用统计磨蚀模型计算了140 MeV的$A$ $^{40,48}$ Ca + $^9$ Be和$^{58,64}$ Ni + $^9$ Be反应中产生的碎片截面，并与美国密歇根州立大学国家超导回旋加速器实验室（NSCL）的实验结果进行了比较.比较了$^{40}$ Ca和$^{48}$ Ca，$^{58}$ Ni和$^{64}$ Ni，$^{40}$ Ca和$^{58}$ Ni，以及$^{48}$ Ca和$^{64}$ Ni的碎片同位素和等渗截面分布，并研究了弹丸碎裂的同位旋依赖性.结果表明，在中心碰撞中，同位旋依赖性减弱甚至消失。碎片同位素和同位素截面分布的形状被发现是非常相似的对称射弹核。在周边反应中产生的不同的不对称射弹的碎片同位素和等渗分布的形状被发现非常相似。在SAA模型的框架下，这些分布的相似性与核内相似的质子和中子密度分布有关。
英文摘要：
The cross sections of fragments produced in 140 $A$ MeV $^{40,48}$Ca + $^9$Be and $^{58,64}$Ni + $^9$Be reactions are calculated by the statistical abration-ablation(SAA) model and compared to the experimental results measured at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The fragment isotopic and isotonic cross section distributions of $^{40}$Ca and $^{48}$Ca, $^{58}$Ni and $^{64}$Ni, $^{40}$Ca and $^{58}$Ni, and $^{48}$Ca and $^{64}$Ni are compared and the isospin dependence of the projectile fragmentation is studied. It is found that the isospin dependence decreases and disappears in the central collisions. The shapes of the fragment isotopic and isotonic cross section distributions are found to be very similar for symmetric projectile nuclei. The shapes of the fragment isotopic and isotonic distributions of different asymmetric projectiles produced in peripheral reactions are found very similar. The similarity of the distributions are related to the similar proton and neutron density distributions inside the nucleus in framework of the SAA model.
A scaling phenomenon in the cross section for fragments has been found in the projectile fragmentation reaction, and an empirical scaling formula is proposed by considering the dependence of cross section on the size and asymmetry of the reaction system and the fragment itself. Furthermore, the empirical scaling formula is used to predict the production of fragment in the $^{68}$Ni/$^{69}$Cu/$^{72}$Zn + $^9$Be reactions around 90$A$ MeV. Compared to the results calculated by the statistical abrasion ablation model and the {\sc epax3} parameterizations, the empirical scaling formula can better …
\item[Purpose] We suppose that the IYR(m) depends on the neutron-skin thickness ($δ_{np}$) of the projectile, and check the idea of whether the neutron-skin thickness effects can fully explain the systematic dependence of the IYR(m). \item[Methods] A modified statistical abrasion-ablation model is used to calculate the reactions induced by projectiles of three series. \item[Results] The IYR(m) shows a distribution of a linear part in the small-$x$ fragments, and a nonlinear part in the large-$x$ fragments. The linear part of IYR(m) is fitted. (1) In the calcium isotopic reactions, the IYR(m) d…
The origin of fluctuations in the average number of intermediate mass fragments seen in experiments in small projectile like fragments is discussed. We argue that these can be explained on the basis of a recently proposed model of projectile fragmentation.
