Isospin dependence of nuclear multifragmentation in statistical model

The evolution of nuclear disintegration mechanisms with increasing excitation energy, from compound nucleus to multifragmentation, has been studied by using the Statistical Multifragmentation Model (SMM) within a micro-canonical ensemble. We discuss the observable characteristics as functions of excitation energy in multifragmentation, concentrating on the isospin dependence of the model in its decaying mechanism and break-up fragment configuration by comparing the A₀=200, Z₀=78 and A₀=200, Z₀=100 systems. The calculations indicate that the neutron-rich system (Z₀=78) translates to a fission-like process from evaporation later than the symmetric nucleus at a lower excitation energy, but gets a larger average multiplicity as the excitation energy increases above 1.0 MeV/u.     

Thermal multifragmentation in p + Au interactions at 2.16, 3.6 and 8.1 GeV incident energies

Multiple emission of intermediate-mass fragments has been studied for the collisions p + Au at 2.16, 3.6 and 8.1 GeV with the FASA setup. The mean IMF multiplicities for events with at least one IMF are equal to 1.7, 1.9 and 2.1 (±0.2) respectively. The multiplicity, charge distributions and kinetic energy spectra of IMF are described in the framework of a intranuclear cascade model followed by the statistical multifragmentation model. However, between the two parts of the calculation the excitation energies and the residual masses and charges are modified to take into account the losses during expansion. The results support a scenario of true thermal multifragmentation of a hot and expanded target spectator. Received: 15 December 1997 / Revised version: 24 April 1998     

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.     

Multifragmentation study on 30 AMeV32S+58Ni

In a multidetector experiment on 26 or 30 AMeV³²S+⁵⁸Ni, up to four coincident heavier or intermediate-mass fragments were observed. One of these occasionally has the characteristics of a projectile-like fragment, up to three may be attributed to the decay of the heavy reaction product. Taking the velocity of the fragments as a measure of the heavy-product excitation energy, one finds evaporation, fission and multifragmentation to follow one another with rising excitation. Model simulations of sequential decay with up to two binary fissions and, alternatively, of simultaneous statistical multifragmentation were performed for comparison with experimental distributions of mass, velocity and (for events with three slow intermediate-mass fragments) relative azimuthal angle. Though in the three-fragment events indications of simultaneous multifragmentation are present, the sequential binary decay predominates. Evaporated protons and α particles detected in coincidence have a mean multiplicity growing with excitation energy, while the temperature governing the spectra has a plateau with a value of about 5.5 MeV.     

Angular distribution of multifragmentation products from interaction of 48 GeV4He with Ag

Angular distribution of multifragmentation products formed in the interaction of 48 GeV⁴He with Ag target has been measured using a CR-39 plastic track detector. The analysis shows that distribution peaks at backward angles.     

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 .     

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.     

Isospin dependence of nuclear multifragmentation in statistical model

The evolution of nuclear disintegration mechanisms with increasing excitation energy, from com- pound nucleus to multifragmentation, has been studied by using the Statistical Multifragmentation Model (SMM) within a micro-canonical ensemble. We discuss the observable characteristics as functions of excitation energy in multifragmentation, concentrating on the isospin dependence of the model in its decaying mechanism and break-up fragment configuration by comparing the A<,0> = 200, Z<,0> = 78 and A<,0> = 200, Z<,0> = 100 systems. The calculations indicate that the neutron-rich system (Z<,0> = 78) translates to a fission-like process from evaporation later than the symmetric nucleus at a lower excitation energy, but gets a larger average multiplicity as the excitation energy increases above 1.0 MeV/u.     

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.     

Production of fragments in He+Au reaction at 12.7 GeV

The emission of fragments (A≥16) from reaction of ⁴He with ¹⁹⁷Au has been studied at bombarding energy of 12.7 GeV. Policarbonate Makrofol in sandwich form was used as a detector. Fragments produced in the experiment were identified and an event by event model-free analysis was performed. The decay channels ending with one, two or more (three, four) fragments were detected. A classification scheme based on the multiplicity (M_H) of heavy fragments (A≥40) was used in order to define multifragmentation (M_H = 0), spallation (M_H = 1) and fission (M_H = 2) events. The various experimental features of the fragmentation process are discussed.     

Many-fragment correlations and possible signature of spinodal fragmentation

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.     

The simulations of Ca-Ca collisions: Binary break-up, onset of multifragmentation and vaporization

The incomplete fusion, onset of multifragmentation and vaporization is studied in Ca-Ca collisions at bombarding energies between 20–1000 A MeV and at impact parameters between b=0 to b _max using quantum molecular dynamics model. We find incomplete fusion events at E/A=20 MeV. The light mass fragment production at a given incident energy does not show any rise and fall with a change in the impact parameter. Whereas, the IMF production at higher energies (≥ 150 A MeV) has a clear rise and fall.     

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.     

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.     

Multifragmentation induced by GeV He beams

Multifragmentation of ^natAg and ¹⁹⁷Au induced by 7 and 14.4 GeV ⁴He has been investigated by using CR-39 plastic track detectors. Since our experimental technique enables the determination of the multiplicity of intermediate mass fragments (IMFs) with uncertainty of only a few percent, the results obtained pointed out the inconsistency in the data regarding the quantity reported by other authors. We have also studied the behavior of characteristics of IMFs dependent on the reaction parameters (incident energy, atomic number of the target). From this analysis, we made some conclusions about the reaction mechanism of multifragmentation.     

有限核多重碎裂的同位旋效应和临界现象的分析

利用非对称核物质状态方程及同位旋相关的量子分子动力学模型对有限核112Sn和132Sn在不同温度下多重碎裂的同位旋效应进行了研究，发现随着温度的升高同位旋效应逐渐消失，并给出了在一定温度下不同密度对产生中等质量碎片的影响. 通过碎片的关联分析,对中高能重离子碰撞中的临界现象做了初步研究.     

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 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.     

处于力学不稳定条件下的受激有限核的动力学演化与确定论混沌

以208Pb为例,研究了不同热力学稳定条件下有限核体系单体耗散的非线性特征。首先,给出了该原子核在不同温度下的压强密度相图以及相图中的力学不稳定区(Spinodal region),在相图中属于不同稳定性区域的温度和密度值下,抽取了208Pb中各核子的坐标和动量,然后,将其作为量子分子动力学(QMD)模型的初始值,模拟受激有限原子核体系仅在平均场作用下的时空演化,分析不同初始分布所对应的系统在时空演化过程中核子的空间分布、密度涨落等随时间的演化特征,重点对比分析了对应于相图中不同区域的初始208Pb原子核在演化过程中的不同表现特征;通过对定义在事件空间和定义在相空间的准Lyapunov指数的计算,清楚地显示,在力学不稳定的条件下,平均场动力学对于核子空间分布的敏感依赖性,定量地揭示了反应动力学中单体耗散的非线性混沌特征,进一步证实了中能重离子碰撞中多重碎裂的混沌机制。