Phase Diagram Of Nuclear Matter Research Articles

Indications for a critical end point in the phase diagram for hot and dense nuclear matter.

Excitation functions for the Gaussian emission source radii difference (R_{out}^{2}-R_{side}^{2}) obtained from two-pion interferometry measurements in Au+Au (sqrt[s_{NN}]=7.7-200 GeV) and Pb+Pb (sqrt[s_{NN}]=2.76 TeV) collisions are studied for a broad range of collision centralities. The observed nonmonotonic excitation functions validate the finite-size scaling patterns expected for the deconfinement phase transition and the critical end point (CEP), in the temperature versus baryon chemical potential (T,μ_{B}) plane of the nuclear matter phase diagram. A finite-size scaling (FSS) analysis of these data suggests a second order phase transition with the estimates T^{cep}∼165 MeV and μ_{B}^{cep}∼95 MeV for the location of the critical end point. The critical exponents (ν≈0.66 and γ≈1.2) extracted via the same FSS analysis place this CEP in the 3D Ising model universality class.

BCS-BEC crossovers and unconventional phases in dilute nuclear matter

The authors examine the phase diagram of neutron-rich nuclear matter, allowing for four competing phases. The resulting phase diagram features two tricritical points as well as crossovers from the BCS phase to a Bose-Einstein deuteron condensate plus a neutron gas. The physics of the individual phases and the transition from weak to strong coupling is traced by examining the Cooper-pair wave function and related quantities.

Equation of state for nuclear matter in core-collapse supernovae by the variational method

We construct a new nuclear equation of state (EOS) for core-collapse supernova (SN) simulations using the variational many-body theory. For uniform nuclear matter, the EOS is constructed with the cluster variational method starting from the realistic nuclear Hamiltonian composed of the Argonne v18 two-body potential and the Urbana IX three-body potential. The masses and radii of neutron stars calculated with the obtained EOS at zero temperature are consistent with recent observational data. For non-uniform nuclear matter, we construct the EOS in the Thomas-Fermi approximation. In this approximation, we assume a functional form of the density distributions of protons, neutrons, and alpha-particles, and minimize the free energy density in a Wigner-Seitz cell with respect to the parameters included in the assumed density distribution functions. The phase diagram of hot nuclear matter at a typical temperature is reasonable as compared with that of the Shen EOS.

Beam energy dependence of the expansion dynamics in relativistic heavy ion collisions: Indications for the critical end point?

The flow harmonic $v_{n}$ and the emission source radii $R_{\text{out}}$, $R_{\text{side}}$ and $R_{\text{long}}$ are studied for a broad range of centrality selections and beam collision energies in Au+Au ($\sqrt{s_{NN}}= 7.7 - 200$ GeV) and Pb+Pb ($\sqrt{s_{NN}}= 2.76$ TeV) collisions at RHIC and the LHC respectively. They validate the acoustic scaling patterns expected for hydrodynamic-like expansion over the entire range of beam energies studied. The combined data sets allow estimates for the \sqsn\ dependence of the mean expansion speed $\left<c_s\right>$, emission duration $\left<\Delta\tau\right>$ and the viscous coefficients $\left<\beta''\right>$ that encode the magnitude of the specific shear viscosity $\left<\eta/s\right>$. The estimates indicate initial-state model independent values of $\left<\eta/s\right>$ which are larger for the plasma produced at 2.76 TeV (LHC) compared to that produced at 200 GeV (RHIC) ($\left<4\pi\eta/s\right>_{\text{LHC}}=2.2\pm 0.2$ and $\left<4\pi\eta/s\right>_{\text{RHIC}}=1.3\pm 0.2$). They also show a non-monotonic \sqsn\ dependence for $\left<\beta''\right>$, $\left<c_s\right>$ and $\left<\Delta\tau\right>$, with minima for $\left<\beta''\right>$ and $\left<c_s\right>$, and a complimentary maximum for $\left<\Delta\tau\right>$. These dependencies signal a significant change in reaction dynamics in a narrow span of $\sqrt{s_{NN}}$, which may be linked to reaction trajectories close to the critical end point (CEP) in the phase diagram for nuclear matter.

