Nuclear Liquid-gas Phase Transition Research Articles

Effect of initial-state geometric configurations on the nuclear liquid-gas phase transition

Effect of initial-state geometric configurations on the nuclear liquid-gas phase transition

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.

Statistical Multifragmentation Model within the Extended Morphological Thermodynamics Approach

On the basis of the morphological thermodynamics, we develop an exactly solvable version of the statistical multifragmentation model for the nuclear liquid-gas phase transition. It is shown that the hard-core repulsion between spherical nuclei generates only the bulk (volume), surface, and curvature parts of the free energy of the nucleus, while the Gaussian curvature one does not appear in the derivation. The phase diagram of the nuclear liquid-gas phase transition is studied for a truncated version of the developed model.

Nuclear liquid-gas phase transition within a Brueckner-Hartree-Fock approach* *Sponsored by the National Natural Science Foundation of China (11975077, 11475045), "PHAROS", COST Action CA16214 and the agreement ASI-INAF n.2017-14-H.O

The critical parameters of the liquid-gas phase transition of symmetric nuclear matter are computed using the Brueckner-Hartree-Fock method at finite temperature by employing different realistic nucleon-nucleon potentials. Temperature effects on single-particle potentials, defect functions, and three-body forces are discussed in detail. Results obtained from the full procedure and frozen-correlations approximation are compared. We find critical temperatures of approximately 14 to 19 MeV and critical densities in the range of to , depending on the interactions employed.

Impact of fragment formation on shear viscosity in the nuclear liquid-gas phase transition region

The dimensionless ratio of shear viscosity to entropy density $\ensuremath{\eta}/s$ typically has a minimum at a phase transition as observed in many atomic and molecular systems. This quantity has been under intense study in high-energy heavy-ion collisions as a sign of a QCD phase transition or rapid crossover between hadronic and quark-gluon degrees of freedom. The authors perform numerical simulations of matter at lower density and temperature associated with a minimum in $\ensuremath{\eta}/s$ which may shed light on the nuclear liquid-gas phase transition and its connection to the QCD transition.

Vector and axial-vector mesons in nuclear matter

As a first step towards a realistic phenomenological description of vector and axial-vector mesons in nuclear matter, we calculate the spectral functions of the $\ensuremath{\rho}$ and the ${a}_{1}$ meson in a chiral baryon-meson model as a low-energy effective realization of QCD, taking into account the effects of fluctuations from scalar mesons, nucleons, and vector mesons within the functional renormalization group (FRG) approach. The phase diagram of the effective hadronic theory exhibits a nuclear liquid-gas phase transition as well as a chiral phase transition at a higher baryon-chemical potential. The in-medium $\ensuremath{\rho}$ and ${a}_{1}$ spectral functions are calculated by using the previously introduced analytically-continued FRG (aFRG) method. Our results show strong modifications of the spectral functions---in particular near the critical endpoints of both phase transitions---which may well be of relevance for electromagnetic rates in heavy-ion collisions or neutrino emissivities in neutron-star merger events.

QCD phase transition and equation of state of stellar strong interaction matter via Dyson\u2013Schwinger equation approach

We study the phase structure and phase transition of cold dense QCD matter via the Dyson–Schwinger equation approach. We take the rainbow approximation and the Gaussian-type gluon model. In order to guarantee that the quark number density begins to appear at the nuclear liquid-gas phase transition chemical potential, we propose a chemical potential dependent modification factor for the gluon model. We find that for the iso-symmetric quark matter, the modification reduces the chemical potential of the phase coexistence region of the first-order phase transition. We also implement the relativistic mean field theory to describe the hadron matter, and make use of the Maxwell and Gibbs construction method to study the phase transition of beta -equilibrium and charge neutral matter in compact stars. The results show that the phase transition will not happen in case of the Gaussian-type gluon model without any modification. The results also indicate that the upper boundary of the coexistence region should be larger than the current Nambu solution existing region. We also calculate the mass-radius relation of the compact stars, and find that the hadron-quark phase transition happens at too high chemical potential so that the maximum mass of the compact star is hardly affected by the hadron-quark phase transition.

Investigation of the nuclear liquid-gas phase transition in the static AMD

Nuclear liquid-gas phase transitions are investigated in the framework of static antisymmetrized molecular dynamics (static AMD) model under either a constant volume or a constant pressure. A deuteron quadrupole momentum fluctuation thermometer is applied to extract the temperature of fragmenting systems of 36Ar and 100Sn. A plateau structure of caloric curves is observed under a constant volume for those system with a density ρ ⩽ 0.03 fm−3. A clear backbending in the caloric curves, which indicates a first order phase transition, is observed under a constant pressure with all pressures studied. The similar behavior of caloric curves of 36Ar and 100Sn systems indicates that there is no strong system size effect under a constant volume or a constant pressure. Both the mass distributions and the light particle multiplicities show a strong α clusterization at low excitation energies in the static AMD simulations. The liquid-gas phase transition measures of the multiplicity derivative (dM/dT) and the normalized variance of Z max (NVZ) are applied. The experimental caloric curves are also compared with those of 100Sn of the static AMD simulations under both the constant volume and the constant pressure conditions. Discussions are presented with the available experimental results and those from the static AMD simulations. Large errors in the experimental temperature measurements and those in the reconstruction technique for the primary fragmenting source hinder to draw a conclusion whether the phase transition occurs under either a constant volume or a constant pressure. This study suggests that different measures for the liquid-gas phase transitions should be examined besides the caloric curves in order to draw a conclusion.

