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In this paper, we review the main challenges associated with the statistical mechanics of finite systems, with a particular emphasis on the present understanding of phase transitions in the framework of information theory. We show that this is a very powerful formalism allowing to treat in a thermody-namically consistent way many difficult problems in the statistical treatment of finite, open, transient and expanding systems. The first point we analyze is the problem of boundary conditions, which in the framework of information theory must also be treated statistically. We recall that the different ensembles do not lead to the same equation of states, in particular in the region of a first-order phase transition, and we stress the fact that different statistical ensembles may be relevant to heavy-ion physics depending upon the actual experimental conditions. Finally, we present a coherent description of first-order phase transitions demonstrating the equivalence between the Yang-Lee theorem, the occurrence of bimodalities in the intensive ensemble and the presence of inverted curvatures of the thermodynamic potential of the extensive ensemble. We stress that this discussion is not restricted to the possible occurrence of negative specific heat, but can also include negative compressibilities and negative susceptibilities, and in fact any curvature anomaly of the thermodynamic potential. Since the relevant entropy surface explored in nuclear multifrag-mentation is not yet well understood and largely debated in the community, the experimental evidence of new thermodynamic anomalies is one of the important challenges of future heavy-ion experiments. [ABSTRACT FROM AUTHOR]

The purpose and contents of this topical issue, Dynamics and Thermodynamics with Nuclear Degrees of Freedom, which grew out of a series of workshops in the years 2004 and 2005, are introduced. The central topics are the nuclear density functional, nuclear multi-fragmentation, and nuclear phase transitions. [ABSTRACT FROM AUTHOR]

The three-dimensional linear stabilities of vertically uniform shear flows and vortex configurations (dipole, couple, von Karman street and double symmetric row) are investigated through experiments, theoretical and numerical analysis when the fluid is stratified. For strong stratification, all the vortex configurations are unstable to the zigzag instability associated to vertically sheared horizontal translations that develop spontaneously. The most unstable wavelength decreases with the strength of the stratification, whereas the maximum growthrate is independent of the stratification and solely proportional to the strain felt by the vortex core. Experiments and direct numerical simulation show that the zigzag instability eventually decorrelates the flow on the vertical. The zigzag instability is therefore a generic instability that constrains turbulent energy cascade in stratified fluid and contributes to structure oceanic and atmospheric flows. [ABSTRACT FROM AUTHOR]

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA). [ABSTRACT FROM AUTHOR]

We discuss three finite fermion systems in comparison: nuclei, metal clusters, and droplets of liquid 3He. A principle sorting in "natural units" of energy and length scales is given. We address the theoretical description in terms of self-consistent mean-field theories and their effective energy-density functionals. We look at the interplay of the different time scales from the various constituents of either system. Finally, we discuss the prospects of more detailed experimental analyses for the case of metal clusters, in particular in the non-linear domain where truly dynamical behaviors are expected. [ABSTRACT FROM AUTHOR]

Heat can flow from cold to hot at any phase separation even in macroscopic systems. Therefore also Lynden-Bell's famous gravo-thermal catastrophe must be reconsidered. In contrast to traditional canonical Boltzmann-Gibbs statistics this is correctly described only by microcanonical statistics. Systems studied in chemical thermodynamics (ChTh) by using canonical statistics consist of several homogeneous macroscopic phases. Evidently, macroscopic statistics as in chemistry cannot and should not be applied to non-extensive or inhomogeneous systems like nuclei or galaxies. Nuclei are small and inhomogeneous. Multifragmented nuclei are even more inhomogeneous and the fragments even smaller. Phase transitions of first order and especially phase separations therefore cannot be described by a (homogeneous) canonical ensemble. Taking this serious, fascinating perspectives open for statistical nuclear fragmentation as test ground for the basic principles of statistical mechanics, especially of phase transitions, without the use of the thermodynamic limit. Moreover, there is also a lot of similarity between the accessible phase space of fragmenting nuclei and inhomogeneous multistellar systems. This underlines the fundamental significance for statistical physics in general. [ABSTRACT FROM AUTHOR]

It is commonly accepted that strongly interacting matter has several phase transitions in different domains of temperature and baryon density. In this contribution I discuss two most popular phase transitions which, in principle, can be accessed in nuclear collisions. One of them, the liquid-gas phase transition, is well established theoretically and studied experimentally in nuclear multifragmentation reactions at intermediate energies. The other one, the deconfinement-hadronization phase transition, is at the focus of present and future experimental studies with relativistic heavy-ion beams at SPS, RHIC and LHC. Possible links between these two phase transitions are identified from the viewpoint of their manifestation in violent nuclear collisions. [ABSTRACT FROM AUTHOR]

