Phase Transition In Nuclear Matter Research Articles

Signatures of quark deconfinement through the r -modes of twin stars

The observation and distinction of two compact stars with an identical mass but a different radius would be a clear sign of hadron-quark phase transition in nuclear matter. Motivated by studies searching for significant deviations in the observables of twin stars, we investigate the differences that manifest in their $r$-mode instability windows and spin-down evolution. Firstly, we obtain a set of hybrid equations of state (which predict the existence of a third stable branch of compact objects) by employing the well-known Maxwell construction within the phenomenological framework of constant speed of sound parametrization. Then, we systematically study the influence of certain parameters, such as the energy density jump (in the resulting hybrid equation of state) and the crust elasticity, on the deviations appearing in the $r$-mode instability windows and spin-down evolution of twin stars. We conclude that two stars with an identical mass and fairly similar spin frequency and temperature, may behave differently with respect to $r$-modes. Thus, the future possible detection of gravitational waves (due to unstable $r$-modes) from a star laying in the stable region of the frequency-temperature plane would be a strong indication for the existence of twin stars. Furthermore, we consider current data for the spin frequencies and temperatures of observed pulsars and compare them to the predictions made from equations of state employed in this study. We find that, depending on the transition density and the rigidness of the crust, hybrid equations of state may be a viable solution for the explanation of existing data.

Fractal Entropy of Nuclear Medium Probed by KS0 Mesons Produced in AuAu Collisions at RHIC

In this paper, we review our findings concerning fractal entropy of microscopic configurations corresponding to the production of KS0 mesons in AuAu collisions in the z-scaling approach. The entropy is expressed via structural and fragmentation fractal dimensions, and model parameter cAuAu is interpreted as a specific heat of produced medium. These parameters are related to the respective momentum fractions of the colliding nuclei, the momentum fractions of the scattered constituents that fragment into the produced hadrons, and the multiplicity density of negative particles in the central interaction region. The dependence of the entropy on the collision energy over the range of 7.7–200 GeV for most central and most peripheral events is studied as a function of the transverse momentum of the produced KS0 mesons. A non-trivial dependence of the entropy on the collision energy with decreasing transverse momentum is found. This reflects the irregularity of the behavior of the specific heat, cAuAu, and can point to a manifestation of phase transition in nuclear matter.

Speed of sound and liquid-gas phase transition in nuclear matter

We investigate the speed of sound in nuclear matter at finite temperature and density (chemical potential) in the nonlinear Walecka model. The numerical results suggest that the behaviors of sound speed are closely related to the the nuclear liquid-gas (LG) phase transition and the associated spinodal structure. The adiabatic sound speed is nonzero at the critical endpoint (CEP) in the mean-field approximation. We further derive the boundary of vanishing sound velocity in the temperature-density phase diagram, and point out the region where the sound wave equation is broken. The distinction between the speed of sound in nuclear matter and that in quark matter contains important information about the equation of state of strongly interacting matter at intermediate and high density. We also formulate the relations between differently defined speeds of sound using the fundamental thermodynamic relations.

First indication on self-similarity of strangeness production in Au+Au collisions at RHIC: Search for signature of phase transition in nuclear matter

New results of analysis of K^0_S-KS0−meson spectra measured over a wide range of energy \sqrt {s_{NN}}=7.7-200sNN=7.7−200 GeV and centrality in Au+AuAu+Au collisions by the STAR Collaboration at RHIC using the zz-scaling approach are presented. Indication on self-similarity of fractal structure of nuclei and fragmentation processes with K^0_SKS0 probe is demonstrated. The energy loss as a function of the collision energy, centrality and transverse momentum of the inclusive strange meson is estimated.

Probing the boundary of phase transition of nuclear matter using proton flows in heavy-ion collisions at 2-8 GeV/nucleon

Based on the relativistic transport model ART with the hadronic equation of state extended to have a phase transition via the use of the MIT bag model, properties of phase transition of dense nuclear matter formed in relativistic heavy-ion collisions are investigated. Proton sideward and directed flows are calculated with different equation of states in Au + Au collisions at beam energies of 2, 4, 6 and 8 GeV/nucleon. Compared with AGS experimental data in existence, the boundary of first-order phase transition is roughly confined, i.e., in the range of 2.5-4 times saturation density with temperature about 64-94 MeV. Such constraints are useful for ongoing RHIC Beam Energy Scan-II program to study the QCD matter phase diagram.