Determining the temperature in heavy-ion collisions with multiplicity distribution

By relating the charge multiplicity distribution and the temperature of a de-exciting nucleus through a deep neural network, we propose that the charge multiplicity distribution can be used as a thermometer of heavy-ion collisions. Based on an isospin-dependent quantum molecular dynamics model, we study the caloric curve of reaction Pd103 + Be9 with the apparent temperature determined through the charge multiplicity distribution. The caloric curve shows a characteristic signature of nuclear liquid-gas phase transition around the apparent temperature Tap = 6.4MeV, which is consistent with that through a traditional heavy-ion collision thermometer, and indicates the viability of determining the temperature in heavy-ion collisions with multiplicity distribution.

Nuclear liquid-gas phase transition with machine learning

The machine-learning techniques have shown their capability for studying phase transitions in condensed matter physics. Here, we employ the machine-learning techniques to study the nuclear liquid-gas phase transition. We adopt an unsupervised learning and classify the liquid and gas phases of nuclei directly from the final state raw experimental data of heavy-ion reactions. Based on a confusion scheme which combines the supervised and unsupervised learning, we obtain the limiting temperature of the nuclear liquid-gas phase transition. Its value $9.24\pm0.04~\rm MeV$ is consistent with that obtained by the traditional caloric curve method. Our study explores the paradigm of combining the machine-learning techniques with heavy-ion experimental data, and it is also instructive for studying the phase transition of other uncontrollable systems, like QCD matter.

Hard-photon production and its correlation with intermediate-mass fragments in a framework of a quantum molecular dynamics model

Hard photon provides a unique probe for nuclear reaction dynamics. In this work, we embedded incoherent neutron-proton bremsstrahlung photon production channel in a framework of isospin-dependent quantum molecular dynamics (IQMD) model and performed a systematic study of multiplicities of hard photons and intermediate-mass fragments (IMFs). It is found that the IQMD model with the in-medium nucleon-nucleon cross section can reproduce previous experimental data of hard-photon energy spectra better. By investigating the incident energy and centrality dependencies of multiplicities of hard photons and IMFs of $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$ collisions, it is found that the multiplicity correlation between thermal photons and IMFs can provide valuable information on nuclear liquid-gas phase transition. Additionally, temperatures from the thermal emitting sources are also investigated. The results indicate that hard photons provide some unique information of the thermodynamical state of multifragmentating nuclear system.

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.

Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD

The nuclear liquid-gas transition at normal nuclear densities, $n\ensuremath{\approx}{n}_{0}=0.16\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, and small temperatures, $T\ensuremath{\approx}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, has a large influence on analytic properties of the QCD grand-canonical thermodynamic potential. A classical van der Waals equation is used to determine qualitatively these unexpected features due to dense cold matter. The existence of the nuclear matter critical point results in thermodynamic branch points, which are located at complex chemical potential values, for $T>{T}_{c}\ensuremath{\simeq}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, and exhibit a moderate model dependence up to rather large temperatures $T\ensuremath{\lesssim}100\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. The behavior at higher temperatures is studied using the van der Waals hadron resonance gas (vdW-HRG) model. The baryon-baryon interactions have a decisive influence on the QCD thermodynamics close to ${\ensuremath{\mu}}_{B}=0$. In particular, nuclear matter singularities limit the radius of convergence ${r}_{{\ensuremath{\mu}}_{B}/T}$ of the Taylor expansion in ${\ensuremath{\mu}}_{B}/T$, with ${r}_{{\ensuremath{\mu}}_{B}/T}\ensuremath{\approx}2--3$ values at $T\ensuremath{\approx}140--170\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ obtained in the vdW-HRG model.

Solidarity of signal of measures for the liquid-gas phase transition in the statistical multifragmentation model