Heavy-ion experiments provide important data to test astrophysical models. The high-density equation of state can be probed in HI collisions and applied to the hot protoneutron star formed in core collapse supernovae. The parity radius experiment (PREX) aims to accurately measure the neutron radius of 208Pb with parity-violating electron scattering. This determines the pressure of neutron-rich matter and the density dependence of the symmetry energy. Competition between nuclear attraction and Coulomb repulsion can form exotic shapes called nuclear pasta in neutron star crusts and supernovae. This competition can be probed with multifragmentation HI reactions. We use large-scale semiclassical simulations to study nonuniform neutron-rich matter in supernovae. We find that the Coulomb interactions in astrophysical systems suppress density fluctuations. As a result, there is no first-order liquid-vapor phase transition. Finally, the virial expansion for low-density matter shows that the nuclear vapor phase is complex with significant concentrations of alpha particles and other light nuclei in addition to free nucleons. [ABSTRACT FROM AUTHOR]

This review on second- and third-generation multidetectors devoted to heavy-ion collisions aims to cover the last twenty years. The presented list of devices is not exhaustive but regroups most of the techniques used during this period for nuclear reactions at intermediate energy (≃ 10 A MeV to 1 A GeV), both for charged-particle and neutron detection. The main part will be devoted to 4π multidetectors, projectile decay fragmentation, high-resolution magnetic spectrometers, auxiliary detectors and neutron detection. The last part will present the progress in electronics and detection in view of the construction of future-generation detectors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Different approaches for measuring nuclear temperatures are described. The quantitative results of different thermometer approaches are often not consistent. These differences are traced back to the different basic assumptions of the applied methods. Moreover, an overview of recent theoretical investigations is given, which study the quantitative influence of dynamical aspects of the nuclear-reaction process on the extracted apparent temperatures. The status of the present experimental and theoretical knowledge is reviewed. Guidelines for future investigations, especially concerning the properties of asymmetric nuclear matter, are given. [ABSTRACT FROM AUTHOR]

This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak and the occurrence of a phase transition or a critical phenomenon is critically analyzed. Many different phenomena can lead both to the creation and to the suppression of a fluctuation peak. In particular, the role of constraints due to conservation laws and to data sorting is shown to be essential. From the experimental point of view, a comparison of the available fragmentation data reveals that there is a good agreement between different data sets of basic fluctuation observables, if the fragmenting source is of comparable size. This compatibility suggests that the fragmentation process is largely independent of the reaction mechanism (central vs. peripheral collisions, symmetric vs. asymmetric systems, light ions vs. heavy-ion-induced reactions). Configurational energy fluctuations, that may give important information on the heat capacity of the fragmenting system at the freeze-out stage, are not fully compatible among different data sets and require further analysis to properly account for Coulomb effects and secondary decays. Some basic theoretical questions, concerning the interplay between the dynamics of the collision and the fragmentation process, and the cluster definition in dense and hot media, are still open and are addressed at the end of the paper. A comparison with realistic models and/or a quantitative analysis of the fluctuation properties will be needed to clarify in the next future the nature of the transition observed from compound nucleus evaporation to multi-fragment production. [ABSTRACT FROM AUTHOR]

Abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation. Many-fragment correlations can be used to enlighten any extra production of events with specific fragment partitions. The high sensitivity of such correlation methods makes it particularly appropriate to look for small numbers of events as those expected to have kept a memory of spinodal decomposition properties and to reveal the dynamics of a first-order phase transition for nuclear matter and nuclei. This paper summarizes results obtained so far for both experimental and dynamical simulations data. [ABSTRACT FROM AUTHOR]

The moment analysis method and nuclear Zipf's law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf law performed so far. The relationship of both methods to a possible critical behavior or phase transition of nuclear disassembly is discussed. In addition, scaled factorial moments and intermittency are reviewed. [ABSTRACT FROM AUTHOR]

Methods for determining the heat content E* /A of hot nuclei formed in energetic nuclear reactions are discussed. The primary factors involved in converting raw data into thermal physics distributions include: 1) design of the detector array, 2) constraints imposed by the physics of the reaction mechanism, and 3) assumptions involved in converting the filtered data into E* /A. The two primary sources of uncertainty in the calorimetry are the elimination of nonequilibrium emissions from the event components and accounting for the contribution of neutron emission to the excitation energy sum. [ABSTRACT FROM AUTHOR]

