Phase Transition In Nuclear Matter Research Articles

Bimodalities: A survey of experimental data and models

Bimodal distributions of some chosen variables measured in nuclear collisions were recently proposed as a non ambiguous signature of a first order phase transition in nuclei. This section presents a compilation of both theoretical and experimental studies on bimodalities performed so far, in relation with the liquid-gas phase transition in nuclear matter.

Bimodality: A possible experimental signature of the liquid–gas phase transition of nuclear matter

We have observed a bimodal behaviour of the distribution of the asymmetry between the charges of the two heaviest products resulting from the decay of the quasi-projectile released in binary Xe + Sn and Au + Au collisions from 60 to 100 MeV/u. Event sorting has been achieved through the transverse energy of light charged particles emitted on the quasi-target side, thus avoiding artificial correlations between the bimodality signal and the sorting variable. Bimodality is observed for intermediate impact parameters for which the quasi-projectile is identified. A simulation shows that the deexcitation step rather than the geometry of the collision appears responsible for the bimodal behaviour. The influence of mid-rapidity emission has been verified. The two bumps of the bimodal distribution correspond to different excitation energies and similar temperatures. It is also shown that it is possible to correlate the bimodality signal with a change in the distribution of the heaviest fragment charge and a peak in potential energy fluctuations. All together, this set of data is coherent with what would be expected in a finite system if the corresponding system in the thermodynamic limit exhibits a first order phase transition.

Laboratory Portrait: The Saclay Nuclear Physics Division

The Nuclear Physics Division (Service de Physique Nucléaire, SPhN) of DAPNIA at Saclay in France is part of the fundamental research divisions of the CEA (Commissariat à l'Energie Atomique). Its programs cover a broad range of topics in Nuclear Physics from low to high energies. They include the study of the structure and dynamics of the nucleus, the structure of the nucleon, and the search for phase transitions of nuclear matter. SPhN also contributes to measurements and modeling of specific nuclear reactions related to nuclear waste transmutation. Furthermore, physicists apply their knowledge, competence, and techniques to the development of innovative nuclear energy cycles, to the production of neutron and radioactive beams and to the decommissioning of nuclear installations. The research activities take place within strong national and international collaborations involving the academic world and enabling the selection and training of high-quality students and post-doctoral researchers.

Phase Transitions from Intermediate to Relativistic Energies

We summarize recent progress in utilizing the spinodal decomposition mechanism to probe the liquid-gas phase transition in nuclear matter, which occurs at subsaturation densities and moderate temperatures, and then discuss the prospects for exploiting this mechanism as a probe of the transition from a quark-gluon plasma to a hadron gas.

Bimodality: a possible signature of the liquid-gas phase transition of nuclear matter

Bimodality has been observed on the asymmetry between the charges of the two heaviest products resulting from the decay of the QP released in peripheral Xe+Sn and Au+Au collisions from 60 to 100 MeV/u. Bimodality is observed for intermediate impact parameters for which the quasi-projectile is clearly identified. The two event families correspond to different excitation energies as it is expected in a first order phase transition picture. It seems that the relevant parameter which governs the phenomenon is the dissipated energy per nucleon. It is also shown that it is possible to correlate the bimodality signal with the negative heat capacity and the Delta scaling. All together, this set of data is coherent with a liquid-gas phase transition of finite pieces of nuclear matter.

Antiferromagnetic spin phase transition in nuclear matter with effective Gogny interaction

The possibility of ferromagnetic and antiferromagnetic phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with the effective Gogny interaction. It is shown that at some critical density nuclear matter with D1S effective force undergoes a phase transition to the antiferromagnetic spin state (the opposite direction of neutron and proton spins). The self--consistent equations of spin polarized nuclear matter with D1S force have no solutions, corresponding to the ferromagnetic spin ordering (the same direction of neutron and proton spins) and, hence, the ferromagnetic transition does not appear. The dependence of antiferromagnetic spin polarization parameter as a function of density is found at zero temperature.

