Symmetry energy from nuclear multifragmentation

Abstract

The ratio of symmetry energy coefficient to temperature Csym/T is extracted from different prescriptions using the isotopic as well as the isobaric yield distributions obtained in different projectile fragmentation reactions. It is found that the values extracted from our theoretical calculation agree with those extracted from the experimental data but they differ very much from the input value of the symmetry energy used. The best possible way to deduce the value of the symmetry energy coefficient is to use the fragment yield at the breakup stage of the reaction and it is better to use the grand canonical model for the fragmentation analysis. This is because the formulas that are used for the deduction of the symmetry energy coefficient are all derived in the framework of the grand canonical ensemble which is valid only at the break-up (equilibrium) condition. The yield of "cold" fragments either from the theoretical models or from experiments when used for extraction of the symmetry energy coefficient using these prescriptions might lead to the wrong conclusion.PACS numbers: 25.70Mn, 25.70PqIntroduction:-Isospin-dependent phenomena in nuclear physics has been an active area of research [1,2] in recent years with the aim of enriching our knowledge about the symmetry term of the nuclear equation of state. The study of this quantity at different regimes of density and temperature is a hot topic [3][4][5] in the nuclear physics community. This term plays an important role in areas of astrophysical interest such as the study of supernova explosions and the properties of neutron stars [6]. This also has significant influence in deciding the structure of neutron-rich and neutron-deficient nuclei. The study of nuclear multifragmentation in heavyion reactions is an important tool for extracting information about the symmetry energy term, and this has created much interest in the nuclear physics community in recent years [7][8][9][10][11][12][13][14][15][16][17]. In nuclear multifragmentation reactions, the neutronproton composition of the break-up fragments is dictated by the asymmetry term of the equation of state and hence the study of the multifragmentation process allows one to obtain information about the symmetry term. Statistical models [18][19][20] that are simple and economic are very successful in predicting the outcome of nuclear multifragmentation reactions. Different formulas [14,[21][22][23] have been proposed in the literature that connect the measurable fragment isotopic and isobaric observables of multifragmentation reactions to the symmetry energy of excited nuclei and these have been applied to the analysis of heavy-ion collision data. These formulas have all been deduced using the grand canonical version of the nuclear multifragmentation model assuming an equilibrium scenario for the break-up stage of the disintegrating system. They have been used to analyze experimental data from different projectile fragmentation as well as central collision reactions and the extracted values for the symmetry ener...

Effect of particle fluctuation on isoscaling and isobaric yield ratio of nuclear multifragmentation

“…Since the above formalisms are valid for equilibrium condition [12] and secondary decay affects the equilibrium scenario [12,18], hence in the entire theoretical calculation secondary decay is not included.…”

Isospin dependent hybrid model for studying isoscaling in heavy ion collisions around the Fermi energy domain

“…The study of isospin dependent observables in nuclear multifragmentation reaction around the Fermi energy domain is a subject of contemporary interest [1,2]. Different statistical models like Statistical Multifragmentation Model (SMM) [3], Canonical Thermodynamical Model [2,4], have been explored to investigate and verify the phenomenon of isoscaling [5][6][7][8][9] as observed in experiments [10][11][12][13][14][15]. The main motivation behind inclusion of isospin in the transport model based on Boltzmann-Uehling-Uhlenbeck (BUU) equation [2,16] was to study the isospin dependent observables in this framework.…”

Neutron-skin effects in isobaric yield ratios for mirror nuclei in a statistical abrasion-ablation model

“…The symmetry energy of fragment at finite temperature in heavy-ion collisions (HICs), which has a finite temperature, is also studied using the isobaric yield ratio (IYR) methods. After the work using the IYR to study the ratio of the symmetry energy coefficient to the temperature (a sym /T ) of a fragment [7], the results using the IYR methods are also discussed using the statistical multifragmentation model [8], the canonical and the grand canonical ensembles methods [9,18], and freeenergy-based models [4,5]. Moreover, the IYR methods are also used to study the a sym /T of neutron-rich fragments [10][11][12][13], the formation time of fragments [14,15], the difference between the chemical potentials of a neutron and proton [16], and the temperature of the heavy fragments [17].…”