Equation of state for hot QCD and compact stars from a mean-field approach

The thermodynamic properties of high temperature and high density QCD-matter are explored within the Chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the $\mu_B=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature/chemical potential plane. The CMF model predicts three consecutive transitions, the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the cross-over transition to a quark-dominated phase. All three phenomena are cross-over, for most of the $T-\mu_B$-plane. The deviations from the free ideal hadron gas baseline at $\mu_B=0$ and $T\approx 100-200$ MeV can be attributed to remnants of the liquid-vapor first order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher $\mu_B\approx1.5$ GeV, and at even higher baryon densities $\mu_B\approx2.4$ GeV, the behavior of fluctuations is controlled by the deconfinement cross-over. The CMF model also describe well the static properties of high $\mu_B$ neutron stars as well as the new neutron star merger observations. The effective EoS presented here describes simultaneously lattice QCD results at $\mu_B=0$, as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong0$ and high densities, $\mu_B>1$ GeV.

Tidal deformability of an anisotropic compact star: Implications of GW170817

We use gravitational wave (GW) and electromagnetic (EM) observations of GW170817 to constrain the extent of pressure anisotropy in it. While it is quite likely that the pressure inside a neutron star is mostly isotropic, certain physical processes or characteristics, such as phase transitions in nuclear matter or the presence of strong magnetic fields, can introduce pressure anisotropy. In this work, we show that anisotropic pressure in neutron stars can reduce their tidal deformability substantially. For the anisotropy-pressure model of Bowers and Liang and a couple of relativistic EOSs -- DDH$\delta$ and GM1 -- we demonstrate that this reduction in spherical neutron stars with masses in the range of 1 to 2 $M_\odot$ can be 23% to 46%. This suggests that certain EOSs that are ruled out by GW170817 observations, under assumptions of pressure isotropy, can become viable if the stars had a significant enough anisotropic pressure component, but do not violate causality. We also show how the inference of the star radius can be used to rule out certain EOSs (such as GM1), even for high anisotropic pressure, because their radii are larger than what the observations find.

Highlights from the STAR experiment

The STAR experiment at the Relativistic Heavy Ion Collider (RHIC) studies properties and phase transitions of nuclear matter in various nucleus-nucleus collisions at center-of-mass energies per nucleon collision sNN=7.7-200GeV. With a fixed target made of gold foils installed inside the beam pipe, STAR also starts to explore high baryon density regime (μB≈420-720MeV) at sNN=3.0-7.7GeV. A few selected results reported by the STAR collaboration at the Quark Matter 2018 (QM2018) conference are described in these proceedings.

Spectra of negative particles in Au+Au collisions from BES-I at RHIC and z-scaling

Negative particle yields in Au + Au collisions obtained by the STAR Collaboration from BES-I at RHIC are analyzed in the framework of the z-scaling approach. The spectra were measured over a wide range of collision energy $\sqrt {{s_{NN}}} = 7.7 - 200\,{\rm{GeV}}$ and transverse momentum of produced particles for different centralities at $\left| \eta \right| \lt 0.5$. The scaling behavior of the spectra as a function of the collision energy and centrality in z-presentation is verified. The constituent energy loss in dependence on the energy and centrality of collision and transverse momentum of inclusive particle is estimated. New indication on self-similarity of fractal structure of nuclei and fragmentation process is found. A discontinuity of the model parameters - fractal and fragmentation dimensions and specific heat - is considered from the point of view of a phase transition in nuclear matter.

Effect of external magnetic fields on nucleon mass in a hot and dense medium: Inverse magnetic catalysis in the Walecka model

Vacuum to nuclear matter phase transition has been studied in presence of constant external background magnetic field with the mean field approximation in Walecka model. The anomalous nucleon magnetic moment has been taken into account using the modified "weak" field expansion of the fermion propagator having non-trivial correction terms for charged as well as for neutral particles. The effect of nucleon magnetic moment is found to favour the magnetic catalysis effect at zero temperature and zero baryon density. However, extending the study to finite temperatures, it is observed that the anomalous nuclear magnetic moment plays a crucial role in characterizing the qualitative behaviour of vacuum to nuclear matter phase transition even in case of the weak external magnetic fields . The critical temperature corresponding to the vacuum to nuclear medium phase transition is observed to decrease with the external magnetic field which can be identified as the inverse magnetic catalysis in Walecka model whereas the opposite behaviour is obtained in case of vanishing magnetic moment indicating magnetic catalysis.

