Similarities between the lattice gas model and some other models of nuclear multifragmentation

We continue our development of the nuclear lattice gas model by exploring links and similarities with other theoretical approaches to nuclear multifragmentation: the percolation model and the statistical multifragmentation model. It is shown that there exists a limit where the lattice gas model reduces to the percolation model. The similarity between the lattice gas model and the statistical multifragmentation model is more indirect and we utilize the equations of state in the two models. By using the law of partial pressures we obtain P-ϱ diagrams for the statistical multifragmentation model and find that these are remarkably similar to those obtained in the lattice gas model via an exact evaluation of the nuclear partition function on the lattice. For completeness, we also compute the P-ϱ diagram for a system obeying pure classical molecular dynamics with a simple two-body force.     

Statistical description of nuclear break-up

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.     

Multifragmentation of charge asymmetric nuclear systems

The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of growth of density fluctuations in unstable expanding nuclear matter. The statistical model makes a choice of the final multifragment configuration according to its statistical weight at a global thermal equilibrium. Similarities and differences in the predictions of the two models on the isotopic composition of the produced fragments are presented and the most sensitive observable characteristics are discussed.     

Nuclear multifragmentation: Basic concepts

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different Z _bound, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.     

Influence of the coulomb interaction on the liquid-gas phase transition and nuclear multifragmentation

The liquid-gas phase transition is analyzed from the topologic properties of the event distribution in the observables space. A multicanonical formalism allows one to directly relate the standard phase transition with neutral particles to the case where the nonsaturating Coulomb interaction is present, and to interpret the Coulomb effect as a deformation of the probability distributions and a rotation of the order parameter. This formalism is applied to a statistical multifragmentation model and consequences for the nuclear multifragmentation phase transitions are drawn.     

Is bimodality a sufficient condition for a first-order phase transition existence?

Here we present two explicit counterexamples to the widely spread beliefs about an exclusive role of bimodality as the first-order phase transition signal. On the basis of an exactly solvable statistical model generalizing the statistical multifragmentation model of nuclei, we demonstrate that the bimodal distributions can naturally appear both in infinite and in finite systems without a phase transition. In the first counterexample a bimodal distribution appears in an infinite system at the supercritical temperatures due to the negative values of the surface tension coefficient. In the second counterexample we explicitly demonstrate that a bimodal fragment distribution appears in a finite volume analog of a gaseous phase. In contrast to the statistical multifragmentation model, the developed statistical model corresponds to the compressible nuclear liquid with the tricritical endpoint located at one third of the normal nuclear density. The suggested parameterization of the liquid phase equation of state is consistent with the L. Van Hove axioms of statistical mechanics and it does not lead to an appearance of the nonmonotonic isotherms in the macroscopic mixed phase region which are typical for the classical models of the Van der Waals type. Peculiarly, such a way to account for the nuclear liquid compressibility automatically leads to an appearance of an additional state that in many respects resembles the physical antinuclear matter.     

Connection between the thermodynamical and the percolation models of nuclear fragmentation

The connection is investigated between the percolation approach to nuclear fragmentation and the statistical multifragmentation model based on thermodynamical equilibrium concepts. The relation between the percolation parameter and the average excitation energy per nucleon of the fragmentating system has been investigated.     

Isospin and symmetry energy effects on nuclear fragment production in liquid-gas-type phase transition region

We have shown that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au¹⁹⁷, Sn¹²⁴, La¹²⁴ and Kr⁷⁸ at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent τ with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have shown that nuclear multifragmentation exhibits a “bimodality” behavior. We have also shown that the symmetry energy has a small influence on fragment mass distribution; however, its effect is more pronounced in the isotope distributions of produced fragments.     

Statistical multifragmentation of nuclei: (I). Formulation of the model

A statistical formulation of the multifragmentation of finite nuclei is given. The approach considers the generalization of the liquid-drop model for hot nuclei and allows one to calculate thermodynamic quantities characterizing the nuclear ensemble at the disassembly stage. It is shown how to determine probabilities of definite partitions of finite nuclei and how to apply a Monte Carlo method. The importance of including finite-size effects is shown by comparison with infinite-like systems.     

Critical exponents for nuclear multifragmentation: dynamical lattice model

We present a dynamical and dissipative lattice model, designed to mimic nuclear multifragmentation. Monte Carlo simulations with this model show a clear signature of critical behaviour and reproduce experimentally observed correlations. In particular, using techniques devised for finite systems, we could obtain two of its critical exponents, whose values are in agreement with those of the universality class to which nuclear multifragmentation is supposed to belong.     