Measurement of dileptons with the CBM experiment at FAIR

Abstract The Compressed Baryonic Matter (CBM) experiment at the upcoming Facility for Antiproton and Ion Research (FAIR) will explore the phase diagram of nuclear matter at very high net-baryon densities and moderate temperatures in nucleus–nucleus collisions at beam energies up to 45 A GeV . One of the key diagnostic probes is electromagnetic radiation. In order to minimize systematic errors of this challenging measurement, CBM aims at an investigation of dielectron and dimuon pairs in the full mass range from the photon point up to charmonium. The results of performance studies for dilepton measurements and the status of the detector developments are presented.

The half-skyrmion phase in a chiral-quark model

The Chiral Dilaton Model, where baryons arise as non-topological solitons built from the interaction of quarks and chiral mesons, shows in the high density low temperature regime a two phase scenario in the nuclear matter phase diagram. Dense soliton matter described by the Wigner–Seitz approximation generates a periodic potential in terms of the sigma and pion fields that leads to the formation of a band structure. The analysis up to three times nuclear matter density shows that soliton matter undergoes two separate phase transitions: a delocalization of the baryon number density leading to B=1/2 structures, as in skyrmion matter, at moderate densities, and quark deconfinement at larger densities. This description fits well into the so-called quarkyonic phase where, before deconfinement, nuclear matter should undergo structural changes involving the restoration of fundamental symmetries of QCD.

Simulation of non-Abelian gauge theories with optical lattices

Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).

Beam energy and centrality dependence of the statistical moments of the net-charge and net-kaon multiplicity distributions in Au + Au collisions at STAR

In part to search for a possible critical point (CP) in the phase diagram of hot nuclear matter, a Beam Energy Scan was performed at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory. The STAR experiment collected significant Au+Au data sets at beam energies, $\sqrt{{\rm s}_{\rm NN}}$, of 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. Lattice and phenomenological calculations suggest that the presence of a CP might result in divergences of the thermodynamic susceptibilities and correlation length. The statistical moments of the multiplicity distributions of particles reflecting conserved quantities, such as net-charge and net-strangeness, are expected to depend sensitively on these correlation lengths, making them attractive tools in the search for a possible critical point. The centrality and beam-energy dependence of the statistical moments of the net-charge multiplicity distributions will be discussed. The observables studied include the lowest four statistical moments (mean, variance, skewness, kurtosis) and the products of these moments. The measured moments of the net-kaon multiplicity distributions will also be presented. These will be compared to the predictions from approaches lacking critical behavior, such as the Hadron Resonance Gas model and Poisson statistics.

Phase diagram of neutron-rich nuclear matter and its impact on astrophysics

Dense matter as it can be found in core-collapse supernovae and neutron stars is expected to exhibit different phase transitions which impact the matter composition and the equation of state, with important consequences on the dynamics of core-collapse supernova explosion and on the structure of neutron stars. In this paper we will address the specific phenomenology of two of such transitions, namely the crust-core solid-liquid transition at sub-saturation density, and the possible strange transition at super-saturation density in the presence of hyperonic degrees of freedom. Concerning the neutron star crust-core phase transition at zero and finite temperature, it will be shown that, as a consequence of the presence of long-range Coulomb interactions, the equivalence of statistical ensembles is violated and a clusterized phase is expected which is not accessible in the grand-canonical ensemble. A specific quasi-particle model will be introduced to illustrate this anomalous thermodynamics and some quantitative results relevant for the supernova dynamics will be shown. The opening of hyperonic degrees of freedom at higher densities corresponding to the neutron stars core modifies the equation of state. The general characteristics and order of phase transitions in this regime will be analyzed in the framework of a self-consistent mean-field approach.