Liquid-gas phase transition in nuclear matter including strangeness

We apply the chiral SU(3) quark mean field model to study the properties of strange hadronic matter at finite temperature. The liquid-gas phase transition is studied as a function of the strangeness fraction. The pressure of the system cannot remain constant during the phase transition, since there are two independent conserved charges (baryon and strangeness number). In a range of temperatures around $15\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ (precise values depending on the model used) the equation of state exhibits multiple bifurcates. The difference in the strangeness fraction ${f}_{s}$ between the liquid and gas phases is small when they coexist. The critical temperature of strange matter turns out to be a nontrivial function of the strangeness fraction.

RELATIVISTIC DIRECT INTERACTION BETWEEN NUCLEONS DERIVED FROM CLASSICAL FIELD THEORY

In order to achieve a realistic description of nuclear matter properties, the nonlinear interactions between nucleons can be introduced into the quantum model on the basis of nonlinear coupling constants solutions to the classical equations for meson fields. In this connection, the quantization of the classical theory is firstly considered in the case of linear solutions. The obtained model is applied to reproduce the "liquid–gas" phase transition in nuclear matter.

The physics of quark‐gluon plasma and relativistic charged particle systems

AbstractQED and QCD describe different systems, but show similar features. An interesting issue is the formation of bound states and their dissolution at high densities, what is described as metallization (plasma phase transition) in Coulomb systems or as hadron to quark‐gluon phase transition in nuclear matter. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

SU(2) Chiral Sigma Model Study of Phase Transition in Hybrid Stars

We use a modified SU(2) chiral sigma model to study nuclear matter component and simple bag model for quark matter constituting a neutron star. We also study the phase transition of nuclear matter to quark matter with the mixed phase characterized by two conserved charges in the interior of highly dense neutron stars. Stable solutions of Tolman–Oppenheimer–Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.67M⊙ and radius around 8.9 km.

The strange-quark chemical potential as an experimentally accessible ‘order parameter’ of the deconfinement phase transition for finite baryon density

We consider the change of the strange-quark chemical potential in the phase diagram of nuclear matter, employing the Wilson loop and scalar quark condensate order parameters, mass-scaled partition functions and enforcing flavour conservation. Assuming the region beyond the hadronic phase to be described by massive, correlated and interacting quarks, in the spirit of lattice and effective QCD calculations, we find the strange-quark chemical potential to change sign: from positive in the hadronic phase, to zero upon deconfinement, to negative in the partonic domain. We propose this change in the sign of the strange-quark chemical potential to be an experimentally accessible order parameter and a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter.

PHASE TRANSITION AND HYBRID STAR IN AN SU(2) CHIRAL SIGMA MODEL

We use a modified SU(2) chiral sigma model to study nuclear matter at high density using mean field approach. We also study the phase transition of nuclear matter to quark matter in the interior of highly dense neutron stars. Stable solutions of Tolman–Oppenheimer–Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.69M⊙, radii around 9.3 km and a quark matter core constituting nearly 55–85% of the star radii.

Generalized isoscaling of isotopic distributions

At incident energies in excess of about E/A530 MeV, a rapid collective expansion of the combined system may occur during the later stages of a central collision between heavy nuclei @1,2#. At densities less than about 1 3 of the saturation density, such systems disassemble into a mixture of fragments and light particles; the duration of fragment emission is of the order of 100 fm/c @3,4#. Even though the emission time is short, statistical models such as bulk multifragmentation models, which assume equilibrium at a single breakup density and temperature, have been used successfully to describe many experimental observables such as fragment multiplicities, charge distributions, and energy spectra of the emitted fragments @2,5–7#. These descriptions require careful, though not necessarily obvious, choices for the source size, excitation energy, and collective velocity of expansion @2,6–8#. Many of these statistical models display a phase transition in nuclear matter with subsaturation density @9,10#; such models have been employed to extract the caloric curve, i.e., the relationship between excitation energy and temperature for the nuclear liquid-gas phase transition @5,11–17# and to address whether finite nuclear systems may display negative heat capacities in analogy to those deduced for finite metallic clusters @18#. The success of thermal models raises the fundamental

Variation of the strange-quark chemical potential in the phase diagram of nuclear matter**Work supported in part by the Research Secretariat of the University of Athens.

