Normal Nuclear Matter Research Articles

Measurement of the Pseudorapidity and Centrality Dependence of the Transverse Energy Density in Pb-Pb Collisions atsNN=2.76 TeV

The transverse energy (E(T)) in Pb-Pb collisions at 2.76 TeV nucleon-nucleon center-of-mass energy (√(s(NN)) has been measured over a broad range of pseudorapidity (η) and collision centrality by using the CMS detector at the LHC. The transverse energy density per unit pseudorapidity (dE(T)/dη) increases faster with collision energy than the charged particle multiplicity. This implies that the mean energy per particle is increasing with collision energy. At all pseudorapidities, the transverse energy per participating nucleon increases with the centrality of the collision. The ratio of transverse energy per unit pseudorapidity in peripheral to central collisions varies significantly as the pseudorapidity increases from η=0 to |η|=5.0. For the 5% most central collisions, the energy density per unit volume is estimated to be about 14 GeV/fm(3) at a time of 1 fm/c after the collision. This is about 100 times larger than normal nuclear matter density and a factor of 2.6 times higher than the energy density reported at √(s(NN))=200 GeV at the Relativistic Heavy Ion Collider.

ISOSPIN DEPENDENCE OF THE SATURATION PROPERTIES OF ASYMMETRIC NUCLEAR MATTER IN NONRELATIVISTIC MEAN FIELD MODEL

A phenomenological momentum dependent interaction (MDI) is considered to describe the equation of state (EOS) for isospin asymmetric nuclear matter (ANM), where the density dependence of the nuclear symmetry is the basic input. In this interaction, the symmetry energy shows soft dependence of density. Within the nonrelativistic mean field approach we calculate the nuclear matter fourth-order symmetry energy E sym, 4 (ρ). Our result shows that the value of E sym, 4 (ρ) at normal nuclear matter density ρ0( = 0.161 fm -3) is less than 1 MeV conforming the empirical parabolic approximation to the EOS of ANM at ρ0. Then the higher-order effects of the isospin asymmetry on the saturation density ρ sat (β), binding energy per nucleon K sat (β) and isobaric incompressibility K sat (β) of ANM is being studied, where [Formula: see text] is the isospin asymmetry. We have found that the fourth-order isospin asymmetry β cannot be neglected, while calculating these quantities. Hence the second-order K sat , 2 parameter basically characterizes the isospin dependence of the incompressibility of ANM at saturation density.

Solving a relativistic hydrodynamic equation in the presence of a magnetic field for a phase transition in a neutron star

A hadronic to quark matter phase transition may occur inside neutron stars having the central densities of the order of three to ten times the normal nuclear matter saturation density (n0). The transition is expected to be a two-step process; transition from hadronic matter to two-flavour matter and two-flavour matter to β equilibrated charge neutral three-flavour matter. In this paper, we concentrate on the first step of the process and solve the relativistic hydrodynamic equations for the conversion front in the presence of a high magnetic field. The Lorentz force due to the magnetic field is included in the energy–momentum tensor by averaging over the polar angles. We find that for an initial dipole configuration of the magnetic field with a sufficiently high value at the surface, the velocity of the front increases considerably.

Nuclear thermodynamics and the in-medium chiral condensate

The temperature dependence of the chiral condensate in isospin-symmetric nuclear matter at varying baryon density is investigated using thermal in-medium chiral effective field theory. This framework provides a realistic approach to the thermodynamics of the correlated nuclear many-body system and permits calculating systematically the pion-mass dependence of the free energy per particle. One- and two-pion exchange processes, Δ(1232)-isobar excitations, Pauli-blocking corrections and three-body correlations are treated up to and including three loops in the expansion of the free energy density. It is found that nuclear matter remains in the Nambu–Goldstone phase with spontaneously broken chiral symmetry in the temperature range T≲100 MeV and at baryon densities at least up to about twice the density of normal nuclear matter, 2ρ0≃0.3 fm−3. Effects of the nuclear liquid–gas phase transition on the chiral condensate at low temperatures are also discussed.

Constraints on the symmetry energy and neutron skins from experiments and theory

The symmetry energy contribution to the nuclear Equation of State (EoS) impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and its density dependence at and somewhat below normal nuclear matter density. Some of these constraints have been derived from properties of nuclei. Others have been derived from the nuclear response to electroweak and hadronic probes. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how the contribution of the three-body force, an essential ingredient in neutron matter models, can be determined.

