Multifragmentation Reactions Research Articles

Relevance of equilibrium in multifragmentation

The relevance of equilibrium in a multifragmentation reaction of very central $^{40}\mathrm{Ca}$ $+$ $^{40}\mathrm{Ca}$ collisions at 35 MeV/nucleon is investigated by using simulations of antisymmetrized molecular dynamics (AMD). Two types of ensembles are compared. One is the reaction ensemble of the states at each reaction time $t$ in collision events simulated by AMD, and the other is the equilibrium ensemble prepared by solving the AMD equation of motion for a many-nucleon system confined in a container for a long time. The comparison of the ensembles is performed for the fragment charge distribution and the excitation energies. Our calculations show that there exists an equilibrium ensemble that well reproduces the reaction ensemble at each reaction time $t$ for the investigated period $80\ensuremath{\leqslant}t\ensuremath{\leqslant}300 \mathrm{fm}/c$. However, there are some other observables that show discrepancies between the reaction and equilibrium ensembles. These may be interpreted as dynamical effects in the reaction. The usual static equilibrium at each instant is not realized since any equilibrium ensemble with the same volume as that of the reaction system cannot reproduce the fragment observables.

Classification of the impact parameter in nucleus–nucleus collisions by a support vector machine method

One of the problems in the analysis of nucleus–nucleus collisions is to get information on the value of the impact parameter b. This work consists in the application of pattern recognition techniques aimed at associating values of b to groups of events. To this end, a support vector machine (SVM) classifier is adopted to analyse multifragmentation reactions. This method allows us to backtrace the values of b through a particular multidimensional analysis. The SVM classification consists of two main phases. In the first one, known as the training phase, the classifier learns to discriminate events that are generated by a model. In this case we used a classical molecular dynamics (CMD) model for the reaction: 58Ni + 48Ca at 25 A MeV. To check the classification of events in the second one, known as the test phase, what has been learned is tested on new events generated by the same model. These new results have been compared to those obtained through others techniques of backtracing the impact parameter (estimate function of b and PCA analysis). This approach better classifies central and peripheral collisions with respect to other techniques. We have finally performed the SVM classification on the experimental data measured by the NUCL-EX Collaboration with CHIMERA apparatus for the previous reaction and we show some results of the method.

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.

Role of bulk energy in nuclear multifragmentation

Because of thermal expansion and residual interactions, hot nuclear fragments produced in multifragmentation reactions may have nucleon density lower than the equilibrium density of cold nuclei. In terms of a liquid-drop model this effect can be taken into account by reducing the bulk energy of fragments. We study the influence of this change on fragment yields and isotope distributions within the framework of the statistical multifragmentation model. Similarities and differences with previously discussed modifications of symmetry and surface energies of nuclei are analyzed.

Break-up stage restoration in multifragmentation reactions

In the case of Xe + Sn at 32MeV/nucleon multifragmentation reaction break-up fragments are built up from the experimentally detected ones using evaluations of light-particle evaporation multiplicities which thus settle fragment internal excitation. Freeze-out characteristics are extracted from experimental kinetic energy spectra under the assumption of full decoupling between fragment formation and energy dissipated in different degrees of freedom. The thermal kinetic energy is determined uniquely while for the freeze-out volume - collective energy a multiple solution is obtained. The coherence between the solutions of the break-up restoration algorithm and the predictions of a multifragmentation model with identical definition of primary fragments is regarded as a way to select the true value. The broad kinetic energy spectrum of 3He is consistent with the break-up genesis of this isotope.

Looking for bimodal distributions in multi-fragmentation reactions

The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multi-fragmentation experiments, with results that do not appear fully consistent. In this paper we discuss the effect of the statistical ensemble or sorting conditions on the shape of fragment distributions, and propose a new method, which can be easily implemented experimentally, to discriminate between different fragmentation scenario. This method, based on a reweighting of the measured distribution to account for the experimental constraints linked to the energy deposit, is tested on different simple models, and appears to provide a powerful discrimination.