A model in which a projectile like fragment can be simply regarded as a remnant after removal of some part of the projectile leads to an excited fragment. This excitation energy can be calculated with a Hamiltonian that gives correct nuclear matter binding, compressibility and density distribution in finite nuclei. In heavy ion collisions the model produces a dependence of excitation energy on impact parameter which appears to be correct but the magnitude of the excitation energy falls short. It is argued that dynamic effects left out in the model will increase this magnitude. The model can be…
This paper presents our recent efforts to study the momentum distributions as well as the production of neutron-rich rare isotopes with heavy-ion beams in the energy region of 15 MeV/nucleon. Experimental cross sections of neutron-rich nuclides from collisions of a 86 Kr (15 MeV/nucleon) beam with 64 Ni and 58 Ni targets are presented. Experimental data were obtained from the previous work of our group with the MARS mass spectrometer at the Cyclotron Institute of Texas A&M University. On that note, detailed calculations of yields and momentum distributions of neutron-rich projectile-like fragm…
The sensitivities of isospin asymmetry and collision geometry dependencies of participant (overlapping region)- spectator (quasiprojectile and quasitarget region) matter towards the symmetry energy using the isospin quantum molecular dynamical model are explored. Particularly, the difference of the number of nucleons in the overlapping zone to the quasi-projectile-target matter is found to be quite sensitive to the symmetry energy at semiperipheral geometries compared to the individual yield. It gives us a clue that this quantity can be used as a measure of isospin migration. Further, the yiel…
The isospin diffusion of the quasi-projectile formed in the $^{64,58}Ni$ on $^{64,58}Ni$ reactions in the Fermi energy domain is investigated in the framework of the Boltzmann-Uehling-Uhlenbeck transport model. The well known isospin transport ratio observable is revisited, with the aim of insuring an optimal comparison between experimental data and theoretical calculations and reducing the present uncertainties in the extraction of empirical equation of state parameters. We show that isospin transport ratios are sensitive to all the low order isovector parameters ($E_{sym}$, $L_{sym}$ and $K_…
We develop a four-body model for the inclusive breakup of two-fragment halo projectiles colliding with two-fragment targets. In the case of a short lived projectiles, such as halo nuclei, on a deuteron target, the model allows the extraction of the neutron capture cross section of such projectiles. We supply examples.
The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80's for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment …
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 ($δ_{np}$) 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 $α$ has a linear dependence on $δ_{np}$. A linear dependence between $δ…
Projectile like fragments emerging from heavy ion collision have an excitation energy which is often labeled by a temperature. This temperature was recently calculated using a geometric model. We expand the geometric model to include also dynamic effects using a transport model. The temperatures so deduced agree quite well with values of temperature needed to fit experimental data.
We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of largest cluster at different …
We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN co…
Isospin relaxation times characterizing isospin transport processes between the projectile and the target with different $N/Z$ ratios and that between the neck and the spectator with different isospin asymmetries and densities in intermediate-energy heavy-ion collisions are studied within an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model using the lattice Hamiltonian approach. The respective roles and time scales of the isospin diffusion and drift as the major mechanisms of isospin transport in intermediate-energy heavy-ion collisions are discussed. Effects of nuclear symmetry e…
An investigation of the isospin equilibration process in the reactions $^{58,64}$Ni+$^{58,64}$Ni at two bombarding energies in the Fermi regime ($32\,$MeV/nucleon and $52\,$MeV/nucleon) is presented. Data have been acquired during the first experimental campaign of the coupled INDRA-FAZIA apparatus in GANIL. Selecting from peripheral to semi-central collisions, both the neutron content of the quasiprojectile residue and that of the light ejectiles coming from the quasiprojectile evaporation have been used as probes of the dynamical process of isospin diffusion between projectile and target for…
The isospin equilibration process in multinucleon transfer reaction is investigated by using the improved quantum molecular dynamics model. The collision processes of $^{124}$Xe+$^{208}$Pb at near-barrier energy are studied with different symmetry energy coefficients. We find that neutrons transfer happens earlier than protons. The large symmetry energy promote the transfer of neutrons. The neutron flow from the target to projectile is along the low-density path of neck. The isospin equilibration process in $^{58}$Ni+$^{208}$Pb reaction is also investigated and compared with available experime…
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-…
