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Register a new userComparison of Statistical Multifragmentation Model simulations with Canonical Thermodynamical Model results: a few representative cases
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The statistical multifragmentation model (SMM) has been widely used to explain experimental data of intermediate energy heavy ion collisions. A later entrant in the field is the canonical thermodynamic model (CTM) which is also being used to fit experimental data. The basic physics of both the models is the same, namely that fragments are produced according to their statistical weights in the available phase space. However, they are based on different statistical ensembles, and the methods of calculation are different: while the SMM uses Monte-Carlo simulations, the CTM solves recursion relations. In this paper we compare the predictions of the two models for a few representative cases.
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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 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 calculate the statistical weights very efficiently, we present an implementation which is efficient enough to allow it to be applied to large systems at high excitation energies. Comparison with the GEMINI++ sequential decay code shows that the predictions obtained with our treatment are fairly similar to those obtained with this more traditional model.
On the basis of morphological thermodynamics we develop an exactly solvable version of statistical mutifragmentation model for the nuclear liquid-gas phase transition. It is shown that the hard-core repulsion between spherical nuclei generates only the bulk (volume), surface and curvature parts of the free energy of the nucleus, while the Gaussian curvature one does not appear in the derivation. The phase diagram of nuclear liquid-gas phase transition is studied for a truncated version of the developed model.
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 quantity, whose behavior may lead to constant internal temperatures over a wide excitation energy range. It thus suggests that the nuclear thermometry may provide valuable information on the nuclear state density.
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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