A model for nuclear matter fragmentation: phase diagram and cluster distributions

We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties of the fragment size distributions. We show that two types of phase transitions can be found for high density systems. They merge into a unique transition at low density. An analysis of the critical exponents which characterize observables for different densities in the thermodynamic limit shows that these transitions look like continuous second order transitions.Comment: 27 pages, 5 figures; comments on microcanonical approach and other minor corrections added; references added; 1 figure change

Finite size effects and the order of a phase transition in fragmenting nuclear systems

We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise the smoothed transition observed in a finite system. We show that the microcanonical ensemble may be a useful framework for the determination of the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change

Thermodynamics of a finite system of classical particles with short and long range interactions and nuclear fragmentation

We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked out in the framework of the grand canonical ensemble. It is shown that the system experiences a phase transition at fixed average density in the thermodynamic limit. The phase diagram and the caloric curve are constructed and compared with numerical simulations. The implications of our results concerning the caloric curve are discussed in connection with the interpretation of corresponding experimental data.Comment: 11pages, LaTeX, 6 figures. Major change : A new section dealing with numerical simulations in the framework of a cellular model has been adde

Determination of the freeze-out temperature by the isospin thermometer

The high-resolution spectrometer FRS at GSI Darmstadt provides the full isotopic and kinematical identification of fragmentation residues in relativistic heavy-ion collisions. Recent measurements of the isotopic distribution of heavy projectile fragments led to a very surprising new physical finding: the residue production does not lose the memory of the N/Z of the projectile ending up in a universal de-excitation corridor; an ordering of the residues in relation to the neutron excess of the projectile has been observed. These unexpected features can be interpreted as a new manifestation of multifragmentation. We have found that at the last stage of the reaction the temperature of the big clusters subjected to evaporation is limited to a universal value. The thermometer to measure this limiting temperature is the neutron excess of the residues.Comment: 8 pages, 6 figures, corrected some misprints in the abstract, to be published in "Yadernaya Fizika" as a proceeding of the "VII International School Seminar on Heavy-Ion Phyics", Dubna (Russia), May 27 - June 1, 200

Breakup Conditions of Projectile Spectators from Dynamical Observables

Momenta and masses of heavy projectile fragments (Z >= 8), produced in collisions of 197Au with C, Al, Cu and Pb targets at E/A = 600 MeV, were determined with the ALADIN magnetic spectrometer at SIS. An analysis of kinematic correlations between the two and three heaviest projectile fragments in their rest frame was performed. The sensitivity of these correlations to the conditions at breakup was verified within the schematic SOS-model. The data were compared to calculations with statistical multifragmentation models and to classical three-body calculations. Classical trajectory calculations reproduce the dynamical observables. The deduced breakup parameters, however, differ considerably from those assumed in the statistical multifragmentation models which describe the charge correlations. If, on the other hand, the analysis of kinematic and charge correlations is performed for events with two and three heavy fragments produced by statistical multifragmentation codes, a good agreement with the data is found with the exception that the fluctuation widths of the intrinsic fragment energies are significantly underestimated. A new version of the multifragmentation code MCFRAG was therefore used to investigate the potential role of angular momentum at the breakup stage. If a mean angular momentum of 0.75$\hbar$/nucleon is added to the system, the energy fluctuations can be reproduced, but at the same time the charge partitions are modified and deviate from the data. PACS numbers: 25.70.Mn, 25.70.Pq, 25.75.Ld, 25.75.-qComment: 38 pages, RevTeX with 21 included figures; Also available from http://www-kp3.gsi.de/www/kp3/aladin_publications.htm

Sequential Decay Distortion of Goldhaber Model Widths for Spectator Fragments

Momentum widths of the primary fragments and observed final fragments have been investigated within the framework of an Antisymmetrized Molecular Dynamics transport model code (AMD-V) with a sequential decay afterburner (GEMINI). It is found that the secondary evaporation effects cause the values of a reduced momentum width, $\sigma_0$, derived from momentum widths of the final fragments to be significantly less than those appropriate to the primary fragment but close to those observed in many experiments. Therefore, a new interpretation for experiemental momentum widths of projectile-like fragments is presented.Comment: 4 pages, 3 figs. Accepted for publication in Phys. Rev. C as a Rapid Communicatio

Sequential Decay Distortion of Goldhaber Model Widths for Spectator Fragments

Momentum widths of the primary fragments and observed final fragments have been investigated within the framework of an Antisymmetrized Molecular Dynamics transport model code (AMD-V) with a sequential decay afterburner (GEMINI). It is found that the secondary evaporation effects cause the values of a reduced momentum width, $\sigma_0$, derived from momentum widths of the final fragments to be significantly less than those appropriate to the primary fragment but close to those observed in many experiments. Therefore, a new interpretation for experiemental momentum widths of projectile-like fragments is presented.Comment: 4 pages, 3 figs. Accepted for publication in Phys. Rev. C as a Rapid Communicatio

Dynamical approach to spectator fragmentation in Au+Au reactions at 35 MeV/A

The characteristics of fragment emission in peripheral $^{197}$Au+$^{197}$Au collisions 35 MeV/A are studied using the two clusterization approaches within framework of \emph{quantum molecular dynamics} model. Our model calculations using \emph{minimum spanning tree} (MST) algorithm and advanced clusterization method namely \emph{simulated annealing clusterization algorithm} (SACA) showed that fragment structure can be realized at an earlier time when spectators contribute significantly toward the fragment production even at such a low incident energy. Comparison of model predictions with experimental data reveals that SACA method can nicely reproduce the fragment charge yields and mean charge of the heaviest fragment. This reflects suitability of SACA method over conventional clusterization techniques to investigate spectator matter fragmentation in low energy domain.Comment: 6 pages, 5 figures, accepte

Breakup Density in Spectator Fragmentation

Proton-proton correlations and correlations of protons, deuterons and tritons with alpha particles from spectator decays following 197Au + 197Au collisions at 1000 MeV per nucleon have been measured with two highly efficient detector hodoscopes. The constructed correlation functions, interpreted within the approximation of a simultaneous volume decay, indicate a moderate expansion and low breakup densities, similar to assumptions made in statistical multifragmentation models. PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn, 25.75.GzComment: 11 pages, LaTeX with 3 included figures; Also available from http://www-kp3.gsi.de/www/kp3/aladin_publications.htm