Equilibrium structure and radial oscillations of dark matter admixed neutron stars

In Phys. Rev. D 84, 107301 (2011), we presented our results on using a general relativistic two-fluid formalism to study the hydrostatic equilibrium configuration of an admixture of degenerate dark matter and normal nuclear matter. In this work, we present more analysis to complement our previous findings. We study the radial oscillation modes of these compact stars in detail. We find that these stars in general have two classes of oscillation modes. For a given total mass of the star, the first class of modes is insensitive to the dark-matter particle mass. They also reduce properly to the oscillation modes of the corresponding ordinary neutron star, with the same total mass, when the mass fraction of dark matter tends to zero. On the other hand, the second class of modes is due mainly to the dark-matter fluid. In the small dark-matter mass fraction limit, these modes are characterized purely by the oscillations of dark matter, while the normal matter is essentially at rest. In the intermediate regime where the mass fractions of the two fluids are comparable, the normal matter oscillates with the dark matter due to their coupling through gravity. In contrast to the first class of modes, the frequencies of these dark-matter dominated modes depend sensitively on the mass of dark-matter particles.

Nuclear matter fourth-order symmetry energy in the relativistic mean field models

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{sym,4}(\rho)$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{sym,4}(\rho)$ at normal nuclear matter density $\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\rho_{0}$. On the other hand, we find that the $E_{sym,4}(\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{sym,4}(\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{sat}(\delta)=K_{0}+K_{sat,2}\delta ^{2}+K_{sat,4}\delta ^{4}+\mathcal{O}(\delta ^{6})$ where $\delta =(\rho_{n}-\rho_{p})/\rho $ is the isospin asymmetry, and we find that the value of $K_{sat,4}$ is generally small compared with that of the $K_{sat,2}$. In addition, we study the effects of the $E_{sym,4}(\rho)$ on the proton fraction $x_{p}$ and the core-crust transition density $\rho_{t}$ and pressure $P_{t}$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{sym,4}(\rho)$ contribution can significantly enhance the $x_{p}$ at high densities and strongly reduce the $\rho_{t}$ and $P_{t}$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_{p}$ at high densities as well as the $\rho_{t}$ and $P_{t}$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.

Formation and Evolution of Neutron Star Binaries: Masses of Neutron Stars

Neutron star (NS) is one of the most interesting astrophysical compact objects for hardronic physics. It is believed that the central density of NS can reach several times the normal nuclear matter density ( ρ 0). Hence, the inner part of NS is the ultimate testing place for the physics of dense matter. Recently, the mass of NS in a NS-white dwarf (WD) binary PSR J1614-2230 has been estimated to be 1.97 ± 0.04 M ๏ [1]. Since this estimate is based on the observed Shapiro delay, it can give the lower limit of the maximum NS mass and rules out many soft equations of state. On the other hand, all the well-measured NS masses in NS-NS binaries are smaller than 1.5 M ๏ . In this work, by introducing the supercritical accretion during the binary evolution, we propose a possibility of forming higher mass NS in NS-WD binaries. In this scenario, the lifetimes of NS and WD progenitors are significantly different, and NS in NS-WD binary can accrete > 0.5 M ๏ after NS formation during the giant phase of the progenitor of WD. On the other hand, for the binary system with NS and heavier (> 8 M ๏ ) giants, the first-born NS will accrete more from the companion and can collapse into black hole. The only way to avoid the supercritical accretion is that the initial masses of progenitors of NS binary should be very close so that they evolve almost at the same time and don’t have time to accrete after NS formation.

Nuclear chiral dynamics and phases of QCD

This presentation starts with a brief review of our current picture of QCD phases, derived from lattice QCD thermodynamics and from models based on the symmetries and symmetry breaking patterns of QCD. Typical approaches widely used in this context are the PNJL and chiral quark-meson models. It is pointed out, however, that the modeling of the phase diagram in terms of quarks as quasiparticles misses important and well known nuclear physics constraints. In the hadronic phase of QCD governed by confinement and spontaneously broken chiral symmetry, in-medium chiral effective field theory is the appropriate framework, with pions and nucleons as active degrees of freedom. Nuclear chiral thermodynamics is outlined and the liquid–gas phase transition is described. The density and temperature dependence of the chiral condensate is deduced. As a consequence of two- and three-body correlations in the nuclear medium, no tendency towards a first-order chiral phase transition is found at least up to twice the baryon density of normal nuclear matter and up to temperatures of about 100 MeV. Isospin-asymmetric nuclear matter and neutron matter are also discussed. An outlook is given on new tightened constraints for the equation-of-state of cold and highly compressed matter as implied by a recently observed two-solar-mass neutron star.