The studies of the evolution of the hot Giant Dipole Resonance (GDR) properties as a function of excitation energy are reviewed. The discussion will mainly focus on the A ∼ 100-120 mass region where a large amount of data concerning the width and the strength evolution with excitation energy are available. Models proposed to interpret the main features and trends of the experimental results will be presented and compared to the available data in order to extract a coherent scenario on the limits of the development of the collective motion in nuclei at high excitation energy. Experimental results on the GDR built in hot nuclei in the mass region A ∼ 60-70 will be also shown, allowing to investigate the mass dependence of the main GDR features. The comparison between limiting excitation energies for the collective motion and critical excitation energies extracted from caloric curve studies will suggest a possible link between the disappearance of collective motion and the liquid-gas phase transition. [ABSTRACT FROM AUTHOR]

We review experimental and theoretical studies devoted to extract information on the behaviour of the symmetry energy, in density regions different from the normal value, with charge-asymmetric reactions at Fermi energies. In particular, we focus on the analysis of fragmentation reactions and isotopic properties of the reaction products. Results concerning "isoscaling" properties and the N/Z equilibration among the reaction partners in semi-peripheral reactions are also discussed. [ABSTRACT FROM AUTHOR]

This paper summarizes theoretical predictions for the density and isospin dependence of the nuclear mean field and the corresponding nuclear equation of state. We compare predictions from microscopic and phenomenological approaches. An application to heavy-ion reactions requires to incorporate these forces into the framework of dynamical transport models. Constraints on the nuclear equation of state derived from finite nuclei and from heavy-ion reactions are discussed. [ABSTRACT FROM AUTHOR]

In this report, we review the isospin dependence of various forms of the collective flow in heavyion reactions from Fermi to relativistic energies. The emphasis will be on suggested possible applications in directly exploring the underlying isovector potential and thus the Equation of State (EoS) of asymmetric nuclear matter, in particular in density regions far away from normal conditions. We also discuss forthcoming challenges and opportunities provided by high-energy radioactive beams. [ABSTRACT FROM AUTHOR]

Spinodal instability in nuclear matter and finite nuclei is investigated. This instability occurs in the low-density region of the phase diagram. The thermodynamical and dynamical analysis is based on Landau theory of Fermi liquids. It is shown that asymmetric nuclear matter can be characterized by a unique spinodal region, defined by the instability against isoscalar-like fluctuation, as in symmetric nuclear matter. Everywhere in this density region the system is stable against isovector-like fluctuations related to the species separation tendency. Nevertheless, this instability in asymmetric nuclear matter induces isospin distillation leading to a more symmetric liquid phase and a more neutron-rich gas phase. [ABSTRACT FROM AUTHOR]

The results from ten statistical multifragmentation models have been compared with each other using selected experimental observables. Even though details in any single observable may differ, the general trends among models are similar. Thus, these models and similar ones are very good in providing important physics insights especially for general properties of the primary fragments and the multifragmentation process. Mean values and ratios of observables are also less sensitive to individual differences in the models. In addition to multifragmentation models, we have compared results from five commonly used evaporation codes. The fluctuations in isotope yield ratios are found to be a good indicator to evaluate the sequential decay implementation in the code. The systems and the observables studied here can be used as benchmarks for the development of statistical multifragmentation models and evaporation codes. [ABSTRACT FROM AUTHOR]

We present an overview of concepts and results obtained with statistical models in the study of nuclear multifragmentation. Conceptual differences between statistical and dynamical approaches and the selection of experimental observables for identification of these processes are outlined. New and perspective developments, like inclusion of in-medium modifications of the properties of hot primary fragments, are discussed. We list important applications of statistical multifragmentation in other fields of research. [ABSTRACT FROM AUTHOR]

The various dynamical models for fragment formation in nuclear collisions are discussed in order to bring out their relative advantages and shortcomings. After discussing the general requirements for dynamical models that aim to describe fragment formation, we consider the various mean-field models that incorporate fluctuations and then turn to models based on molecular dynamics. [ABSTRACT FROM AUTHOR]

Dynamical and thermal characterizations of excited nuclear systems produced during the collisions between two heavy ions at intermediate incident energies are presented by means of a review of experimental and theoretical work performed in the last two decades. Intensity interferometry, applied to both charged particles (light particles and intermediate mass fragments) and to uncharged radiation (gamma rays and neutrons) has provided relevant information about the space-time properties of nuclear reactions. The volume, lifetime, density and relative chronology of particle emission from decaying nuclear sources have been extensively explored and have provided valuable information about the dynamics of heavy-ion collisions. Similar correlation techniques applied to coincidences between light particles and complex fragments are also presented as a tool to determine the internal excitation energy of excited primary fragments as it appears in secondary-decay phenomena. [ABSTRACT FROM AUTHOR]