Multifragmentation of Au induced by 14.6 GeVHe4

The multifragmentation reaction channel was investigated in 14.6 GeV $^{4}\mathrm{He}$+Au interactions. The experimental setup enabled event-by-event analysis. An internal correlation study suggests a nearly simultaneous emission of fragments. The velocities ($V{}_{\mathrm{c.m.}}$) of the center-of-mass system of correlated fragments were calculated. The transverse component of $V{}_{c.m.}$ with respect to the beam direction has higher values than the longitudinal one, which corresponds to large recoil angles of the source. The angular distributions of fragments are sideways peaked. The peak angle is dependent on the atomic number of fragment and multiplicity. Our results show that the heaviest fragment in one event corresponds, on average, to the largest emission angle, the second heaviest fragment corresponds to the second largest emission angle, and so on.

Modification of surface energy in nuclear multifragmentation

Within the statistical multifragmentation model we study modifications of the surface and symmetry energy of primary fragments in the freeze-out volume. The ALADIN experimental data on multifragmentation obtained in reactions induced by high-energy projectiles with different neutron richness are analyzed. We have extracted the isospin dependence of the surface energy coefficient at different degrees of fragmentation. We conclude that the surface energy of hot fragments produced in multifragmentation reactions differs from the values extracted for isolated nuclei at low excitation. At high fragment multiplicity, it becomes nearly independent of the neutron content of the fragments.

Possible links between the liquid-gas and deconfinement-hadronization phase transitions

It is commonly accepted that strongly interacting matter has several phase transitions in different domains of temperature and baryon density. In this contribution I discuss two most popular phase transitions which in principle can be accessed in nuclear collisions. One of them, the liquid-gas phase transition, is well established theoretically and studied experimentally in nuclear multifragmentation reactions at intermediate energies. The other one, the deconfinement-hadronization phase transition, is at the focus of present and future experimental studies with relativistic heavy-ion beams at SPS, RHIC and LHC. Pssible links between these two phase transitions are identified from the viewpoint of their manifestation in violent nuclear collisions.

Nuclear liquid-gas phase transition studied with antisymmetrized molecular dynamics

The nuclear liquid-gas phase transition of the system in ideal thermal equilibrium is studied with antisymmetrized molecular dynamics. The time evolution of a many-nucleon system confined in a container is solved for a long time to get a microcanonical ensemble of a given energy and volume. The temperature and the pressure are extracted from this ensemble and the caloric curves are constructed. The present work is the first time that a microscopic dynamical model which describes nuclear multifragmentation reactions well is directly applied to get the nuclear caloric curve. The obtained constant pressure caloric curves clearly show the characteristic feature of the liquid-gas phase transition, namely negative heat capacity (backbending), which is expected for the phase transition in finite systems.

Multifragmentation reactions and properties of stellar matter at subnuclear densities

We point out similarity of thermodynamic conditions reached in intermediate energy nuclear collisions and in supernova explosions. We show that a statistical approach, which has been previously applied for nuclear multifragmentation reactions, can be very useful for description of electro-neutral stellar matter. Then properties of hot unstable nuclei extracted from analysis of multifragmentation data can be used for construction of a realistic equation of state of supernova matter.

Origin of Fragments in Multifragmentation Reactions

Using the quantum molecular dynamics approach we have started to analyze the results of the recent INDRA experiments at GSI experiments. For the first time we could identify a midrapidity source in which fragments are formed from a almost identical fraction of projectile and target nucleons. In smaller systems we have not found this source. Nevertheless the fragment spectra at small and large angles are completely determined by the dynamics. We discuss how fragments are formed in the different regions of phase space and what they tell us about the reaction mechanism.

