Isoscaling Parameters Research Articles

Isoscaling properties for neutron-rich fragments in highly asymmetric heavy ion collision systems* *Supported by the National Natural Science Foundation of China (12375123, 11975091) and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

Traditionally, isoscaling has been interpreted and applied within the framework of the grand canonical ensemble, based on the assumption that fragment production occurs following the attainment of a statistical equilibrium state. However, the influence of the symmetry energy can lead to differences in the neutron and density distribution in neutron-rich nuclei. This in turn may impact the isoscaling parameters (usually denoted by α and β). We examine the isoscaling properties for neutron-rich fragments produced in highly asymmetric systems on inverse kinematics, namely Ca and Ni + Be at 140 MeV per nucleon. We evaluate α and β values and sort them as a function of the neutron excess . The significant differences in α extracted from fragments within different ranges of I emphasize the importance of understanding the dependence of isoscaling parameters on fragments generated in various collision regions. Furthermore, the value for a specific fragment in small size and highly isospin asymmetry systems can serve as a probe to detect the variations in neutron density and proton density in different regions of the nucleus and indicate the limitations of theoretical models in investigating these issues.

Understanding the isoscaling relationship in the fissioning system with evaluated data * *Supported by the National Natural Science Foundation of China (11790325, 11875323, 11875125, 11947410, 11705163, 11790320, 11790323, 11961141003), the National Key R&D Program of China (2018 YFA0404404), the Continuous Basic Scientific Research Project (WDJC-2019-09, WDJC-2019-13, BJ20002501) of the funding of China Institute of Atomic Energy, and Chinese-Polish Joint project

The isoscaling parameters in the fissioning systems, i.e., those extracted from the Evaluated Nuclear Data Library (ENDF/B-VIII.0) and the Joint Evaluated Fission and Fusion File (JEFF-3.3), show an obvious difference from simple statistic model prediction where only the symmetry energy plays the dominant role. To explain the as a function of the charge number of the fission fragment, a statistic scission point model is adopted. Our analysis shows that the effects of the shell correction, nuclear shape deformation, and intrinsic temperature of fission fragments are indispensable as well as the symmetry energy. Furthermore, an alternative method for extracting the intrinsic temperatures of fission fragments is proposed based on the isoscaling relationship in fission fragments. The intrinsic temperatures of the light fragments are higher than those of the heavy fragments.

Isospin dependence of fragment yields in peripheral heavy ion collisions

We have theoretically investigated isospin dependence in peripheral isospin asymmetric $$^{112}$$Sn + $$^{124}$$Sn and $$^{124}$$Sn + $$^{112}$$Sn reaction systems at 50 MeV/nucleon projectile energy. Mass, charge and isotope yields emitted from the excited quasiprojectile sources are obtained within a statistical approach. In order to interpret the experimental data, the N/Z ratio, isotope yield, and isoscaling analyses were carried out for light intermediate mass fragments (with $$Z\le 8$$, at available data range). We show that predicted results produced for fragment yields, are consistent with the experimental data for peripheral isospin asymmetric reaction systems. From the comparison of the statistical model predictions with experimental data, it is concluded that a lower value of the effective symmetry-term coefficient $$\gamma $$ must be considered at low density freeze-out. Statistical analysis of isoscaling shows that the isoscaling parameter $$\alpha $$ is very sensitive to the isospin composition (N/Z ratio) of the the sources, and it is proportional to the strength of the symmetry-term coefficient.

Isoscaling and nuclear reaction dynamics

Isoscaling parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ have been explored as a function of breakup angle in binary excited projectile-like fragment decays produced in collisions of $^{70}\mathrm{Zn}+^{70}\mathrm{Zn}$ and $^{64}\mathrm{Zn}+^{64}\mathrm{Zn}$ at 35 MeV per nucleon. In this analysis, focus was placed on isoscaling the second heaviest fragment with $4\phantom{\rule{0.16em}{0ex}}\ensuremath{\le}\phantom{\rule{0.16em}{0ex}}{Z}_{L}\phantom{\rule{0.16em}{0ex}}\ensuremath{\le}\phantom{\rule{0.16em}{0ex}}8$ emitted from the excited projectile-like fragment in events that contained a heavy fragment with ${Z}_{H}\phantom{\rule{0.16em}{0ex}}\ensuremath{\ge}\phantom{\rule{0.16em}{0ex}}12$. The breakup orientation ${\ensuremath{\theta}}_{\mathrm{prox}}$ was defined as the angle between the heavy and light fragments' center-of-mass velocity and the fragment pairs' relative velocity. Breakups between ${0}^{\ensuremath{\circ}}<{\ensuremath{\theta}}_{\mathrm{prox}}\ensuremath{\le}{80}^{\ensuremath{\circ}}$ have been shown to be dominated by dynamical contributions, while break-up angles of ${\ensuremath{\theta}}_{\mathrm{prox}}>{100}^{\ensuremath{\circ}}$ are predominantly statistical. Historically, isoscaling has often been understood and applied in a statistical context, assuming that the fragments are produced after statistical equilibrium is achieved. Studying isoscaling parameters as a function of ${\ensuremath{\theta}}_{\mathrm{prox}}$ reveals the sensitivity of $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ to the mechanism of fragment production.