Dark-matter admixed neutron stars

We study the hydrostatic equilibrium configuration of an admixture of degenerate dark matter and normal nuclear matter by using a general relativistic two-fluid formalism. We consider non-self-annihilating dark matter particles of mass $\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$. The mass-radius relations and moments of inertia of these dark-matter admixed neutron stars are investigated and the stability of these stars is demonstrated by performing a radial perturbation analysis. We find a new class of compact stars which consists of a small normal matter core with radius of a few kilometers embedded in a ten-kilometer-sized dark matter halo. These stellar objects may be observed as extraordinarily small neutron stars that are incompatible with realistic nuclear matter models.

Dense stellar matter with strange quark matter driven by kaon condensation

The core of neutron-star matter is supposed to be at a much higher density than the normal nuclear matter density for which various possibilities have been suggested such as, for example, meson or hyperon condensation and/or deconfined quark or color-superconducting matter. In this work, we explore the implication on hadron physics of a dense compact object that has three "phases", nuclear matter at the outer layer, kaon condensed nuclear matter in the middle and strange quark matter at the core. Using a drastically simplified but not unreasonable model, we develop the scenario where the different phases are smoothly connected with the kaon condensed matter playing a role of "doorway" to a quark core, the equation of state (EoS) of which with parameters restricted within the range allowed by nature could be made compatible with the mass vs. radius constraint given by the 1.97-solar mass object PSR J1614-2230 recently observed.

Pion Electromagnetic Form Factor and ??-meson Mass Shift at Finite Density

We investigate the pion electromagnetic charge radii and mass dropping of themeson at finite density. We first calculate the pion charge radii within the framework of the nonlocal chiral quark model from the instanton vacuum both at zero and finite densities. In order to relate the change of the pion charge radius to that of the �-meson mass at finite density, we employ the vector-meson dominance for the pion electromagnetic form factor. It turns out that the pion charge radius is getting larger as the quark chemical potential increases. As a result, the �-meson mass falls off as the quark chemical potential grows and is found to be dropped by about 10% at normal nuclear matter density: m � /m� ≈ 1 − 0.12µB/µ0, which is compatible to the results of the measurement

Effects of a weakly interacting light U boson on the nuclear equation of state and properties of neutron stars in relativistic models

We investigate the effects of the light vector U boson that couples weakly to nucleons in relativistic mean-field models on the equation of state and subsequently the consequence in neutron stars. It is analyzed that the U boson can lead to a much clearer rise of the neutron star maximum mass in models with the much softer equation of state. The inclusion of the U boson may thus allow the existence of the non-nucleonic degrees of freedom in the interior of large mass neutron stars initiated with the favorably soft EOS of normal nuclear matter. In addition, the sensitive role of the U boson in the neutron star radius and its relation to the test of the non-Newtonian gravity that is herein addressed by the light U boson are discussed.

THE PROPERTIES OF THE ${\bar K}^*$ MESON IN DENSE MATTER

In this talk we review the properties of [Formula: see text] mesons in nuclear matter. A unitary approach in coupled channels within the framework of the local hidden gauge formalism is used to account for the interaction of the antikaon with the nucleons and the [Formula: see text] decay channel is incorporated in matter. The in-medium [Formula: see text] interaction accounts for Pauli blocking effects and the inclusion of the [Formula: see text] self-energy in a self-consistent manner. At normal nuclear matter density, the [Formula: see text] meson feels a moderately attractive potential while the [Formula: see text] width increases enormously becoming up to five times larger than in free space. We also perform the transparency ratio for the γA → K+K*-A′ reaction, which can be a feasible scenario in experimental facilities.

