Nuclear Liquid Gas Research Articles

Nuclear liquid-gas transition in the strong coupling regime of lattice QCD

The nuclear liquid-gas transition from a gas of hadrons to a nuclear phase cannot be determined numerically from conventional lattice QCD due to the severe sign problem at large values of the baryon chemical potential. In the strong coupling regime of lattice QCD with staggered quarks, the dual formulation is suitable to address the nuclear liquid gas transition. We determine this first order transition at low temperatures and as a function of the quark mass and the inverse gauge coupling $\beta$. We also determine the baryon mass and discuss the nuclear interactions as a function of the quark mass, and compare to mean field results.

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.

Coupling dynamical and statistical mechanisms for baryonic cluster production in nucleus collisions of intermediate and high energies

Central nucleus-nucleus collisions produce many new baryons and the nuclear clusters can be formed from these species. The phenomenological coalescence models were sufficiently good for description of light nuclei yields in a very broad range of collision energies. We demonstrate that in reality the coalescence process can be considered as 1) the formation of primary diluted excited baryon clusters and 2) their following statistical decay leading to the final cold fragment production. We argue that the formation of such excited systems from the interacting baryons is a natural consequence of the nuclear interaction at subnuclear densities resulting in the nuclear liquid-gas type phase transition in finite systems. In this way one can provide a consistent interpretation of the experimental fragment yields (FOPI data) including the important collision energy dependence in relativistic ion reactions. We investigate the regularities of this new kind of fragment production, for example, their yield, isospin, and kinetic energy characteristics. A generalization of such a clusterization mechanism for hypernuclear matter is suggested. The isotope yields and particle correlations should be adequate for studying these phenomena.

Perturbative RG Analysis of the Condensate Dependence of the Axial Anomaly in the Three-Flavor Linear Sigma Model

Coupling of ‘t Hooft’s determinant term is investigated in the framework of the three-flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field-dependent correction to the coupling of the conventional UA(1) breaking determinant term. It is found that, at low temperatures, mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid–gas transition.

Baryon number fluctuations induced by hadronic interactions at low temperature and large chemical potential

We investigate the density fluctuations induced by hadronic interactions at low temperatures and large chemical potentials after the hadronization of quark-gluon plasma~(QGP). We analyze the structures of net-baryon number kurtosis and skewness and elaborate on their relations with the nuclear liquid-gas~(LG) phase transition and hadronic interactions above the critical temperature. Combining with the relevant experimental projects at RHIC/NICA/FAIR/J-PARC/HIAF with collision energies from $200\,$GeV to $1.8\,$GeV, we propose a double-peak structure of kurtosis (skewness) as a function of collision energy, which can be taken to identify the chiral phase transition and the nuclear liquid-gas phase transition. In particular, the fluctuation distributions at low temperatures provide a new method to explore hadronic interactions and nuclear liquid-gas transition.

Evolution of Quasiperiodic Structures in a Non-Ideal Hydrodynamic Description of Phase Transitions

Various phase transitions could have taken place in the early universe, and may occur in the course of heavy-ion collisions and supernova explosions, in proto-neutron stars, in cold compact stars, and in the condensed matter at terrestrial conditions. Most generally, the dynamics of the density and temperature at first- and second-order phase transitions can be described with the help of the equations of non-ideal hydrodynamics. In the given work, some novel solutions are found describing the evolution of quasiperiodic structures that are formed in the course of the phase transitions. Although this consideration is very general, particular examples of quark-hadron and nuclear liquid-gas first-order phase transitions to the uniform k 0 = 0 state and of a pion-condensate second-order phase transition to a non-uniform k 0 ≠ 0 state in dense baryon matter are considered.

Effects of a non-zero strangeness-chemical potential in strong interaction models

The effect of a non-zero strangeness chemical potential on the strong interaction phase diagram has been studied within the framework of the SU(3) quark-hadron chiral parity-doublet model. Both, the nuclear liquid-gas and the chiral/deconfinement phase transitions are modified. The first-order line in the chiral phase transition is observed to vanish completely, with the entire phase boundary becoming a crossover. These changes in the nature of the phase transitions are expected to modify various susceptibilities, the effects of which might be detectable in particle-number distributions resulting from moderate-temperature and high-density heavy-ion collision experiments.