Isoscaling of mass A ≃ 40 reconstructed quasiprojectiles from collisions in the Fermi energy regime

Isoscaling studies of fragments with Z=1-8 from reconstructed quasiprojectiles of mass A ≃40 from the 40Ca + 112,124Sn and 40Ar + 112,124Sn reactions at beam energy of 45 MeV/nucleon were performed. After initial efforts to obtain isoscaling using pairs of systems differing in their neutron-to-proton ratio N/Z, “intra-system” isoscaling for each of these four systems was obtained using fragment sources restricted in two narrow N/Z zones, one neutron rich and one neutron poor. The observed isoscaling behaviour was excellent and the isoscaling parameter α was found to decrease as the excitation energy increases. Corrections due to undetected neutrons were also taken into account in the source N/Z determination by using the theoretical models DIT (Deep Inelastic Transfer) and SMM (Statistical Multifragmentation Model) along with a software replica of the experimental setup. The reduced isoscaling parameter α/∆ was found to decrease as the excitation energy of the quasiprojectile source increases, in good agreement with recent work on reconstructed mass A ≃ 80 quasiprojectiles. This decrease of α/∆ may point to a decrease of the symmetry energy coefficient with increasing excitation energy.

Neutron-proton equilibration in 35 MeV/ u collisions of 64,70 Zn + 64,70 Zn and 64 Zn, 64 Ni + 64 Zn, 64 Ni quantified using triplicate probes

Previous work has quantified the degree of neutron-proton equilibration in heavy-ion nuclear collisions by observing the convergence of isospin observables (such as the isoscaling parameter $\ensuremath{\alpha}$) to an expected value based on similar symmetric reaction systems. We present a new signature of equilibration: the convergence of the isospin asymmetry (as quantified by three isoscaling metrics) of two mirror asymmetric reaction systems toward each other rather than a predefined point. For the reactions of 35 MeV/$u$ $^{64,70}\mathrm{Zn}+^{64,70}\mathrm{Zn}$ and $^{64}\mathrm{Zn},^{64}\mathrm{Ni}+^{64}\mathrm{Zn},^{64}\mathrm{Ni}$ the neutron-proton equilibration was found to be approximately 80%, and this result is compared directly to previous work.

Observation of different isoscaling behavior between emitted fragments and residues

The traditional isoscaling technique has been used to analyze all isotopically identified particles from 70Zn+70Zn and 64Zn+64Zn collisions at 35 MeV/u. Two additional techniques, using an energy-averaged ratio and using the data present in the tail of energy spectra, are compared to the traditional method and show similar results. Isoscaling fit parameters α and β are found both globally and for each individual series of constant Z and N. The data are then split up between emitted fragments and projectile-like fragments. Isoscaling values for the two different types of fragments are shown to be different, emphasizing the importance of experimentally distinguishing between projectile-like fragments and emitted fragments in order to achieve accurate isoscaling parameters.

Effect of neutron skin thickness on projectile fragmentation

The fragment production in collisions of $^{48,50}$Ca+$^{12}$C at 50 MeV/nucleon are simulated via the Isospin-Dependent Quantum Molecular Dynamics (IQMD) model followed by the {GEMINI code}. {By changing the diffuseness parameter of neutron density distribution to obtain different neutron skin size, the effects of neutron skin thickness (${\delta}_{np}$) on projectile-like fragments (PLF) are investigated. The sensitivity of isoscaling behavior to neutron skin size is studied, from which it is found that the isoscaling parameter $\alpha$ has a linear dependence on ${\delta}_{np}$. A linear dependence between ${\delta}_{np}$ and the mean $N/Z$ [N(Z) is neutron(proton) number] of PLF is obtained as well.} The results show that thicker neutron skin will lead to smaller {isoscaling parameter} $\alpha$ and N/Z. Therefore, it may be probable to extract information of neutron skin thickness from {isoscaling parameter} $\alpha$ and N/Z.

