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Critical Exponents for Nuclear Multifragmentation: dynamical lattice model  [PDF]
J. S. Sa' Martins,P. M. C. de Oliveira
Physics , 1998, DOI: 10.1016/S0375-9474(98)00559-4
Abstract: We present a dynamical and dissipative lattice model, designed to mimic nuclear multifragmentation. Monte-Carlo simulations with this model show 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.
Nuclear Multifragmentation Critical Exponents  [PDF]
Wolfgang Bauer,William Friedman
Physics , 1994, DOI: 10.1103/PhysRevLett.75.767
Abstract: We show that the critical exponents of nuclear multi-fragmentation have not been determined conclusively yet.
Comparison of 1A GeV $^{\bf 197}$Au + C data with thermodynamics: the nature of phase transition in nuclear multifragmentation  [PDF]
EOS Collaboration,R. P. Scharenberg,B. K. Srivastava
Physics , 2001,
Abstract: Multifragmentation (MF) results from 1A GeV Au on C have been compared with the Copenhagen statistical multifragmentation model (SMM). A large number of observables, including the fragment charge yield distributions, fragment multiplicity distributions, caloric curve, critical exponents, and the critical scaling function are explored in this comparison. The nature of the phase transition in SMM is studied as a function of the remnant mass and charge using the microcanonical equation of state. For light remnants $A \leq $ 100, backbending is observed indicating negative specific heat, while for $A \geq$ 170 the effective latentheat approaches zero. Thus for heavier systems this transition can be identified as a continuous thermal phase transition.
The critical indices of the Quark-Gluon Bags with Surface Tension Model with tricritical endpoint  [PDF]
A. I. Ivanytskyi
Physics , 2011, DOI: 10.1016/j.nuclphysa.2012.02.004
Abstract: The critical indices \alpha', \beta, \gamma' and \delta of the Quark Gluon Bags with Surface Tension Model with the tricritical endpoint are calculated as functions of the usual parameters of this model and two newly introduces parameters (indices). They are compared with the critical exponents of other models. It is shown that for the newly introduced indices \chi = 0 and \xi^T < 1 there is a branch of solutions for which the critical exponents of the present model and the statistical multifragmentation model coincide, otherwise these models belong to different universality classes. It is shown that for realistic values of the parameter \varkappa the critical exponents \alpha', \beta, \gamma' and \delta of simple liquids and 3-dimensional Ising model can be only described by the branch of solutions in which all indices except for \alpha' correspond to their values within the statistical multifragmentation model. The scaling relations for the found critical exponents are verified and it is demonstrated that for the standard definition of the index \alpha' the Fisher and Griffiths scaling inequalities are not fulfilled for some values of the model parameters, whereas the Liberman scaling inequality is always obeyed. Although it is shown that the specially defined index \alpha'_s recovers the scaling relations, another possibility, an existence of the non-Fisher universality classes, is also discussed.
Fermi breakup and the Statistical Multifragmentation Model  [PDF]
B. V. Carlson,R. Donangelo,S. R. Souza,W. G. Lynch,A. W. Steiner,M. B. Tsang
Physics , 2010, DOI: 10.1088/1742-6596/312/8/082017
Abstract: We demonstrate the close similarity of a generalized Fermi breakup model, in which densities of excited states are taken into account, to the microcanonical statistical multifragmentation model used to describe the desintegration of highly excited fragments of nuclear reactions.
Exact Analytical Solution of the Constrained Statistical Multifragmentation Model  [PDF]
Kyrill A. Bugaev
Physics , 2004,
Abstract: A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the finite volume of the system. A complete analysis of the isobaric partition singularities is done for finite system volumes. The finite size effects for large fragments and the role of metastable (unstable) states are discussed.
Multifragmentation and the Phase Transition: A Systematic Study of the MF of 1A GeV Au, La, and Kr  [PDF]
B. K. Srivastava
Physics , 2002, DOI: 10.1103/PhysRevC.65.054617
Abstract: A systematic analysis of the multifragmentation (MF) in fully reconstructed events from 1A GeV Au, La and Kr collisions with C has been performed. This data is used to provide a definitive test of the variable volume version of the statistical multifragmentation model (SMM). A single set of SMM parameters directly determined by the data and the semi-empiricalmass formula are used after the adjustable inverse level density parameter, $\epsilon_{o}$ is determined by the fragment distributions. The results from SMM for second stage multiplicity, size of the biggest fragment and the intermediate mass fragments are in excellent agreement with the data. Multifragmentation thresholds have been obtained for all three systems using SMM prior to secondary decay. The data indicate that both thermal excitation energy $E_{th}^{*}$ and the isotope ratio temperature $T_{He-DT}$ decrease with increase in system size at the critical point. The breakup temperature obtained from SMM also shows the same trend as seen in the data. The SMM model is used to study the nature of the MF phase transition. The caloric curve for Kr exhibits back-bending (finite latent heat) while the caloric curves for Au and La are consistent with a continuous phase transition (nearly zero latent heat) and the values of the critical exponents $\tau$, $\beta$ and $\gamma$, both from data and SMM, are close to those for a 'liquid-gas' system for Au and La. We conclude that the larger Coulomb expansion energy in Au and La reduces the latent heat required for MF and changes the nature of the phase transition. Thus the Coulomb energy plays a major role in nuclear MF.
The Statistical Multifragmentation Model with Skyrme Effective Interactions  [PDF]
S. R. Souza,B. V. Carlson,R. Donangelo,W. G. Lynch,A. W. Steiner,M. B. Tsang
Physics , 2009, DOI: 10.1103/PhysRevC.79.054602
Abstract: The Statistical Multifragmentation Model is modified to incorporate the Helmholtz free energies calculated in the finite temperature Thomas-Fermi approximation using Skyrme effective interactions. In this formulation, the density of the fragments at the freeze-out configuration corresponds to the equilibrium value obtained in the Thomas-Fermi approximation at the given temperature. The behavior of the nuclear caloric curve at constant volume is investigated in the micro-canonical ensemble and a plateau is observed for excitation energies between 8 and 10 MeV per nucleon. A kink in the caloric curve is found at the onset of this gas transition, indicating the existence of a small excitation energy region with negative heat capacity. In contrast to previous statistical calculations, this situation takes place even in this case in which the system is constrained to fixed volume. The observed phase transition takes place at approximately constant entropy. The charge distribution and other observables also turn out to be sensitive to the treatment employed in the calculation of the free energies and the fragments' volumes at finite temperature, specially at high excitation energies. The isotopic distribution is also affected by this treatment, which suggests that this prescription may help to obtain information on the nuclear equation of state.
The critical temperature of nuclear matter and fragment distributions in multifragmentation of finite nuclei  [PDF]
R. Ogul,A. S. Botvina
Physics , 2002, DOI: 10.1103/PhysRevC.66.051601
Abstract: The fragment production in multifragmentation of finite nuclei is affected by the critical temperature of nuclear matter. We show that this temperature can be determined on the basis of the statistical multifragmentation model (SMM) by analyzing the evolution of fragment distributions with the excitation energy. This method can reveal a decrease of the critical temperature that, e.g., is expected for neutron-rich matter. The influence of isospin on fragment distributions is also discussed.
A study of the phase transition in the usual statistical model for nuclear multifragmentation  [PDF]
S. Das Gupta,A. Z. Mekjian
Physics , 1997, DOI: 10.1103/PhysRevC.57.1361
Abstract: We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of particles. This enables us to study a phase transition in the model. A first order phase transition can be tracked down. There are significant differences between this phase transition and some other well-known cases.
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