We study the equilibration of isospin degree of freedom in intermediate energy heavy-ion collisions using an isospin-dependent BUU model. It is found that there exists a transition from the isospin equilibration at low energies to non-equilibration at high energies as the beam energy varies across the Fermi energy in central, asymmetric heavy-ion collisions. At beam energies around 55 MeV/nucleon, the composite system in thermal equilibrium but isospin non-equilibrium breaks up into two primary hot residues with N/Z ratios closely related to those of the target and projectile respectively. The…
The production of $α$-particles in reactions using both the strongly and weakly bound projectiles at energies around the Coulomb barrier show several interesting features. To understand these, the role of various reaction mechanisms responsible for $α$-production, such as non-capture breakup, capture of only one of the fragments subsequent to projectile breakup and their contribution to reaction cross sections have been investigated. A systematic study of the $α$-particle production based on available data for various projectile target systems have been performed and a classification based on …
In a recent paper [Phys. Rev. C 044612 (2011)] we proposed a model for calculating cross-sections of various reaction products which arise from disintegration of projectile like fragment resulting from heavy ion collisions at intermediate or higher energy. The model has three parts: (1) abrasion, (2) disintegration of the hot abraded projectile like fragment (PLF) into nucleons and primary composites using a model of equilibrium statistical mechanics and (3) possible evaporation of hot primary composites. It was assumed that the PLF resulting from abrasion has one temperature T. Data suggested…
Collective-flow signatures of bubble nuclei in intermediate-energy projectile fragmentation reactions
Henan Normal University（河南师范大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学技术的研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论物理上海研究中心）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
We analyze the production cross sections and isotopic distributions of projectile-like residues in the reactions $^{112}$Sn + $^{112}$Sn and $^{124}$Sn + $^{124}$Sn at an incident beam energy of 1 GeV/nucleon measured with the FRS fragment separator at the GSI laboratory. Calculations within the statistical multifragmentation model (SMM) for an ensemble of excited sources were performed with ensemble parameters determined previously for similar reactions at 600 MeV/nucleon. The obtained good agreement with the experiment establishes the universal properties of the excited spectator systems pro…
To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin dependent quantum molecular dynamics model. Here simulations have been carried out for $^{124}X_{n}+ ^{124}X_{n}$, where n varies from 47 to 59 and for $^{40}Y_{m}+ ^{40}Y_{m}$, where m varies from 14 to 23. Our study shows that isospin dependent cross-section shows its influence on fragmentation in the collision of neutron rich nuclei.
To understand the isospin effects in nearly symmetric nuclear matter we performed a complete systematical theoretical study within an Isospin dependent Quantum Molecular Dynamical Model (IQMD) and using Minimum Spanning Tree (MST) algorithm. Simulations are carried out for the reactions $_{124}Sn^{50}+_{124}Sn^{50}$ and $_{107}Sn^{50}+_{124}Sn^{50}$. The collision geometry is varied from central to peripheral. We find that neutron rich colliding nuclei are better candidate to study the isospin effects
In the present paper, we explore the idea of isospin conservation in new situations and contexts based on the directions provided by our earlier works. We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in fast neutron-induced fission, 238U (n, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. Our results successfully reproduced the gross features of partition wise fission fragments distribution of 238U (n, fission). This confirms that in all kinds of fission, isospin remains p…
We have studied the fragment yields emitted from the fragmentation of excited projectile nuclei in peripheral collisions of 136Xe+Pb at 1 GeV/nucleon, and measured with the high-resolution magnetic spectrometer, the Fragment Separator (FRS) of GSI. The mass, charge and isotope distributions of nuclear fragments formed in the reactions were calculated within a statistical ensemble approach and compared to the experimental data. The ensemble of excited projectilelike source nuclei were created in the framework of a previous analysis of similar reactions performed at 600 MeV/nucleon (ALADIN-exper…
Aladin data on fragmentation of 197Au projectiles are remarkably well reproduced by a bond percolation model. A critical behavior is identified on the basis of fluctuations of the largest fragment size.
Following upon our earlier paper [1] containing some initial results, we present detailed discussion and complete results in this paper, which provide the first direct evidence for the validity of isospin as a nearly good quantum number in neutron-rich systems. The evidence comes from the reproduction of the general features of the partition-wise relative yields of neutron-rich fission fragments produced in two heavy-ion induced fusion fission reactions, namely $^{208}$Pb ($^{18}$O, f) and $^{238}$U ($^{18}$O, f), by using the concept of isospin conservation. To fix the isospin values and use …
