Isoscaling in the lattice gas model

Abstract

The isoscaling behavior is investigated using the isotopic/isobaric yields from the equilibrated thermal source which is prepared by the lattice gas model (LGM) for lighter systems with A = 36. The isoscaling parameters α and -β are observed to drop with temperature for the LGM with the asymmetric nucleon-nucleon potential. However, the isoscaling parameters do not show temperature dependence for the LGM with the symmetric nucleon-nucleon potential. The relative neutron or proton density shows a nearly linear relation with the N/Z ( neutron to proton ratio ) of system. PACS numbers: 25.70.Pq, 24.10.Pa, 05.70.JkIsoscaling has been observed in a variety of reactions under the conditions of statistical emission and equal temperature recently by Tsang et al [1,2,3]. This kind of scaling means that the ratio R 21 (N,Z) of the yields of a given fragment (N,Z) exhibits an exponential dependence on N and Z when these fragments are produced in two reactions with different isospin asymmetry, but at the same temperature. Experimentally the isoscaling has been explored in various reaction mechanisms, ranging from the evaporation [1], fission [4,5] and deep inelastic reaction at low energies to the projectile fragmentation [6,7] and multi-fragmentation at intermediate energy [1,8,9]. While, the isoscaling has been extensively examined in different theoretical frameworks, ranging from dynamical model, such as Anti-symmetrical Molecular Dynamics model [10] and BUU model [8], to statistical models, such as Expansion Emission Source Model and statistical multi-fragmentation model [2,3,11,12]. From all these reaction mechanisms and models, it looks that isoscaling is a robust probe to relate with the symmetrical term of the nuclear equation of state.Typically, the investigations of isoscaling focused on yields of light fragments with Z=2-8 originating from deexcitation of massive hot systems produced using reactions of mass symmetric projectile and target at intermediate energies, such as 112,124 Sn + 112,124 Sn in Michigan State University (MSU) data [1,2,3] or by reactions of high-energy light particle with massive target nucleus [11,13]. In a recent article [6], the isoscaling using the heavy projectile residue from the reactions of 25 MeV/nucleon 86 Kr projectiles with 124 Sn, 112 Sn and 64 Ni, 58 Ni targets which was performed at Texas A&M University (TAMU) and the isoscaling phenomenon on the full sample of fragments emitted by the hot thermally equilibrated quasi-projectiles with mass A = 20-30 are also reported [7].

Isoscaling behavior in fission dynamics

“…It shows that both α and β decrease as the increasing beam energy which means that the isospin effect fades away with the increasing of E beam /A. This behavior is similar to the case in the fragmentation where the isoscaling parameter drops with the temperature in the statistical models as well as experiments [6,16,38,44].…”

“…So far, the isoscaling behavior has been experimentally explored in various reaction mechanisms, ranging * Email: ygma@sinap.ac.cn from the evaporation [4], fission [8,9] and deep inelastic reaction at low energies to the projectile fragmentation [10,11] and multi-fragmentation at intermediate energy [4,12,13]. While, the isoscaling phenomenon has been extensively examined in different theoretical frameworks, ranging from dynamical transport models, such as Blotzmann-Uehling-Uhlenbeck model [12], Quantum Molecular Dynamics model [14] and Anti-symmetrical Molecular Dynamics model [15], to the statistical models, such as the expansion emission source model, the statistical multi-fragmentation model and the lattice gas model [5,6,16,17,18]. In this work, we will focus on the detailed simulation studies on the isoscaling behavior of the fission fragments.…”

Improved thermometer for intermediate-mass fragments in heavy-ion collisions with isobaric yield ratio difference

“…Temperature (T ) is one of the key questions in heavyion collision physics since the nuclear system experiences evolution changing from a very high temperature to a very low one to form the final fragments. At a high enough temperature, the liquid-gas phase transition can lead to nuclear disassembly [1][2][3][4][5][6]. Using the Albergo isotopic thermometer, the temperature, its systematic dependence on the incident energy, and its evolution along the reaction time have been studied based on the yields of protons, neutrons, and some light isotopes, [6][7][8][9][10][11][12][13][14].…”

Isotopic Ratio, Isotonic Ratio, Isobaric Ratio and Shannon Information Uncertainty

“…The isoscaling method, which uses the isotopic or isotonic yield ratio, is one of the important methods to study the nuclear symmetry energy of the sub-saturation * Supported by National Natural nuclear matter produced in HICs [4][5][6]. The isobaric ratio methods, which use the isobaric yield ratios, have been proposed to study the nuclear symmetry energy of finite nuclei [7][8][9][10][11][12][13][14][15][16][17], the chemical potential difference between neutrons and protons [18,19], and the density difference between projectiles [20].…”