neutron stars within the framework of quantum mean field theory. We use the SLy4 Skyrme interaction in the particle-hole channel, and a density dependent contact interaction in the particle-particle channel. We discuss the results obtained for the spatial dependence of the pairing gap and the density dependence of the pinning energy. A comparison with a semiclassical model is also presented.

The energetically-preferred rotational state of the inner-crust superfluid (SF) involves pinning of the neutron vortices to the lattice through a vortex-nucleus interaction. The question of whether or not vortices actually reach this state is crucial toward understanding the rotational modes of a neutron star (NS). I describe the physics of relaxation of unpinned vortices to the pinned state and show that vortices can pin only if the differential velocity between the SF and the solid is very low, ≲ 10 cm s^-1. I argue that the pinned state is possibly dynamically inaccessible in a typical NS. I conclude with discussion of the implications for understanding NS spin jumps and long-period precession (nutation).

Due to the difficulty of hydrodynamic simulations to reproduce type II supernovae explosions, we investigate possible missing microscopic physics, such as neutrino trapping near the critical temperature of the nuclear liquid-gas phase transition, temperature dependant neutrino mean free paths or electron capture rates on nuclei to evaluate the impact on the improvement of the supernova outgoing shock propagation.

The parity doublet model containing the SU(2) multiplets including the baryons identified as the chiral partners of the nucleons is applied for neutron star matter. The chiral restoration is analyzed and the maximum mass of the star is calculated.

The transition to the quark phase in the core of a neutron star is studied with both Maxwell and Glendenning construction. The hadron phase is described within the Brueckner theory with three body forces. For the confined quark phase we adopt the Density Dependent Quark Mass Model, which is consistent with chiral symmetry requirements.

A nuclear three-body force based on the meson-exchange approach is constructed using the same meson parameters and the exponential form factors as in the Nijmegen potential, involving four kinds of important mesons, π, ρ, ω, and σ [f₀(975) and ∊(760)]. For the 2π-exchange three-nucleon component, we adopt the new expansion strength constants a, b, c consistent with the contemporary πN-scattering data base and the corresponding dipole form factor. An effective two-body interaction is derived by averaging out the third nucleon, and is self-consistently used together with the Nijmegen potential in the Brueckner-Hartree-Fock approximation. The empirical nuclear matter saturation properties are reproduced very well. At higher density the equation of state becomes rather stiff due to the strong repulsion from the (σ, ω)-N three-body contribution.

We present results for the monopole excitation strength function in tin isotopes obtained by means of a self-consistent Quasiparticle-Random-Phase-Approximation (QRPA) which employs the canonical Skyrme-Hartree-Fock-Bogoliubov (HFB) basis. The effect of pairing correlations on the monopole excitation strength function, and centroid energy, is studied by comparing with the results of RPA.

The effects of scalar-isovector meson δ field on the neutron star matter is investigated in the framework of relativistic mean field (RMF) theory. We find that the δ-field reduces the binding energy per baryon and enhances the strangeness contents of the neutron star. The moment of inertia of neutron stars is enhanced by including the δ-field.

We show that the magnetization in color-flavor locked superconductors can be so strong that homogeneous quark matter becomes metastable for a wide range of magnetic field values. This indicates that magnetic domains or other type of magnetic inhomogeneities can be present in the quark cores of magnetars.

The gap equation for ¹S₀ NN-pairing is solved for a nuclear slab with two realistic bare NN-interactions, the separable form of the Paris potential and the Argonne potential v₁₈. For solving the gap equation the renormalization method based on the effective pairing interaction concept is used. Calculations are performed for various values of the chemical potential μ in the range from -8 MeV, which corresponds to stable nuclei, to -0.1 MeV which corresponds to nuclei in the vicinity of the drip line. A detailed comparison of the results for two nuclear potentials is performed.

Recently, it has been shown that the standard Nambu-Jona-Lasinio (NJL) model is not able to reproduce the correct QCD behavior of the gap equation at large density, and therefore a different cutoff procedure at large momenta has ben proposed. We found that, even with this density dependent cutoff procedure, the pure quark phase in neutron stars (NS) interiors is unstable, and we argue that this could be related to the lack of confinement in the original NJL model.

The following sections are included:

• Acknowledgments

• References

Exploring the isospin dependence of the nuclear matter is one of the main challenges of modern nuclear physics. The ab initio calculations are the proper tool for these investigations. Results of the Dirac-Brueckner-Hartree-Fock calculations for asymmetric nuclear matter, which are based on improved approximation schemes, are presented. Furthermore, the application to finite nuclei is discussed.

We perform two-dimensional, magneto-hydrodynamical simulations of "petit" collapse and bounce of neutron stars by QCD phase transition. We study how the phase transition affects the elements of the ejecta near the epoch of core-bounce. We find that the elements of envelope can eject without nucleosynthesis for such a "petit" collapse and bounce by the transition. In addition, we estimate the gravitational wave using the quadrupole formula.

We provide a microscopic calculation of neutron-proton and proton-proton cross sections in symmetric nuclear matter at various densities, using the Brueckner-Hartree-Fock approximation scheme with the Argonne V₁₄ potential including the contribution of microscopic three body force. In the present calculation, the rearrangement contribution of three body force is considered, which will reduces the neutron and proton effective mass, and suppresses the amplitude of cross section. The effect of three body force is shown to be repulsive, especially in high densities and large momenta, which will suppress the cross section markedly.

In the attempt to reach a global view of the effects on single-particle states caused by the tensor interaction, we analyze the evolution of the spin-orbit splittings in the Ca isotopes and in the N = 28 isotones.

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