B. V. Carlson, R. Donangelo, S. R. Souza, W. G. Lynch, A. W. Steiner, M. B. Tsang
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.
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The Generalized Fermi Breakup recently demonstrated to be formally equivalent to the Statistical Multifragmentation Model, if the contribution of excited states are included in the state densities of the former, is implemented. Since this treatment requires the application of the Statistical Multifragmentation Model repeatedly on the hot fragments until they have decayed to their ground states, it becomes extremely computational demanding, making its application to the systems of interest extremely difficult. Based on exact recursion formulae previously developed by Chase and Mekjian to calcul…
The excitation energy and the nuclear density at the time of breakup are extracted for the $α+ ^{197}Au$ reaction at beam energies of 1 and 3.6 GeV/nucleon. These quantities are calculated from the average relative velocity of intermediate mass fragments (IMF) at large correlation angles as a function of the multiplicity of IMFs using a statistical model coupled with many-body Coulomb trajectory calculations. The Coulomb component $\vec{v}_{c}$ and thermal component $\vec{v}_{0}$ are found to depend oppositely on the excitation energy, IMFs multiplicity, and freeze-out density. These dependenc…
The sensitivity of the Statistical Multifragmentation Model to the underlying statistical assumptions is investigated. We concentrate on its micro-canonical, canonical, and isobaric formulations. As far as average values are concerned, our results reveal that all the ensembles make very similar predictions, as long as the relevant macroscopic variables (such as temperature, excitation energy and breakup volume) are the same in all statistical ensembles. It also turns out that the multiplicity dependence of the breakup volume in the micro-canonical version of the model mimics a system at (appro…
We study the size properties of the largest intermediate mass fragments in each partition mode, produced in the prompt statistical breakup of a thermally equilibrated nuclear source, at different temperatures. We find that an appreciable amount of events have primary intermediate mass fragments of similar sizes. Our results suggest that, depending on the temperature of the fragmenting source, their production may be much larger than what would be expected from considerations based on purely combinatorial arrangements of the nucleons in the fragmenting system. We also find that the isospin comp…
The deexcitation of the primary hot fragments, produced in the breakup of an excited nuclear source, during their propagation under the influence of their mutual Coulomb repulsion is studied in the framework of a recently developed hybrid model. The latter is based on the Statistical Mul- tifragmentation Model (SMM), describing the prompt breakup of the source, whereas the particle emission from the hot fragments, that decay while traveling away from each other, is treated by the Weisskopf-Ewing evaporation model. Since this treatment provides an event by event descrip- tion of the process, in…
The agreement between the fragments' internal and kinetic temperatures with the breakup temperature is investigated using a Statistical Multifragmentation Model which makes no a priori as- sumption on the relationship between them. We thus examine the conditions for obtaining such agreement and find that, in the framework of our model, this holds only in a relatively narrow range of excitation energy. The role played by the qualitative shape of the fragments' state densities is also examined. Our results suggest that the internal temperature of the light fragments may be affected by this quant…
Within Fermionic Molecular Dynamics we investigate fragmentation of a compound system which was created in a heavy-ion collision at a beam energy in the Fermi energy domain and the decay of excited iron nuclei. We show that in FMD many-body correlations play an important role in the formation of fragments.
Experimental data for central collisions of $^{129}$Xe on $^{119}$Sn at beam energies of (a) 32 MeV/nucleon, (b) 39 MeV/nucleon, (c) 45 MeV/nucleon and (d) 50 MeV/nucleon are compared with results calculated using a hybrid model. We use a transport model (BUU) to obtain the excitation energy per nucleon in the center of mass of the multifragmenting system. The canonical thermodynamic model is then used to determine the temperature which would lead to this excitation energy. With this temperature we use the canonical thermodynamic model to calculate various experimental data such as multiplicit…
In Fermionic Molecular Dynamics the occurrence of multifragmentation depends strongly on the intrinsic structure of the many-body state. Slater determinants with narrow single-particle states and a cluster substructure show multifragmentation in heavy-ion collisions while those with broad wave functions, which resemble more a shell-model picture, deexcite by particle emission. Which of the two type of states occurs as the ground state minimum or as a local minimum in the energy depends on the effective interaction. Both may equally well reproduce binding energy and radii of nuclei. This ambigu…
Heavy ion collisions in the Fermi energy regime may simultaneously show features of direct and dissipative processes. To investigate this behavior in detail, we study isotope and velocity distributions of projectile-like fragments in the reactions $^{18}$O (35 $A\cdot$MeV) + $^9$Be($^{181}$Ta) at forward angles. We decompose the experimental velocity distributions empirically into two contributions: a direct, `breakup' component centered at beam velocity and a dissipative component at lower velocities leading to a tail of the velocity distributions. The direct component is interpreted in the G…
We present an analysis of multifragmentation events observed in central Xe+Sn reactions at Fermi energies. Performing a comparison between the predictions of the Stochastic Mean Field (SMF) transport model and experimental data, we investigate the impact of the compression-expansion dynamics on the properties of the final reaction products. We show that the amount of radial collective expansion, which characterizes the dynamical stage of the reaction, influences directly the onset of multifragmentation and the kinematic properties of multifragmentation events. For the same set of events we als…
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 …
Isotopic effects observed in fragmentation reactions induced by protons, deuterons, and alpha particles of incident energies between 660 MeV and 15.3 GeV on 112-Sn and 124-Sn targets are discussed. The exponential scaling of the yield ratios with the third component of the fragment isospin (N-Z)/2 is observed in all reactions, with scaling parameters that depend on the incident energy. Breakup temperatures for these reactions are deduced from double ratios of isotopic yields and tested for their relation with the isoscaling parameters. The quantum statistical (QSM) and the statistical multifra…
In the framework of a 2D Vlasov model, we study the time evolution of the "coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase-space: at variance with the exact time evolution, no entropy change is fou…
Investigation of observables from nuclear multifragmentation reactions depending on isospin led to the development of a hybrid model. The mass and charge distribution as well as isotopic distribution was studied using this model for $^{112}$Sn+$^{112}$Sn reaction as well as $^{124}$Sn+$^{124}$Sn reactions at different energies. The agreement of the results obtained from the model with those from experimental data confirms the accuracy of the model. Isoscaling coefficients were extracted from these observables which can throw light on the symmetry energy coefficient. Another important facet of …
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