Effect of liquid drop model parameters on nuclear liquid-gas phase transition

The phenomenon of liquid-gas phase transition occurring in heavy ion collisions at intermediate energies is a subject of contemporary interest. In statistical models of fragmentation, the liquid drop model is generally used to calculate the ground state binding energies of the fragments. It is well known that the surface and symmetry energy of the hot fragments at the low density freeze out can be considerably modified. In addition to this, the level density parameter also has a wide variation. The effect of variation of these parameters is studied on fragmentation observables which are related to the nuclear liquid gas phase transition. The canonical thermodynamical model which has been very successful in describing the phenomenon of fragmentation is used for the study. The shift in transition temperature owing to the variation in liquid drop model parameters has been examined.

Towards a theoretical description of dense QCD

The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite baryon densities. I review alternative attempts to treat dense QCD with an effective lattice theory derived by analytic strong coupling and hopping expansions, which close to the continuum is valid for heavy quarks only, but shows all qualitative features of nuclear physics emerging from QCD. In particular, the nuclear liquid gas transition and an equation of state for baryons can be calculated directly from QCD. A second effective theory based on strong coupling methods permits studies of the phase diagram in the chiral limit on coarse lattices.

A 3d effective lattice theory for phase transitions in Yang-Mills and heavy dense QCD

QCD thermodynamics is crucial for the physics of the early universe, heavy ion collisions and compact stars. However, predictions by lattice simulations are very costly or, in the case of finite baryon density, even impossible because of a sign problem. Starting from Yang- Mills theory, I review how to use strong coupling methods to construct a 3d effective theory which reproduces the deconfinement phase transition to about 10% accuracy. The generalisation to QCD, which is valid for heavy quarks, has only a mild sign problem in the case of finite density and can be simulated efficiently. Moreover, it allows to address the nuclear liquid gas transition in the cold and dense regime for the first time directly from QCD.

Heavy dense QCD and nuclear matter from an effective lattice theory

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, \kappa, whose action is correct to \kappa^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as gap between the onset of isospin and baryon condensation.

Noncongruence of the nuclear liquid-gas and deconfinement phase transitions

First order phase transitions (PTs) with more than one globally conserved charge, so-called non-congruent PTs, have characteristic differences compared to congruent PTs (e.g., dimensionality of phase diagrams, location and properties of critical points and endpoints). In the present article we investigate the non-congruence of the nuclear liquid-gas PT at sub-saturation densities and the deconfinement PT at high densities and/or temperatures in Coulomb-less models, relevant for heavy-ion collisions and neutron stars. For the first PT, we use the FSUgold relativistic mean-field model and for the second one the relativistic chiral SU(3) model. The chiral SU(3) model is one of the few models for the deconfinement PT, which contains quarks and hadrons in arbitrary proportions (i.e. a "solution") and gives a continuous transition from pure hadronic to pure quark matter above a critical point. The study shows the universality of the applied concept of non-congruence for the two PTs with an upper critical point, and illustrates the different typical scales involved. In addition, we find a principle difference between the liquid-gas and the deconfinement PTs: in contrast to the ordinary Van-der-Waals-like PT, the phase coexistence line of the deconfinement PT has a negative slope in the pressure-temperature plane. As another qualitative difference we find that the non-congruent features of the deconfinement PT become vanishingly small around the critical point.

Nonextensive nuclear liquid–gas phase transition

We study an effective relativistic mean-field model of nuclear matter with arbitrary proton fraction at finite temperature in the framework of nonextensive statistical mechanics, characterized by power-law quantum distributions. We investigate the presence of thermodynamic instability in a warm and asymmetric nuclear medium and study the consequent nuclear liquid–gas phase transition by requiring the Gibbs conditions on the global conservation of baryon number and electric charge fraction. We show that nonextensive statistical effects play a crucial role in the equation of state and in the formation of mixed phase also for small deviations from the standard Boltzmann–Gibbs statistics.