Formula omitted] mass shift in nuclear matter

The J/Ψ mass shift in cold nuclear matter is computed using an effective Lagrangian approach. The mass shift is computed by evaluating D and D⁎ meson loop contributions to the J/Ψ self-energy employing medium-modified meson masses. The modification of the D and D⁎ masses in nuclear matter is obtained using the quark–meson coupling model. The loop integrals are regularized with dipole form factors and the sensitivity of the results to the values of form-factor cutoff masses is investigated. The J/Ψ mass shift arising from the modification of the D and D⁎ loops at normal nuclear matter density is found to range from −16 MeV to −24 MeV under a wide variation of values of the cutoff masses. Experimental perspectives for the formation of a bound state of J/Ψ to a nucleus are investigated.

Charm Hadrons in Dense Matter

The properties of the D and Ds charmed mesons in normal nuclear matter density are studied within a coupled channel approach using a t-channel vector-meson exchange mechanism as driving force. The in-medium scattering amplitudes are obtained by solving the Lippmann–Schwinger equation including Pauli blocking effects and medium self-energies in a self-consistent way.

COLD COMPRESSED BARYONIC MATTER WITH HIDDEN LOCAL SYMMETRY AND HOLOGRAPHY

I describe a novel phase structure of cold dense baryonic matter predicted in a hidden local symmetry approach anchored on gauge theory and in a holographic dual approach based on the Sakai-Sugimoto model of string theory. This new phase is populated with baryons with half-instanton quantum number in the gravity sector which is dual to half-skyrmion in gauge sector in which chiral symmetry is restored while light-quark hadrons are in the color-confined phase. It is suggested that such a phase that aries at a density above that of normal nuclear matter and below or at the chiral restoration point can have a drastic influence on the properties of hadrons at high density, in particular on short-distance interactions between nucleons, e.g., multi-body forces at short distance and hadrons – in particular kaons – propagating in a dense medium. Potentially important consequences on the structure of compact stars will be predicted.

(P)arity violation in QCD motivated hadronic models at extreme conditions

We investigate the possibility of parity being spontaneously violated in QCD at finite baryon density and temperature. QCD is approximated by a generalized σ model with two isomultiplets of scalars and pseudoscalars. The mechanism of parity violation is based on interplay between lightest and heavier degrees of freedom and it cannot be understood in simple models retaining the pion and nucleon sectors solely. We argue that, in the dense and hot nuclear matter of a few normal densities and moderate temperatures, parity violation may arise due to a second-order phase transition and its occurrence is well compatible with the existence of stable bound state of normal nuclear matter.

K̄*mesons in dense matter

We study the properties of ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ mesons in nuclear matter using a unitary approach in coupled channels within the framework of the local hidden gauge formalism and incorporating the $\mathrm{K\ifmmode \bar{}\else \={}\fi{}}\ensuremath{\pi}$ decay channel in matter. The in-medium ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}N$ interaction accounts for Pauli blocking effects and incorporates the ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ self-energy in a self-consistent manner. We also obtain the ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ (off-shell) spectral function and analyze its behavior at finite density and momentum. At a normal nuclear matter density, the ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ meson feels a moderately attractive potential, while the ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ width becomes five times larger than in free space. We estimate the transparency ratio of the $\ensuremath{\gamma}A\ensuremath{\rightarrow}{K}^{+}{K}^{*\ensuremath{-}}{A}^{\ensuremath{'}}$ reaction, which we propose as a feasible scenario at the present facilities to detect changes in the properties of the ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{*}$ meson in nuclear medium.

In-mediumωmass from theγ+Nb→π0γ+Xreaction

Data on the photoproduction of $\omega$ mesons on nuclei have been re-analyzed in a search for in-medium modifications. The data were taken with the Crystal Barrel(CB)/TAPS detector system at the ELSA accelerator facility in Bonn. First results from the analysis of the data set were published by D. Trnka et al. in Phys. Rev. Lett 94 (2005) 192303 \cite{david}, claiming a lowering of the $\omega$ mass in the nuclear medium by 14$%$ at normal nuclear matter density. The extracted $\omega$ line shape was found to be sensitive to the background subtraction. For this reason a re-analysis of the same data set has been initiated and a new method has been developed to reduce the background and to determine the shape and absolute magnitude of the background directly from the data. Details of the re-analysis and of the background determination are described. The $\omega$ signal on the $Nb$ target, extracted in the re-analysis, does not show a deviation from the corresponding line shape on a $LH_2$ target, measured as reference. The earlier claim of an in-medium mass shift is thus not confirmed. The sensitivity of the $\omega$ line shape to different in-medium modification scenarios is discussed.