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Register a new userIsoscaling and the high Temperature limit
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This study shows that isoscaling, usually studied in nuclear reactions, is a phenomenon common to all cases of fair sampling. Exact expressions for the yield ratio $R_{21}$ and approximate expressions for the isoscaling parameters $alpha$ and $beta$ are obtained and compared to experimental results. It is concluded that nuclear isoscaling is bound to contain a component due to sampling and, thus, a words of caution is issued to those interested in extracting information about the nuclear equation of state from isoscaling.
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The properties of the nuclear isoscaling at finite temperature are investigated and the extent to which its parameter $alpha$ holds information on the symmetry energy is examined. We show that, although finite temperature effects invalidate the analytical formulas that relate the isoscaling parameter $alpha$ to those of the mass formula, the symmetry energy remains the main ingredient that dictates the behavior of $alpha$ at finite temperatures, even for very different sources. This conclusion is not obvious as it is not true in the vanishing temperature limit, where analytical formulas are available. Our results also reveal that different statistical ensembles lead to essentially the same conclusions based on the isoscaling analysis, for the temperatures usually assumed in theoretical calculations in the nuclear multifragmentation process.
Isoscaling and its relation to the symmetry energy in the fragmentation of excited residues produced at relativistic energies were studied in two experiments conducted at the GSI laboratory. The INDRA multidetector has been used to detect and identify light particles and fragments with Z <= 5 in collisions of 12C on 112,124Sn at incident energies of 300 and 600 MeV per nucleon. Isoscaling is observed, and the deduced parameters decrease with increasing centrality. Symmetry term coefficients, deduced within the statistical description of isotopic scaling, are near gamma = 25 MeV for peripheral and gamma < 15 MeV for central collisions. In a very recent experiment with the ALADIN spectrometer, the possibility of using secondary beams for reaction studies at relativistic energies has been explored. Beams of 107Sn, 124Sn, 124La, and 197Au were used to investigate the mass and isospin dependence of projectile fragmentation at 600 MeV per nucleon. The decrease of the isoscaling parameters is confirmed and extended over the full fragmentation regime covered in these reactions.
The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that manifests the consistency of the adiabatic zero-temperature formalism with perturbative statistical mechanics---for both isotropic and anisotropic systems---and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermiliquid theory. These properties are proved to all orders.
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.
Generalized isoscaling relationships are proposed that may permit one to relate the isotopic distributions of systems that may not be at the same temperature. The proposed relationships are applied to multifragmentation excitation functions for central Kr+Nb and Ar+Sc collisions.
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