Isoscaling of heavy projectile residues andN/Zequilibration in peripheral heavy-ion collisions below the Fermi energy

The isoscaling of heavy projectile residues from peripheral heavy-ion reactions at 15--25 MeV/nucleon is employed to obtain information on the process of $N/Z$ equilibration. Recent mass spectrometric data of projectile residues from the reactions of $^{86}\mathrm{Kr}$ (15 MeV/nucleon) with $^{64,58}\mathrm{Ni}$ and $^{124,112}\mathrm{Sn}$ were first analyzed. The isotopically resolved yield distributions of the fragments in the range $Z=26--39$ were employed for the isoscaling analysis. The yield ratios ${R}_{21}(N,Z)$ of the fragments from each pair of systems exhibit isoscaling (i.e., an exponential dependence on the fragment neutron number $N$ for each atomic number $Z$) with the isoscaling parameter $\ensuremath{\alpha}$ increasing with decreasing (or increasing) $Z$ away from the projectile. This variation is related to the evolution toward $N/Z$ equilibration with increasing energy dissipation estimated from the residue velocities. In parallel to the new heavy-residue isoscaling data of $^{86}\mathrm{Kr}$ at 15 MeV/nucleon, our previous data at 25 MeV/nucleon for the reactions $^{86}\mathrm{Kr}+^{124,112}\mathrm{Sn}$ and $^{64}\mathrm{Ni}+^{64,58}\mathrm{Ni}$, $^{64}\mathrm{Ni}+^{124,112}\mathrm{Sn}$, as well as our data at 15 MeV/nucleon of the lighter system $^{40}\mathrm{Ar}+^{64,58}\mathrm{Ni}$, were analyzed in a similar way. Calculations with the stochastic nucleon-exchange model DIT (deep inelastic transfer) and the microscopic many-body model CoMD (constrained molecular dynamics) provided an overall fair description of data and valuable guidance for their interpretation. Interestingly, the data of the $^{86}\mathrm{Kr}+\mathrm{Ni},\mathrm{Sn}$ reactions at 15 MeV/nucleon show a retardation of the process of $N/Z$ equilibration which, as suggested by the CoMD calculations, is indicative of the collective character of the process. This retardation is not present in the investigated systems at 25 MeV/nucleon (and the light $^{40}\mathrm{Ar}+\mathrm{Ni}$ systems at 15 MeV/nucleon), whose behavior is found to be consistent with stochastic nucleon exchange.

Chemical properties of colliding sources in 124, 136Xe and 112, 124Sn induced collisions in isobaric yield ratio difference and isoscaling methods

Isoscaling and isobaric yield ratio difference (IBD) methods are used to study Δμ/T (Δμ being the difference between the chemical potentials of the neutron and proton, and T being the temperature) in the measured 1 A GeV 124Sn + 124Sn, 112Sn + 112Sn, 136Xe + Pb and 124Xe + Pb reactions. The isoscaling phenomena in the 124Sn/112Sn and 136Xe/124Xe reaction pairs are investigated, and the isoscaling parameters α and β are obtained. The Δμ/T determined by the isoscaling method (IS-Δμ/T) and the IBD method (IB-Δμ/T) in the measured Sn and Xe reactions are compared. It is shown that in most fragments, the IS- and IB-Δμ/T are consistent in the Xe reactions, while the IS- and IB-Δμ/T ones are only similar in the less neutron-rich fragments in the Sn reactions. The shell effects in IB-Δμ/T are also discussed.

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

Isoscaling and isobaric yield ratio parameters are compared from canonical and grand canonical ensembles when applied to multifragmentation of finite nuclei. Source dependence of isoscaling parameters and source and isospin dependence of isobaric yield ratio parameters are examined in the framework of the canonical and the grand canonical models. It is found that as the nucleus fragments more, results from both the ensembles converge and observables calculated from the canonical ensemble coincide more with those obtained from the formulae derived using the grand canonical ensemble.

Investigation of features of isotope effect

Isotope effect is investigated for the products formed in various channels of nuclear reactions. The separate consideration of neutron-poor and neutron-rich products shows difference in values of isoscaling parameters. The largest difference is observed for spallation products. This difference decreases with reduction of the mass number of products.

Isobaric yield ratio difference in heavy-ion collisions, and comparison to isoscaling

An isobaric yield ratio difference (IBD) method is proposed to study the ratio of the difference between the chemical potential of neutron and proton to temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$ determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni + $^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with a plateau in the small mass fragments plus an increasing part in the fragments of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show dependence on the $n/p$ ratio of the projectile. It is suggested that the height of the plateau is decided by the difference between the neutron density ($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles, and the width shows the overlapping volume of the projectiles in which $\rho_n$ and $\rho_p$ change very little. The difference between the IB- and IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by the many isotopes and isotones, while the IBD method only uses the yields of two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the density or the temperature, the density dependence is preferred since the low density can result in low temperature in the peripheral reactions.