Selected problems in astrophysics of compact objects

I review three problems in astrophysics of compacts stars: (i) the phase diagram of warm pair-correlated nuclear matter at sub-saturation densities at finite isospin asymmtery; (ii) the Standard Model neutrino emission from superfluid phases in neutron stars within the Landau theory of Fermi (superfluid) liquids; (iii) the beyond Standard Model physics of axionic cooling of compact stars by the Cooper pair-breaking processes.

Exploring the nuclear matter phase diagram with heavy ion reactions

We review recent results concerning heavy ion reactions between charge asymmetric systems from low up to intermediate energies.Solving numerically self-consistent transport equations for neutrons and protons, we focus on isospin sensitivite observables, aiming at extracting information on the density dependence of the nuclear symmetry energy. For reactions close to the Coulomb barrier, we explore the structure of pre-equilibrium dipole oscillations, rather sensitive to the low-density behavior of the isovector component of the nuclear effective interaction. In the Fermi energy regime, we investigate the interplay between dissipation mechanisms, fragmentation and isospin effects. At intermediate energies, where regions with higher density and momentum are reached, we discuss collective flows and their sensitive to neutron and proton effective masses.

Phase diagram of dilute nuclear matter: Unconventional pairing and the BCS-BEC crossover

We report on a comprehensive study of the phase structure of cold, dilute nuclear matter featuring a SD condensate at non-zero isospin asymmetry, within wide ranges of temperatures and densities. We find a rich phase diagram comprising three superfluid phases, namely a Larkin-Ovchinnikov-Fulde-Ferrell phase, the ordinary BCS phase, and a heterogeneous, phase-separated BCS phase, with associated crossovers from the latter two phases to a homogeneous or phase-separated Bose-Einstein condensate of deuterons. The phase diagram contains two tricritical points (one a Lifshitz point), which may degenerate into a single tetracritical point for some degree of isospin asymmetry.

Investigating the microscopic properties of strongly interacting matter with HADES

Abstract In the energy domain of 1–2 GeV kinetic energy per nucleon, HADES has measured rare and penetrating probes in elementary and heavy ion collisions. Our results demonstrate that electron pair emission in C+C collisions can essentially be explained as a superposition of independent N+N collisions. HADES results on e+e− production in Ar+KCl collisions, however, show a strong enhancement of the dilepton yield relative to a reference spectrum obtained from elementary nucleon-nucleon reactions, signal the onset of medium effects beyond the superposition of individual N+N collisions. Intriguing results where also obtained from the reconstruction of hadrons with open and hidden strangeness. Analyses of the experimentally obtained hadronic yields measured in Ar+KCl allows to extract the chemical freeze-out conditions in the T -µB phase diagram of strongly interacting matter. While the measured abundance of all reconstructed particles are well described assuming thermalization, the also reconstructed double strange baryon ≡− appears about ten times more abundant than expected. This result will be discussed in the context of the exploration of the nuclear matter phase diagram in the region of finite density. Further investigations to search for significant medium effects, will be followed over the coming years with an upgraded HADES detector.

Chiral thermodynamics of nuclear matter

The free energy and the equation of state of isospin-asymmetric nuclear matter are calculated at finite temperature up to three loop order in the framework of in-medium chiral perturbation theory, systematically incorporating one- and two-pion exchange dynamics to this order. Effects from the two-pion exchange with explicit {\Delta}-isobar excitation are included, as well as three-body forces. We construct the phase diagram of nuclear matter for different proton fractions x_p and investigate the dependence of nuclear matter properties on the isospin-asymmetry. A detailed study of the liquid-gas phase transition is performed. For isospin-symmetric nuclear matter we find a critical temperature of 15.1 MeV; as the isospin-asymmetry is increased, the liquid-gas coexistence region decreases until it disappears at x_p \approx 0.05, while nuclear matter becomes unbound at x_p \approx 0.12. The quadratic expansion of the free energy in the asymmetry parameter {\delta} is a good approximation at low temperature even for large {\delta}. An estimate of chiral four-body correlations in nuclear and neutron matter is also performed and the corrections from such four-body interactions are found to be small.