Multifragmentation is observed in many reaction types: light-ion-induced reactions at large incident energies (in the GeV region), central heavy-ion collisions from 30 to 100 MeV/u, and peripheral heavy-ion collisions between 30 and 1000 MeV/u or above. When nucleus-nucleus collisions are considered, another entrance channel parameter is the corresponding mass asymmetry. The first question which is addressed in this contribution is: do we observe similar reactions in each case? Multifragmentation may be related to a phase transition of nuclear matter. Some others features indicate that dynamical features are dominant. It is a priori possible that the underlying mechanisms are different in proton- and nucleus-induced reactions, in central and in peripheral collisions, at limited and at large bombarding energies. In order to see to what extent they can reflect similar behaviour, it is useful to compare the results of various reactions. The observables can be the fragment multiplicity, the mass distributions or the kinematical properties. In this contribution, we are looking for such general features. We will limit the discussion to the observations themselves, rather than the interpretation, which is the subject of numerous entries in this volume. The experimental results indicate that multifragmentation exhibits at the same time universal and entrance-channel-dependent properties. [ABSTRACT FROM AUTHOR]

Intermediate-energy heavy-ion reactions produce a mid-rapidity region or neck, mostly in the semiperipheral collisions. Brief theory and experiment surveys are presented. General properties of the mid-rapidity zone are reviewed and discussed in the framework of reaction dynamics. Hierarchy effect, neutron enrichment, isospin diffusion are all new neck phenomena which are surveyed. The main neck observables are also examined, mainly in the context of the symmetry term of the nuclear equation of state. [ABSTRACT FROM AUTHOR]

We review some results on energetic particle production in heavy-ion collisions below roughly 100 A·MeV, both theoretically and experimentally. We discuss the possible mechanisms of particle production, as well as the possibility to gather information on the nuclear equation of state (EOS) from data. Results on subthreshold pions, energetic photons, nucleons and light charged particles (Z ≤ 2) are discussed and contrasted to microscopic models. Important information about the first stages of the reaction are obtained by such probes. At present, we can conclude that we have at least a qualitative understanding of the processes involved when such particles are produced. However, a quantitative determination of relevant EOS parameters is still missing. The production mechanism close to the kinematical threshold (incoherent, cooperative or statistical) is not completely elucidated either. This calls for new data using more modern detector systems and comparison to more refined microscopic models. [ABSTRACT FROM AUTHOR]

Excitation functions of flow and stopping observables for the Au+Au system at energies from 40 to 1500 MeV per nucleon are presented. The systematics were obtained by merging the results of the INDRA and FOPI experiments, both performed at the GSI facility. The connection to the nuclear equation of state is discussed. [ABSTRACT FROM AUTHOR]

The 5H system was produced in the 3H(t; p)5H reaction studied at small CM angles with a 58MeV tritium ion beam. High statistics data were used to reconstruct the energy and angular correlations between the 5H decay fragments. A broad structure in the 5H missing-mass spectrum showing up above 2.5MeV was identified as a mixture of the 3/2+ and 5/2+ states. The data also present an evidence that the 1/2+ ground state of 5H is located at about 2MeV. Then, the 5H and 5He systems were explored by means of transfer reactions occurring in the interactions of 132MeV 6He beam nuclei with deuterium. In the 2H(6He,3H) reaction aT = 3/2 isobaric analog state of 5H in 5He was observed at an excitation energy of 22.0 ± 0.3MeV with a width of 2.5 ± 0.3MeV. [ABSTRACT FROM AUTHOR]

Reactions induced on protons at low incident energy (3.5 MeV/n) were measured with a 8He beam accelerated by Spiral at Ganil. The particles were detected in the active target Maya, filled with C4H10 gas. The beam was stopped in the detector, so energies from incident beam energy down to detector threshold were covered. Proton elastic scattering, one neutron pick-up (p; d) and (p; t) reactions were observed. In the (p; d) reaction very high cross-sections of the order of 1barn were observed, that could be reproduced using a direct reaction formalism. This is the first time that this strong increase of transfer reaction cross-sections at very low energy predicted for loosely bound systems was observed. Spectroscopic factors are in agreement with a simple shell model configuration. No evidence for a low lying excited state in 7He was found. [ABSTRACT FROM AUTHOR]