A systematic study of system size, $N/Z$ asymmetry, and fragmenting volume effects as well as the Coulomb effect on experimental measures for the nuclear liquid-gas phase transition and the mechanism of phase transition are carried out in the framework of the statistical multifragmentation model (SMM). The measures examined here are the caloric curve, the specific heat capacity (${C}_{v}$), the multiplicity derivative ($dM/dT$), the moment parameters (${M}_{2}$ and ${\ensuremath{\gamma}}_{2}$), the fluctuation of maximum fragment charge number (NVZ), the Fisher exponent ($\ensuremath{\tau}$), and the Zipf's law parameter ($\ensuremath{\xi}$). A signal for the first-order phase transition for all the measures is observed. A stronger signal is observed in the system with smaller sizes or with more neutron rich or in smaller fragmenting volumes for the caloric curve, ${C}_{v}$, and $dM/dT$. The phase-transition temperatures are independent of the system size, $N/Z$ asymmetry, fragmenting volume, and Coulomb force, which indicates these measures give a solid signal for the liquid-gas phase transition in SMM. On the other hand, the phase transition temperature and its behavior of the others slightly depend on the size, the $N/Z$ asymmetry and the volume of the system. A negative heat capacity is observed for systems with ${A}_{s}\ensuremath{\ge}$ 100 without the Coulomb force but disappears with the Coulomb. An instructive picture is given in the charge distributions for the observed first-order phase transition.

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.

Critical point of nuclear matter and beam-energy dependence of net-proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $S\sigma$ and kurtosis $\kappa\sigma^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $\kappa\sigma^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

Sensitivity study of experimental measures for the nuclear liquid-gas phase transition in the statistical multifragmentation model

The experimental measures of the multiplicity derivatives, the moment parameters, the bimodal parameter, the fluctuation of maximum fragment charge number (NVZ), the Fisher exponent ($\tau$) and Zipf's law parameter ($\xi$), are examined to search for the liquid-gas phase transition in nuclear multifragmention processes within the framework of the statistical multifragmentation model (SMM). The sensitivities of these measures are studied. All these measures predict a critical signature at or near to the critical point both for the primary and secondary fragments. Among these measures, the total multiplicity derivative and the NVZ provide accurate measures for the critical point from the final cold fragments as well as the primary fragments. The present study will provide a guide for future experiments and analyses in the study of nuclear liquid-gas phase transition.

Dynamical and statistical bimodality in nuclear fragmentation

The origin of bimodal behavior in the residue distribution experimentally measured in heavy ion reactions is reexamined using Boltzmann-Uehling-Uhlenbeck simulations. We suggest that, depending on the incident energy and impact parameter of the reaction, both entrance channel and exit channel effects can be at the origin of the observed behavior. Specifically, fluctuations in the reaction mechanism induced by fluctuations in the collision rate, as well as thermal bimodality directly linked to the nuclear liquid-gas phase transition are observed in our simulations. Both phenomenologies were previously proposed in the literature, but presented as incompatible and contradictory interpretations of the experimental measurements. These results indicate that heavy ion collisions at intermediate energies can be viewed as a powerful tool to study both bifurcations induced by out-of-equilibrium critical phenomena, as well as finite size precursors of thermal phase transitions.

Geometrical clusterization and deconfinement phase transition in SU(2) gluodynamics

A novel approach to identify the geometrical (anti)clusters formed by the Polyakov loops of the same sign and to study their properties in the lattice SU(2) gluodynamics is developed. The (anti)cluster size distributions are analyzed for the lattice coupling constant β ∈ 2 [2:3115; 3]. The found distributions are similar to the ones existing in 2- and 3-dimensional Ising systems. Using the suggested approach, we explain the phase transition in SU(2) gluodynamics at β = 2.52 as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while another droplet (the next to the largest cluster of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid drop formula is used to analyze the distributions of the gas (anti)clusters and to determine their bulk, surface and topological parts of free energy. Surprisingly, even the monomer multiplicities are reproduced with high quality within such an approach. The behavior of surface tension of gaseous (anti)clusters is studied. It is shown that this quantity can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. Moreover, the critical exponent β of surface tension coefficient of gaseous clusters is found in the upper vicinity of critical temperature. Its value coincides with the one found for 3-dimensional Ising model within error bars. The Fisher topological exponent τ of (anti)clusters is found to have the same value 1:806±0:008, which agrees with an exactly solvable model of the nuclear liquid-gas phase transition and disagrees with the Fisher droplet model, which may evidence for the fact that the SU(2) gluodynamics and the model are in the same universality class.

Geometrical clusterization of Polyakjov loops in SU(2) lattice gluodynamics

The liquid droplet formula is applied to an analysis of the properties of geometrical (anti)clusters formed in SU(2) gluodynamics by the Polyakov loops of the same sign. Using this approach, we explain the phase transition in SU(2) gluodynamics as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while the droplet of another liquid (the next to the largest cluster of the opposite sign of Polyakov loop) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid droplet formula is used to analyze the size distributions of the gas (anti)clusters. The fit of these distributions allows us to extract the temperature dependence of surface tension and the value of Fisher topological exponent τ for both kinds of gaseous clusters. It is shown that the surface tension coefficient of gaseous (anti)clusters can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. The Fisher topological exponent τ of (anti)clusters is found to have the same value 1.806 ± 0.008. This value disagrees with the famous Fisher droplet model, but it agrees well with an exactly solvable model of the nuclear liquid-gas phase transition. This finding may evidence for the fact that the SU(2) gluodynamics and this exactly solvable model of nuclear liquid-gas phase transition are in the same universality class.