Isoscaling in dissipative projectile breakup

Dynamical breakup of projectile-like fragments (PLF) following dissipative reactions of 48 Ca projectiles with 112 Sn and 124 Sn is shown to exhibit “isoscaling” regularities that can be understood in terms of phase space governed by ground state masses. Ambiguities in isoscaling parameters obscure information on nuclear symmetry energy at subnormal densities.

Influence of statistical sequential decay on isoscaling and symmetry energy coefficient in a gemini simulation

Extensive calculations on isoscaling behavior with the sequential-decay model gemini are performed for the medium-to-heavy nuclei in the mass range A = 60-120 at excitation energies up to 3 MeV/nucleon. The comparison between the products after the first-step decay and the ones after the entire-steps decay demonstrates that there exists a strong sequential decay effect on the final isoscaling parameters and the apparent temperature. Results show that the apparent symmetry energy coefficient $\gamma_{app}$ does not reflect the initial symmetry energy coefficient $C_{sym}$ embedded in the mass calculation in the present GEMINI model.

Isoscaling and the nuclear EoS

Experiments with rare isotopes are shedding light on the role isospin plays in the equation of state (EoS) of nuclear matter, and isoscaling—a straightforward comparison of reactions with different isospin—could deliver valuable information about it. In this work, we test this assertion pragmatically by comparing molecular dynamics simulations of isoscaling reactions using different EoS and looking for changes in the isoscaling parameters; to explore the possibility of isoscaling carrying information from the hot-and-dense stage of the reaction, we perform our study in confined and expanding systems. Our results indicate that indeed isoscaling can help us learn about the nuclear EoS, but only in some ranges of excitation energies.

The influence of Multi-Step Sequential Decay on Isoscaling and Fragment Isospin Distribution in GEMINI Simulation

Extensive calculations on isoscaling behavior with the sequential-decay model GEMINI are performed for the mediate-heavy nuclei in the mass range A = 110 and at excitation energies of up to 3MeV per nucleon. Isoscaling can still be observed after entire-step decays are considered for the light products as in the only first-step decay process case. Comparison between the products after the first-step decay and the ones after entire-step decay demonstrates that multi-step secondary sequential decay strongly influences the isoscaling parameters α, β as well as the fragment isospin distribution. After entire-step decays, the isoscaling parameters α, and β are decreased and the fragment isospin distribution can better reproduce the isospin distribution shape as the experimental data.

Isospin-dependent multifragmentation of relativistic projectiles

The N/Z dependence of projectile fragmentation at relativistic energies has been studied with the ALADIN forward spectrometer at the GSI Schwerionen Synchrotron (SIS). Stable and radioactive Sn and La beams with an incident energy of 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. For the interpretation of the data, calculations with the statistical multifragmentation model for a properly chosen ensemble of excited sources were performed. The parameters of the ensemble, representing the variety of excited spectator nuclei expected in a participant-spectator scenario, are determined empirically by searching for an optimum reproduction of the measured fragment-charge distributions and correlations. An overall very good agreement is obtained. The possible modification of the liquid-drop parameters of the fragment description in the hot freeze-out environment is studied, and a significant reduction of the symmetry-term coefficient is found necessary to reproduce the mean neutron-to-proton ratios 〈N〉/Z and the isoscaling parameters of Z⩽10 fragments. The calculations are, furthermore, used to address open questions regarding the modification of the surface-term coefficient at freeze-out, the N/Z dependence of the nuclear caloric curve, and the isotopic evolution of the spectator system between its formation during the initial cascade stage of the reaction and its subsequent breakup.22 MoreReceived 4 June 2010DOI:https://doi.org/10.1103/PhysRevC.83.024608©2011 American Physical Society

Effect of secondary decay on isoscaling: Results from the canonical thermodynamical model

The projectile fragmentation reactions using 58Ni and 64Ni beams at 140 MeV/n on targets 9Be and 181Ta are studied using the canonical thermodynamical model coupled with an evaporation code. The isoscaling property of the fragments produced is studied using both the primary and the secondary fragments and it is observed that the secondary fragments also respect isoscaling though the isoscaling parameters α and β changes. The temperature needed to reproduce experimental data with the secondary fragments is less than that needed with the primary ones. The canonical model coupled with the evaporation code successfully explains the experimental data for isoscaling for the projectile fragmentation reactions.

PROJECTILE FRAGMENTATION OF 36,40Ar INDUCED REACTIONS

Fragment yields for Z ≥ 5 from projectile fragmentation using primary beams of 36,40Ar at 50 MeV/nucleon on 64 Ni target have been measured in RIBLL fragment separator. We compare the fragment cross sections with the predictions of the empirical EPAX parametrization of fragmentation cross-sections and Statistical Abration-Ablation model (SAA) by considering the RIBLL separator transmission rate. Isotope yield ratios between these two reactions were calculated and isoscaling parameters α and β are extracted, their dependences on fragment atomic number Z and neutron number N were presented.