Nuclear matter phase diagram from compound nucleus decay

The finite size of nuclei and the Coulomb interaction make it di ffi cult to de- scribe systems interacting through the strong force into thermodynamic terms. Our task is to extract the phase diagram of the theoretical infinite symmetrical uncharged nuclear mat- ter from experiments of nuclear collisions where the systems are neither infinite, symmet- rical, nor uncharged. Decay yields from such experiments are translated into coexistence densities and pressures by use of Fisher's droplet model. This method is tested on model systems such as the Ising model and a system of particles interacting via the Lennard- Jones potential. The specific problems inherent to nuclear reactions are considered. These include finite size e ffects, Coulomb repulsion, and the lack of a physical vapor in contact with a decaying system. Experimental data of compound nucleus experiments are studied within this framework, which is also shown to extend to higher energy reactions. Finally, the phase diagram of nuclear matter is extracted.

Search for the critical point of the nuclear matter phase diagram. first results from the beam energy SCAN program at RHIC

Author(s): Odyniec, G | Abstract: In 2010, the Relativistic Heavy Ion Collider (RHIC) launched a multistep experimental program to investigate the QCD Phase Diagram in general, and to search for the QCD Critical Point (CP) and/or 1st order phase transition in particular. The BES (Beam Energy Scan) program involves an scan of Au+Au collisions from the top RHIC energy (ρs = 200 GeV) down to energies as low as 5 GeV in NN center of mass. During the first BES run (2010), data were collected at 7.7, 11.5 and 39 GeV. It was complemented in 2011 by two other data sets at 27 and 19.6 GeV. The preparations for the remaining data taking at ps = 5 GeV are in progress. The overview of the BES program and the first experimental results are presented and discussed.

Phase diagram for asymmetric nuclear matter in the multifragmentation model

We assume that, in equilibrium, nuclear matter at reduced density and moderate finite temperature breaks up into many fragments. Strong support for this assumption is provided by data accumulated from intermediate-energy heavy ion collisions. The breakup of hot and expanded nuclear matter according to the rules of equilibrium statistical mechanics is the multifragmentation model, which gives a first-order phase transition. This is studied in detail here. Phase-equilibrium lines for different degrees of asymmetry are computed.

Zipf's law in nuclear multifragmentation and percolation theory

We investigate the average sizes of the n largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte Carlo simulations of the percolation type. We find that previous claims of manifestations of Zipf's Law in the rank-ordered fragment size distributions are not borne out in our result, in neither finite nor infinite systems. Instead, we find that Zipf-Mandelbrot distributions are needed to describe the results, and we show how one can derive them in the infinite size limit. However, we agree with previous authors that the investigation of rank-ordered fragment size distributions is an alternative way of looking for the critical point in the nuclear matter diagram.

Isospin dependent thermodynamics of fragmentation

The thermal and phase properties of a multifragmentation model that uses clusters as degrees of freedom are explored as a function of isospin. Good qualitative agreement is found with the phase diagram of asymmetric nuclear matter as established by different mean-field models. In particular, from the convexity properties of the nuclear entropy, we show that uncharged finite nuclei display first- and second-order liquid-gas-like phase transitions. Different quantities are examined to connect the thermal properties of the system to cluster observables. In particular, we show that fractionation is only a loose indication of phase coexistence. A simple analytical formula is proposed and tested to evaluate the symmetry (free) energy from the widths of isotopic distributions. Assuming that one may restore the isotopic composition of breakup fragments, it is found that some selected isotopic observables can allow one to quantitatively access the freeze-out symmetry energy in multifragmentation experiments.

Fragmentation and the Nuclear Equation of State

Progress on the determination of the order of the fragmentation phase transition, the location of its critical point in the nuclear matter phase diagram, the values of the critical exponents that determine the universality class of the transition, and finite size scaling effects is discussed. Evidence for the presence of Zipf-Mandelbrot-scaling in the relative size of the largest clusters is examined, and the connection to the value of the critical exponent τ is established.