Publisher's Note: Fragment yield distribution and the influence of neutron composition and excitation energy in multifragmentation reactions [Phys. Rev. C 71, 024602 (2005)

Received 4 February 2005DOI:https://doi.org/10.1103/PhysRevC.71.029903©2005 American Physical Society

Model-independent tracking of criticality signals in nuclear multifragmentation data

We look for signals of a phase transition in multifragmentation reactions using the model-independent theory of universal fluctuations. It is show that, in central collisions of symmetric systems around the Fermi energy, the fluctuations of the size of the largest fragment in each event can be used two energy- and mass-dependent fragmentation regimes, which may be interpreted as ordered and disordered phases of an aggregation-like phenomenon.

Fragment yield distribution and the influence of neutron composition and excitation energy in multifragmentation reactions

The isotopic properties of the primary and secondary fragment yield distribution in the multifragmentation of {sup 58}Fe+{sup 58}Ni and {sup 58}Fe+{sup 58}Fe reactions are studied with respect to the {sup 58}Ni+{sup 58}Ni reaction at 30, 40, and 47 MeV/nucleon. The reduced neutron and proton densities from the observed fragment yield distribution show primary fragment yield distribution to undergo strongly secondary deexcitations. The effect is small at the lowest excitation energy and smallest neutron-to-proton ratio and becomes large at higher excitation energies and higher neutron-to-proton ratio. The symmetry energy of the primary fragments deduced from the reduced neutron density is significantly lower than that for the normal nuclei at saturation density, indicating that the fragments are highly excited and formed at a reduced density. Furthermore, the symmetry energy is also observed to decrease slowly with increasing excitation energy. The observed effect is explained using the statistical multifragmentation model.

Equilibrium under flow

Using information theory we derive a thermodynamics for systems evolving under a collective flow, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex particles leading to an incomplete relaxation of the incoming momentum, and a self-similar expansion. A connection with the determination of thermodynamical quantities in multifragmentation reactions is done showing that they are affected in a sizeable way only when the flow dominates the global energetics.

Equilibrium under flow

Using information theory we derive a thermodynamics for systems evolving under a collective flow, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex particles leading to an incomplete relaxation of the incoming momentum, and a self-similar expansion. A connection with the determination of thermodynamical quantities in multifragmentation reactions is done showing that they are affected in a sizeable way only when the flow dominates the global energetics.

Total Energy Dependence of Angular Distributions of IMFs Produced in Proton and Heavy-Ion Induced Target Multifragmentation Reactions at around 10 GeV

We have extended our investigations on nuclear multifragmentations induced by GeV-energy light projectiles using light heavy-ion beams ( 16O, 20Ne and 28Si) provided from the Heavy-Ion Medical Accelerator in Chiba (HIMAC) at the National Institute for Radi- ological Science (NIRS). At a total beam energy of 8 GeV we found there are noticeable differences in spectrum shapes of Intermediate-Mass Fragment (IMF) and their magni- tudes depending upon the projectile mass, but all of their angular distributions clearly exhibit the existence of sideward-peaked components, indicating fragment formations are mainly governed by a total energy of the projectile, not by a incident energy per nucleon.

Formation of hot heavy nuclei in supernova explosions

We point out that during the supernova II type explosion the thermodynamical conditions of stellar matter between the protoneutron star and the shock front correspond to the nuclear liquid–gas coexistence region, which can be investigated in nuclear multifragmentation reactions. We have demonstrated, that neutron-rich hot heavy nuclei can be produced in this region. The production of these nuclei may influence dynamics of the explosion and contribute to the synthesis of heavy elements.

Nuclear Liquid-Gas Phase Transition Studied with Antisymmetrized Molecular Dynamics

The nuclear liquid-gas phase transition of the system in ideal thermal equilibrium is studied with antisymmetrized molecular dynamics. The time evolution of a many-nucleon system confined in a container is solved for a long time to get a microcanonical ensemble of a given energy and volume. The temperature and the pressure are extracted from this ensemble and the caloric curves are constructed. The present work is the first time that a microscopic dynamical model which describes nuclear multifragmentation reactions well is directly applied to get the nuclear caloric curve. The obtained constant pressure caloric curves clearly show the characteristic feature of the liquid-gas phase transition, namely negative heat capacity (backbending), which is expected for the phase transition in finite systems.