Dynamical Phase Transition in Neutron Stars

Abstract We have studied the dynamical evolution of the shock in a neutron star (NS). The conversion of nuclear to quark matter (QM) is assumed to take place at the shock discontinuity. The density and pressure discontinuity is studied both spatially and temporally as it starts near the center of the star and moves toward the surface. Polytropic equations of state (EoS), which mimic original nuclear and QM EoS, are used to study such dynamical phase transition (PT). Solving relativistic hydrodynamic equations for a spherically symmetric star, we study the PT, assuming a considerable density discontinuity near the center. We find that as the shock wave propagates outward, its intensity decreases with time; however, the shock velocity peaks up and reaches a value close to that of light. Such fast shock velocity indicates rapid PT in NS taking place on a timescale of some 10s of microseconds. Such a result is quite interesting, and it differs from previous calculations that the PT in NSs takes at least some 10s of milliseconds. Rapid PT can have significant observational significance, because such fast PT would imply rather strong gravitational wave (GW) signals that are rather short lived. Such short-lived GW signals would be accompanied with short-lived gamma-ray bursts and neutrino signals originating from the neutrino and gamma-ray generation from the PT of nuclear matter to QM.

Effect of the Coulomb interaction on the liquid-gas phase transition of nuclear matter

We investigate the role of the Coulomb interaction on the liquid-gas phase transition of nuclear matter with three different values of proton fraction ($Y_p$=0.5,0.3 and 0.1), relevant for heavy-ion physics as well as various astrophysical scenarios, within the framework of quantum molecular dynamics. We perform simulations for a wide range of density and temperature with and without the Coulomb interaction and calculate the two-point correlation functions of nucleon density fluctuations for all the configurations to determine the phase transition region. We also determine the critical end point of the liquid-gas phase transition for all three values of proton fraction considered. We observe that the Coulomb interaction reduces the transition temperature by about 2 MeV for nuclear matter with $Y_p$=0.5 and 0.3 and by about 1 MeV for nuclear matter with $Y_p$=0.1. However, the critical density is found to be more or less insensitive to the Coulomb interaction.

Hot magnetized nuclear matter: Thermodynamic and saturation properties

We have used a realistic nuclear potential, AV18, and a many body technique, the lowest order constraint variational (LOCV) approach, to calculate the properties of hot magnetized nuclear matter. By investigating the free energy, spin polarization parameter, and symmetry energy, we have studied the temperature and magnetic field dependence of the saturation properties of magnetized nuclear matter. In addition, we have calculated the equation of state of magnetized nuclear matter at different temperatures and magnetic fields. It was found that the flashing temperature of nuclear matter decreases by increasing the magnetic field. In addition, we have studied the effect of the magnetic field on liquid gas phase transition of nuclear matter. The liquid gas coexistence curves, the order parameter of the liquid gas phase transition, and the properties of critical point at different magnetic fields have been calculated.

The hadron production inπ−-C interaction at 40 GeV/c and QCD phase transition

In this paper, we proposed to study the phase transition process to use the new pair of variables, the temperature T and the cumulative number n c (T, n c ). We considered the transverse energy spectra of protons and π − -mesons produced in π − -C interactions at 40 GeV/c as a function of cumulative number n c (or four-dimensional momentum transfer t) and the baryonic chemical potential μ b (√ t ). Obtained results indicate the possible appearance of QCD phase transition of nuclear matter.

Heavy-ion collisions in a fixed target mode at the LHC beams

The interaction of high-energy LHC beams with fixed target, including polarized nuclei targets, can expand the range of fundamental physical investigations accessible at CERN. High-intensity beam of protons and lead ions accumulated in the LHC collider allows to apply the gas-target system like the LHCb SMOG or HERMES systems. It is also possible to use the beam halo by placing in the halo the fixed target in the form of thin ribbon or use a bend crystal to extract the beam. In the extracted beam it is possible to install a polarized target. Using the proton and ion beams of the LHC with fixed targets, the data in the energy interval between maximum energy of the SPS and the nominal RHIC energy in p-A and A-A collisions could be obtained. The fixed target mode allows the intensive study of rare processes, the study of polarization phenomena, the measurements of the parameters needed to analyze the data of cosmic rays and neutrino astrophysics, detailed study of the processes of quarkonia production and suppression. The high statistics data on quarkonium production at these energies will give the possibility to clarify the mechanism of production, to investigate the importance of recombination process and the energy dependence on the phase transition of nuclear matter to the quark-gluon phase. Also the physical program includes the study of the Drell-Yan process, D-meson production, flow and spin physics.

