The Shannon information-entropy uncertainty (in brief as "information uncertainty") is used to analyze the fragments in the measured 140A MeV 40,48 Ca + 9 Be and 58,64 Ni + 9 Be reactions. A scaling phenomenon is found in the information-uncertainty difference of fragments between the reactions. The scaling phenomenon is explained in a manner of canonical ensemble theory, and is reproduced in the simulated reactions by the antisymmetric molecular dynamics (AMD) and AMD + GEMINI models. The probes based on information uncertainty, requiring no equilibrium state of reaction, can be used in the non-equilibrium system, and bridge the results of the static thermodynamics models and the evolving dynamical transport models.
The cross sections of fragments produced in the 140 A MeV58,64Ni+9 Be projectile fragmentation reactions are calculated by using the antisymmetrized molecular dynamics (AMD) model, the modified statistical abrasion-ablation (SAA) model, and the empirical EPAX2/EPAX3 formulae. The Gogny-g0 interaction is taken as the effective nucleon-nucleon interaction in the AMD calculation, and the decays of fragments obtained from the AMD results are calculated by using the GEMINI code. The calculated cross sections of fragments are compared.
Background: Temperature is an important parameter in studying many important questions in heavy-ion collisions. A thermometer based on the isobaric yield ratio (IYR) has been proposed [Ma et al., Phys. Rev. C 86, 054611 (2012) and Ma et al., ibid., Phys. Rev. C 88, 014609 (2013)].Purpose: An improved thermometer (TIB) is proposed based on the difference between IYRs. TIB obtained from isobars in different reactions will be compared.Methods: The yields of three isobars are employed in TIB. The residual free energy of the three isobars are replaced by that of the binding energy. No secondary decay modification for odd A fragment is used in TIB.
Results:The measured fragment yields in the 140A MeV 40,48 Ca + 9 Be ( 181 Ta) and 58,64 Ni + 9 Be ( 181 Ta), the 1A GeV 124,136 Xe + Pb, and the 112,124 Sn + 112,124 Sn reactions have been analyzed to obtain TIB from IMFs. TIB from most of the fragments in the 40,48 Ca and 58,64 Ni reactions is in the range of 0.6 MeV < TIB < 3.5 MeV. TIB from most of the fragments in the 124 Xe and 112,124 Sn reactions is in the range of 0.5 MeV < TIB < 2.5 MeV, while the range is 0.5 MeV < TIB < 4 MeV from most of the fragments in the 136 Xe reaction. In general, for most of the fragments TIB in the 40,48 Ca and 58,64 Ni reactions are very similar (except in the very neutron-rich fragments), and TIB from IMFs in the 124,136 Xe and 112,124 Sn reactions is also similar. A slightly dependence of TIB on A is found.Conclusions: Using the binding energy of the nucleus, TIB can be obtained without the knowledge of the free energies of fragments. In the investigated reactions, TIB from most of the IMFs is low.
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