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Register a new userStudy of Isoscaling with Statistical Multifragmentation Models
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Different statistical multifragmentation models have been used to study isoscaling, i.e. the factorization of the isotope ratios from two reactions, into fugacity terms of proton and neutron number, R21(N,Z)=Y2(N,Z)/Y1(N,Z)=C*exp(a*N+b*Z). Even though the primary isotope distributions are quite different from the final distributions due to evaporation from the excited fragments, the values of a and b are not much affected by sequential decays. a is shown to be mainly sensitive to the proton and neutron composition of the emitting source and may be used to study isospin-dependent properties in nuclear collisions such as the symmetry energy in the equation of state of asymmetric nuclear matter.
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A phase transition signature associated with cumulants of the largest fragment size distribution has been identified in statistical multifragmentation models and examined in analysis of the ALADIN S254 data on fragmentation of neutron-poor and neutron-rich projectiles. Characteristics of the transition point indicated by this signature are weakly dependent on the A/Z ratio of the fragmenting spectator source. In particular, chemical freeze-out temperatures are estimated within the range 5.9 to 6.5 MeV. The experimental results are well reproduced by the SMM model.
The isospin effect and isoscaling behavior in projectile fragmentation have been systematically investigated by a modified statistical abrasion-ablation (SAA) model. The normalized peak differences and reduced isoscaling parameters are found to decrease with ($Z_{proj}-Z$)/$Z_{proj}$ or the excitation energy per nucleon and have no significant dependence on the size of reaction systems. Assuming a Fermi-gas behavior, the excitation energy dependence of the symmetry energy coefficients are tentatively extracted from $alpha$ and $beta$ which looks consistent with the experimental data. It is pointed out that the reduced isoscaling parameters can be used as an observable to study excitation extent of system and asymmetric nuclear equation of state in heavy ion collisions.
Some characteristics of midvelocity emissions in semiperipheral heavy-ion collisions at Fermi energies are discussed in the framework of a multifragmenting scenario. We report on binary dissipative collisions of 93Nb + 93Nb at 38AMeV in which we measured an abundant emission of particles and fragments not originated from the usual evaporative decay of hot primary fragments. We checked the compatibility of these emissions with the multifragmentation of a source which forms in the overlap region. One can fairly well reproduce the data assuming a hot and dilute source, possibly more n-rich than the initial nuclei; the results appear to be insensitive to the source size.
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 cumulant ratios up to fourth order of the $Z$ distributions of the largest fragment in spectator fragmentation following $^{107,124}$Sn+Sn and $^{124}$La+Sn collisions at 600 MeV/nucleon have been investigated. They are found to exhibit the signatures of a second-order phase transition established with cubic bond percolation and previously observed in the ALADIN experimental data for fragmentation of $^{197}$Au projectiles at similar energies. The deduced pseudocritical points are found to be only weakly dependent on the $A/Z$ ratio of the fragmenting spectator source. The same holds for the corresponding chemical freeze-out temperatures of close to 6 MeV. The experimental cumulant distributions are quantitatively reproduced with the Statistical Multifragmentation Model and parameters used to describe the experimental fragment multiplicities, isotope distributions and their correlations with impact-parameter related observables in these reactions. The characteristic coincidence of the zero transition of the skewness with the minimum of the kurtosis excess appears to be a generic property of statistical models and is found to coincide with the maximum of the heat capacity in the canonical thermodynamic fragmentation model.
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