High energy heavy ion interactions studied with SSNTDs

We have continued our studies of heavy ion projectile fragmentation using nuclear track detectors. Based on automatic track measurement it was possible to perform experiments with high statistical significance. Beams of different ions from the Berkeley BEVALAC, the Dubna Synchrophasotron, the Brookhaven AGS and the GSI Darmstadt SIS have been used. With CR-39 and BP-1 glass detectors we have studied the process of electromagnetic dissociation, we investigated multifragmentation and continued the search for quark nuclear complexes. This paper gives an overview of these experiments. Details of the experimental technique are discussed.     

Comparisons of statistical multifragmentation and evaporation models for heavy-ion collisions

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. An erratum to this article is available at .     

Critical temperature for the nuclear liquid-gas phase transition (from multifragmentation and fission)

Critical temperature T _c for the nuclear liquid-gas phase transition is estimated from both the multifragmentation and fission data. In the first case, the critical temperature is obtained by analysis of the intermediate-mass-fragment yields in p(8.1 GeV) + Au collisions within the statistical model of multifragmentation. In the second case, the experimental fission probability for excited ¹⁸⁸Os is compared with the calculated one with T _c as a free parameter. It is concluded for both cases that the critical temperature is higher than 15 MeV. The text was submitted by the authors in English.     

Stellar matter in supernova explosions and nuclear multifragmentation

During the collapse of massive stars and type-II supernova explosions, stellar matter reaches densities and temperatures which are similar to ones obtained in intermediate-energy nucleus-nucleus collisions. The nuclear multifragmentation reactions can be used for determination of properties of nuclear matter at subnuclear densities, in the region of the nuclear liquid-gas phase transition. It is demonstrated that the modified properties of hot nuclei (in particular, their symmetry energy) extracted from the multifragmentation data can essentially influence the nuclear composition of stellar matter. The effects of the modification of nuclear properties on weak processes and on nucleosynthesis are also discussed. The text was submitted by the authors in English.     

Nuclear multifragmentation, percolation, and the fisher droplet model: common features of reducibility and thermal scaling

It is shown that the Fisher droplet model, percolation, and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42+/-0.02. The EOS Collaboration Au multifragmentation data yield barriers with a power-law exponent of 0.68+/-0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted.     

Nuclear multifragmentation and phase transitions in hot nuclei

Nuclear multifragmentation is a new, multibody, decay mode of very hot nuclei. The key properties of this process that were measured are considered, such as the space-time and temperature characteristics. The experimental data for the critical temperature of the nuclear liquid-gas-phase transition are analyzed. Thermal multifragmentation is interpreted as a result of spinodal decomposition, which is actually the specific nuclear liquid-fog-phase transition of the first order. The text was submitted by the author in English.     

Balance of mass, momentum, and energy in splintering central collisions for 40Ar up to 115 MeV /Nucleon

For central collisions of (17-115)A MeV 40Ar+Cu, Ag, Au, an overall balance is determined for the average mass, energy, and longitudinal momentum. Light charged particles and fragments are separated into forward-focused and isotropic components in the frame of the heaviest fragment. Energy removal by the isotropic component reaches 1-2 GeV. For such high deposition energies, statistical multifragmentation models predict much more extensive nuclear disassembly than is observed.     

Multifractal critical thermodynamics in nucleus-nucleus collisions

Critical points approach in the frames of multifractal thermodynamics is suggested to interpret the experimental data on nuclear multifragmentation which come from interactions in nuclear emulsion (in which ¹⁹⁷ ₇₉Au₁₁₈ nuclei of energy ∼1 GeV/nucleon break up into fragments) and from the charge distributions of projectile fragments in sulphur (³²S) fragmentation at 200 GeV/nucleon. It is also shown that multifragmentation after macro-solids collisions exhibits properties analogous to those observed in the nuclear multifragmentation experiments. Received: 19 October 1999     

Fragmentation of nuclei at intermediate and high energies in modified cascade model

The process of nuclear multifragmentation has been implemented, together with evaporation and fission channels of the disintegration of excited remnants, in nucleus-nucleus collisions using percolation theory and the intranuclear cascade model. Colliding nuclei are treated as face-centered-cubic lattices with nucleons occupying the nodes of the lattice. The site-bond percolation model is used. The code can be applied for calculation of the fragmentation of nuclei in spallation and multifragmentation reactions.     

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.