Shear-viscosity-to-entropy-density ratio and phase transition in multifragmentation of quasiprojectile

Heavy-ion collisions at relativistic energy are studied by the isospin-dependent quantum molecular dynamics model in the company of the GEMINI model. The present study mainly focuses on the liquid-gas phase transition in nuclear matter. We calculate the shear-viscosity-to-entropy-density ratio \( \eta /s\), \( \gamma_{2}\) and the multiplicity of intermediate-mass fragment (\( M_{IMF}\)) in finite-size nuclear sources. At excitation energy 8 MeV a minimum of \( \eta /s\) is found in the coexistence phase of intermediate-mass fragments and light particles. At similar excitation energy a maximum of the \( M_{IMF}\) is also observed at the same density condition which is an indication of the liquid-gas phase transition.

New results on relativistic nucleus-nucleus collisions and plans for their future studies

A comparative analysis of the results of the most recent experiments devoted to studying collisions of high-energy nuclei at the Large Hadron Collider (LHC), Relativistic Heavy Ion Collider (RHIC), and Super Proton Synchrotron (SPS) is performed. It is shown that, despite a significant amount of experimental data, conditions necessary for the phase transition from normal to quark-gluon matter have not yet been determined. New experiments planned for the near future that are intended to cover a broad interval of energies of colliding nuclei of different mass with the aim of studying phase transitions in nuclear matter are discussed.

Effects of the liquid-gas phase transition and cluster formation on the symmetry energy

Various definitions of the symmetry energy are introduced for nuclei, dilute nuclear matter below saturation density and stellar matter, which is found in compact stars or core-collapse supernovae. The resulting differences are exemplified by calculations in a theoretical approach based on a generalized relativistic density functional for dense matter. It contains nucleonic clusters as explicit degrees of freedom with medium-dependent properties that are derived for light clusters from a quantum statistical approach. With such a model the dissolution of clusters at high densities can be described. The effects of the liquid-gas phase transition in nuclear matter and of cluster formation in stellar matter on the density dependence of the symmetry energy are studied for different temperatures. It is observed that correlations and the formation of inhomogeneous matter at low densities and temperatures causes an increase of the symmetry energy as compared to calculations assuming a uniform uncorrelated spatial distribution of constituent baryons and leptons.

Beam Energy Scan at RHIC and z-Scaling

Beam Energy Scan (BES) data obtained at RHIC are briefly reviewed. Method of data analysis (z-scaling approach) based on self-similarity and locality of constituent interactions in hadron and nucleus collisions at high energy is described. The method is applied for analysis of BES data to search for signatures of phase transition and Critical Point (CP). Some results of analysis of hadron spectra measured in heavy ion collisions (HIC) at RHIC over a wide range of the energy sNN=7.7–200 GeV are presented. Microscopic scenario of constituent interactions in the framework of this approach is discussed. Dependence of the energy loss on the momentum of the produced hadron, energy and centrality of the collision is studied. Self-similarity of the constituent interactions in terms of momentum fractions is used to characterize the nuclear medium by a “specific heat” and the colliding nuclei by fractal dimensions. Kinematic regions which are assumed to be most preferable for search for signatures of phase transition of nuclear matter produced in HIC in BES are discussed.

PHASE TRANSITION PATTERNS OF NUCLEAR MATTER BASED ON EXTENDED LINEAR SIGMA MODEL

We study systematically various types of phase transitions in nuclear matter at finite temperature T and baryon chemical potential μ based on the extended linear sigma model with nucleon degrees of freedom. It is shown that there are three types of phase transitions in nuclear matter: the chiral symmetry nonrestoration (SNR) at high temperature, the well-known liquid–gas (LG) phase transition at sub-saturation density and the Lifshitz phase transition (LPT) from the fully-gapped state to the state with Fermi surface. Their phase diagrams are established in the (T, μ)-plane and their physical properties are investigated in detail. The relationship between the chiral phase transition and the LG phase transition in nuclear matter is discussed.