Isospin transport occurring within dinuclear projectile-like fragments (PLFs) produced in heavy- ion collisions is explored as a probe of the nuclear symmetry energy. Within the framework of the Constrained Molecular Dynamics model (CoMD), the existence of the long-lived dinuclear PLFs, for up to 800 fm/c, is observed. It is demonstrated that changes in the <N/Z> of the two fragments resulting from the breakup of the dinuclear PLF is due to isospin transport. The rate of the transport between the two fragments is shown to be dependent on the slope of the symmetry energy at saturation density. …
We report here an empirical formalism for predicting the cross-sections of neutron-rich nuclei produced in fragmentation of relativistic \b{eta}-unstable neutron-rich projectiles in the mid-mass region. The formalism is based on the abrasion-ablation picture of the projectile fragmentation reaction. It has been shown that the formalism can accurately reproduce the experimental cross-section data for nuclei produced in the fragmentation of 132Sn. The formalism, it is shown, can also reproduce the experimental cross-sections of neutron-rich nuclei produced in the fragmentation of 129Xe fairly ac…
We have, recently, shown that the general trends of partition-wise fission fragment mass distribution in heavy ion (HI) induced compound nuclear (CN) fission of heavy nuclei can be reproduced reasonably well by using the concept of isospin conservation, hence providing a direct evidence of isospin conservation in neutron-rich systems [1, 2, 3, 4]. In this paper, we test the concept of isospin conservation to reproduce the fission fragment mass distribution emerging from thermal neutron-induced CN fission reaction, 245Cm(nth, f). As earlier, we use Kelson's conjectures [5] to assign isospin to …
On the occasion of the $75^{th}$ anniversary of the fission phenomenon, we present a surprisingly simple result which highlights the important role of isospin and its conservation in neutron rich fission fragments. We have analysed the fission fragment mass distribution from two recent heavy-ion reactions $^{238}$U($^{18}$O,f) and $^{208}$Pb($^{18}$O,f) as well as a thermal neutron fission reaction $^{245}$Cm(n$^{th}$,f). We find that the conservation of the total isospin explains the overall trend in the observed relative yields of fragment masses in each fission pair partition. The isospin v…
We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in $^{208}$Pb ($^{18}$O, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. We take into account a range of isospin values allowed by the isospin algebra and assume that the fission fragments are formed in Isobaric Analog States. We also take into account the neutron multiplicity data for various neutron-emission channels in each partition, and use them to obtain the weight factors in calculating the yields. We then calculate th…
This work focuses on the study of temperature associated with the final heavy fragments in reactions induced by both the neutron-proton symmetric and the neutron-rich projectiles, and with incident energy ranges from 60$A$ MeV to 1$A$ GeV. Isobaric yield ratio (IYR) is used to determine the temperature of heavy fragments. Cross sections of measured fragment in reactions are analyzed, and a modified statistical abrasion-ablation (SAA) model is used to calculate the yield of fragment in 140$A$ MeV $^{64}$Ni + $^{9}$Be and 1$A$ GeV $^{136}$Xe + $^{208}$Pb reactions. Relatively low $T$ of heavy fr…
The isobaric yield ratio difference (IBD) between two reactions of similar experimental setups is found to be sensitive to nuclear density differences between projectiles. In this article, the IBD probe is used to study the density variation in neutron-rich $^{48}$Ca. By adjusting diffuseness in the neutron density distribution, three different neutron density distributions of $^{48}$Ca are obtained. The yields of fragments in the 80$A$ MeV $^{40, 48}$Ca + $^{12}$C reactions are calculated by using a modified statistical abrasion-ablation model. It is found that the IBD results obtained from t…
We introduce isospin dependence in the cluster recognition algorithms used in the Quantum Molecular Dynamics model to describe fragment formation in heavy ion collisions. This change reduces the yields of emitted nucleons and enhances the yields of fragments, especially heavier fragments. The enhancement of neutron-rich lighter fragments mainly occurs at mid-rapidity. Consequently, isospin dependent observables, such as isotope distributions, yield ratios of $n/p$, $t/^3He$, and isoscaling parameters are affected. We also investigate how equilibration in heavy ion collisions is affected by thi…
The fragmentation of projectile and spectator is studied at the different incident energies using isospin dependent QMD model with reduced isospin dependent cross-section. Different systems have been used for the analysis of fragment production(IMF). We have used enhanced constant isospin dependent cross-section to explain the experimental findings which is valid for soft equation of state. In addition to that we have tried to study the influence of density dependent symmetry energy on fragment production.
The neck dynamics in Fermi-energy heavy-ion collisions, to probe the nuclear symmetry energy in the domain of sub-saturation densities, is investigated within an isospin dependent transport model. The single and double ratios of neutron/proton from free nucleons and light clusters (complex particles) in the isotopic reactions are analyzed systematically. Isospin effects of particles produced from the neck fragmentations are explored, which are constrained within the midrapidities ($|y/y_{proj}|<$0.3) and azimuthal angles (70$^{o}\sim$110$^{o}$, 250$^{o}\sim$290$^{o}$) in semiperipheral nuclear…