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.

Viscosity and thermal conductivity effects at first-order phase transitions in heavy-ion collisions

Effects of viscosity and thermal conductivity on the dynamics of first-order phase transitions are studied. The nuclear gas-liquid and hadron-quark transitions in heavy-ion collisions are considered. We demonstrate that at non-zero thermal conductivity, $\kappa \neq 0$, onset of spinodal instabilities occurs on an isothermal spinodal line, whereas for $\kappa =0$ instabilities take place at lower temperatures, on an adiabatic spinodal.

Ratio of shear viscosity to entropy density in multifragmentation of Au + Au

The ratio of the shear viscosity (η) to entropy density (s) for the intermediate energy heavy-ion collisions has been calculated by using the Green-Kubo method in the framework of the quantum molecular dynamics model. The theoretical curve of η/s as a function of the incident energy for the head-on Au + Au collisions displays that a minimum region of η/s has been approached at higher incident energies, where the minimum η/s value is about 7 times Kovtun-Son-Starinets (KSS) bound (1/4π). We argue that the onset of minimum η/s region at higher incident energies corresponds to the nuclear liquid gas phase transition in nuclear multifragmentation.

Caloric curve for nuclear liquid–gas phase transition in relativistic mean-field hadronic model

The main thermodynamical properties of the first order phase transition of the relativistic mean-field (RMF) hadronic model were explored in the isobaric, the canonical and the grand canonical ensembles on the basis of the method of the thermodynamical potentials and their first derivatives. It was proved that the first order phase transition of the RMF model is the liquid-gas type one associated with the Gibbs free energy $G$. The thermodynamical potential $G$ is the piecewise smooth function and its first order partial derivatives with respect to variables of state are the piecewise continuous functions. We have found that the energy in the caloric curve is discontinuous in the isobaric and the grand canonical ensembles at fixed values of the pressure and the chemical potential, respectively, and it is continuous, i.e. it has no plateau, in the canonical and microcanonical ensembles at fixed values of baryon density, while the baryon density in the isotherms is discontinuous in the isobaric and the canonical ensembles at fixed values of the temperature. The general criterion for the nuclear liquid-gas phase transition in the canonical ensemble was identified.

Phase structure of quark systems in models with four-fermion interaction

The features of a hot and dense gas of quarks that are considered as quasiparticles of a model Hamiltonian with four-fermion interaction are studied. Adapted to the Nambu-Jona-Lasinio model, this approach allows us to accommodate a phase transition similar to the nuclear liquid-gas one. Arguments are given in favor of the statement that a plausible scenario of (partial) chiral-symmetry restoration (even at zero temperature) in such a system could be a mixed phase of the vacuum and normal baryonic matter. The properties of the transition layer separating the two media in question are also discussed.

Thermodynamics of quark quasiparticle ensemble

The features of the hot and dense gas of quarks, which are considered as the quasiparticles of the model Hamiltonian with a four-fermion interaction, are studied. Being adapted to the Nambu--Jona-Lasinio model, this approach allows us to accommodate a phase transition similar to the nuclear liquid-gas one at the proper scale and to argue the existence of the mixed (inhomogeneous) phase of vacuum and normal baryonic matter as a plausible scenario of chiral symmetry (partial) restoration. Analyzing the transition layer between two phases, we estimate the surface tension coefficient and speculate on the possible existence of a quark droplet.

Bimodality in multifragmentation of finite nuclei

Fragment production during the nuclear liquid gas phase transition is studied on the basis of the Statistical Multifragmentation Model (SMM) (Bondorf et al 1995 Phys. Rep.257 133). By selecting partitions according to the maximum fragment charge we demonstrate ‘bimodality’ as an essential feature of the phase transition in finite nuclear systems. We show that the variation of entropies of these two events with excitation energy exhibits a bimodality behaviour as well.