On the basis of lattice calculations, we require the existence of a deconfined quark matter region (0 < as < 1) beyond the hadron gas phase, which goes asymptotically into the ideal quark–gluon plasma domain, in the phase diagram of nuclear matter. We consider empirically the dynamics of this region in terms of the order parameters and mass-scaled partition functions and derive an EoS. Then, the strange-quark chemical potential is expressed in a functional form of the temperature and light-quark chemical potential and its variation throughout the 3-region phase diagram is studied. We propose the change of the sign of the strange-quark chemical potential, from positive in the hadronic region to negative beyond, to be a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter. Analysis of the nucleus–nucleus collision data from AGS and SPS is presented giving strong support to our proposal.

A NUCLEAR MANY-BODY THEORY AT FINITE TEMPERATURE APPLIED TO A PROTONEUTRON STAR

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars

Echoes of the liquid–gas phase transition in multifragmentation

A general discussion is made concerning the ways in which one can get signatures about a possible liquid–gas phase transition in nuclear matter. Microcanonical temperature, heat capacity and second-order derivative of the entropy versus energy formulas have been deduced in a general case. These formulas are exact, simply applicable and do not depend on any model assumption. Therefore, they are suitable to be applied on experimental data. The formulas are tested in various situations. It is evidenced that when the freeze-out constraint is of fluctuating volume type the deduced (heat capacity and second-order derivative of the entropy versus energy) formulas will prompt the spinodal region through specific signals. Finally, the same microcanonical formulas are deduced for the case when an incomplete number of fragments per event are available. These formulas could overcome the freeze-out backtracking deficiencies.

Event-by-event analysis of proton-induced nuclear multifragmentation: determination of the phase transition universality class in a system with extreme finite-size constraints.

A percolation model of nuclear fragmentation is used to interpret 10.2 GeV/c p+197Au multifragmentation data. Emphasis is put on finding signatures of a continuous nuclear matter phase transition in finite nuclear systems. Based on model calculations, corrections accounting for physical constraints of the fragment detection and sequential decay processes are derived. Strong circumstantial evidence for a continuous phase transition is found, and the values of two critical exponents, sigma = 0.5+/-0.1 and tau = 2.35+/-0.05, are extracted from the data. A critical temperature of T(c) = 8.3+/-0.2 MeV is found.

Momentum dependence of the mean field and equation of state of nuclear matter

The momentum and density dependence of the mean field and other properties of nuclear matter are studied with finite-range effective interactions having different functional forms by evaluating the single-particle momentum distribution function self-consistently. In these calculations relativistic effects and supraluminous behaviour of nuclear matter are also taken into account. The equation of states obtained from these effective interactions are used to study liquid–gas phase transition in nuclear matter.

The Nuclear Fragmentation Phase Transition and Rare Isotope Production

Of all phase transitions in nuclear matter, the fragmentation phase transition is perhaps the one for which there is the best experimental evidence as of now. In addition, theoretical models have been developed to a degree where detailed comparisons are possible. With the advent of rare isotope production facilities using projectile fragmentation techniques (NSCL, GSI, ..., and hopefully RIA in the coming decade), the main interest in this field is beginning to shift towards the exploration of the isospin degree of freedom in the nuclear equation of state. Here we employ a statistical multifragmentation model and discuss the connection between the width of the isotope distribution and the isospin term in the nuclear equation of state.

Nuclear isotope thermometry

We discuss different aspects which might influence temperatures deduced from experimental isotopic yields in the multifragmentation process. It is shown that fluctuations due to the finite size of the system and distortions due to the decay of hot primary fragments conspire to blur the temperature determination in multifragmentation reactions. These facts suggest that caloric curves obtained through isotope thermometers, which were taken as evidence for a first-order phase transition in nuclear matter, should be investigated very carefully.