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.     

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.     

Isospin Dependence in Nuclear Multifragmentation Within Site Percolation and Nucleation Pictures

The isospin dependence, recently observed in Sn + Sn reactions at 40 MeV/nucleon, is discussed within the framework of two simple nuclear multifragmentation models, namely the site percolation and the nucleation-evaporation models. It is shown that both the models are able to discriminate between ¹¹²Sn+ ¹¹²Sn and ¹²⁴Sn+ ¹²⁴Sn reactions. The nucleation-evaporation model succeeds to reproduce nicely the experimental data, but the site percolation model fails in doing that, even if the cluster noncompactive effect is taken into account. The calculations indicate that the data are originated mainly from a single source.     

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.     

Percolation of diffusional creep: a new universality class

We study the percolation aspects of diffusional "Coble" creep on heterogeneous grain boundary networks, assuming free grain boundary sliding. A novel percolation threshold is obtained for the honeycomb lattice when two representative types of grain boundaries are randomly distributed, p(cc)=0.5416+/-0.0036. The creep viscosity diverges near the percolation threshold with power-law exponents t=1.69+/-0.09 and s=1.88+/-0.12, different from the standard conduction and rigidity percolation exponents. The moments of both the force and flux distributions all conform to finite-size scaling at p(cc), but with new exponents. These new scaling behaviors seen in the creeping system are proposed to arise from the unique coupling of both force and flux balances in the network.     

Superheavies and beyond

The extension of the periodic system into various new areas is investigated. Experiments for the synthesis of superheavy elements and the predictions of magic numbers are reviewed. Different ways of nuclear decay are discussed like cluster radioactivity, cold fission and cold multifragmentation. Further on, investigations on hypernuclei and the possible production of antimatter-clusters in heavy-ion collisions are reported. Various versions of the meson-field theory serve as effective field theories at the basis of modern nuclear structure and suggest structure in the vacuum which might be important for the production of hyper- and antimatter. A perspective for future research is given.     

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.     

Nuclear cluster structure: Superheavies, cluster-radioactivity and exotic fission processes

The extension of the periodic system into various new areas is investigated. Experiments for the synthesis of superheavy elements and the predictions of magic numbers are reviewed. Different channels of nuclear decay are discussed like cluster radioactivity, cold fission and cold multifragmentation, including the recent discovery of the tripple fission of ²⁵²Cf.     

Multifragmentation and incomplete fusion in central heavy ion collisions within a schematic phenomenological model

The projectile-energy thresholds for nuclear multifragmentation in the collisions of ¹²C, ²⁰Ne and ⁴⁰Ar with ¹⁹⁷Au have been calculated using a schematic model applicable to central collisions of intermediate energy heavy ions. The properties of the composite nucleus which remains following the incomplete fusion of the projectile and target nuclei are calculated using the master equation approach of Harp and Miller to determine the number of preequilibrium nucleons emitted and the energy and linear momentum removal by these nucleons. This nucleus is followed through an isentropic expansion phase and the probability distribution of clusters is determined using a percolation approach based on a 3-dimensional cubic lattice. The input parameters for the percolation calculation are derived from the results of the preequilibrium calculation. While the calculated thresholds in projectile energy per nucleon decrease rapidly as the projectile mass increases, the excitation energy at which multifragmentation is first predicted to occur is approximately the same for each system, i.e., 4.5 to 5 MeV/u. This result is consistent with the apparent disappearance of residual heavy products at such bombarding energies.     

Percolation in Media with Columnar Disorder

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.     

Mass yield distributions for 1 GeV proton-induced nuclear reactions on Ni and Ag

For 1 GeV proton-induced reactions on Ni and Ag the inclusive mass spectra covering a wide range of masses are analyzed with a two-step statistical multifragmentation model which considers the secondary decay of the primordial fragments. It is found that the yield of lighter clusters can only be reproduced by considering the evaporation processes. The experimentally observed U-shaped mass spectra are described by essentially one parameter - the temperature of about 6 MeV. The power-law fit gives an exponent about one unit lower than the critical one.     

Multifragmentation of hot and compressed nuclei within a time dependent thomas fermi and percolation model

We have used a spherical time dependent Thomas Fermi model to study the expansion of hot and/or compressed nuclei. This approach was coupled to a site-bond percolation model to study the disassembly of the nucleus into many pieces (multifragmentation). We find that a non compressed nucleus undergoes multifragmentation if the thermal excitation energy is larger than 70% of its binding energy. If the nucleus is compressed this value is notably decreased.     

Fragment charge correlations and spinodal decomposition in finite nuclear systems

Enhanced production of events with almost equal-sized fragments is experimentally revealed by charge correlations in the multifragmentation of a finite nuclear system selected in ¹²⁹Xe central collisions on ^nat Sn. The evolution of their weight with the incident energy: 32, 39, 45, 50 AMeV, is measured. Dynamical stochastic mean-field simulations performed at 32 AMeV, in which spinodal instabilities are responsible for multifragmentation, exhibit a similar enhancement of this kind of events. The above experimental observation evidences the spinodal decomposition of hot finite nuclear matter as the origin of multifragmentation in the Fermi energy regime.Received: 22 November 2002, Revised: 22 April 2003, Published online: 30 September 2003PACS: 25.70.Pq Multifragment emission and correlations - 24.60.Ky Fluctuation phenomenaG. Tabacaru: Present address: Cyclotron Institute, Texas A&M University, College station, Texas 77845, USA.N. Le Neindre: Permanent address: Institut de Physique Nucléaire, IN2P3-CNRS, F-91406 Orsay cedex, France.     

Stability and instability of a hot and dilute nuclear droplet

The diabatic approach to dissipative collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with similar growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition). Received: 4 September 2000 / Accepted: 14 November 2000     

Scaling properties of percolation models for multifragmentation

We have used scaling properties of nuclear multifragmentation, which have been observed with emulsion data, to investigate the properties of some approaches based on percolation. We have studied different percolation models on a cubic lattice and shown that they can rather well reproduce the data except for binary break up. We have described what the mean field approximation would give in this context and showed that it cannot reproduce the experimental results. Most of the paper is focused on the restructured aggregation model introduced earlier which allows to well reproduce the scaling properties observed experimentally. This model has been studied in details and extended to take account of bonds breaking. It is shown that, in some cases, a nucleus can break up in two pieces. This process cannot be obtained in conventional percolation or aggregation but is observed experimentally in the emulsion data. Other features like the dimensionality of the aggregation model, the restructuration of the clusters and a schematic constraint in momentum space have also been investigated.     

Erdös Rényi随机网络上爆炸渗流模型相变性质的数值模拟研究

基于改进的Newman和Ziff算法以及有限尺寸标度理论, 通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟, 分析研究了Erdös Rényi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明: 尽管序参量表现出了不连续相变的特征, 但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erdös Rényi随机网络中的爆炸渗流相变是一种奇异相变, 它既不是标准的不连续相变, 又与常规随机渗流表现出的连续相变处于不同的普适类. 关键词： Erdös Rényi随机网络 爆炸渗流模型 相变 幂律标度行为     

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.     

Search for a signal on QCD critical point in central nucleusnucleus collisions

We discuss that the QCD critical point could appear in central collisions in percolation cluster. We suggest to use the effects of nuclear transparency and that of the light nuclear production to identify the critical point.     

Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis

The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.     

Transition probabilites betweenvh 11 2/n states in Sn isotopes

A simple evaporation and percolation model is applied to calculate the amount of excitation energy needed to have multifragmentation.