We call "projectile fragmentation" of neutron halo nuclei the elastic breakup (diffraction) reaction, when the observable studied is the neutron-core relative energy spectrum. This observable has been measured in relation to the Coulomb breakup on heavy target and recently also on light targets. Such data enlighten the effect of the neutron final state interaction with the core of origin. Projectile fragmentation is studied here by a time dependent model for the excitation of a nucleon from a bound state to a continuum resonant state in a neutron-core complex potential which acts as a final state interaction.
The final state is described by an optical model S-matrix so that both resonant and non resonant states of any continuum energy can be studied as well as deeply bound initial states. It turns out that due to the coupling between the initial and final states, the neutron-core free particle phase shifts are modified, in the exit channel, by an additional phase.
Some typical numerical calculations for the relevant observables are presented and compared to experimental data. It is suggest that the excitation energy spectra of an unbound nucleus might reflect the structure of the parent nucleus from whose fragmentation they are obtained.
For projectile fragmentation we work out details of a model whose origin can be traced back to the Bevalac era. The model positions itself between the phenomenological EPAX parametrization and microscopic transport models like "Heavy Ion Phase Space Exploration Model" (HIPSE) and antisymmetrised molecular dynamics(AMD). We apply the model to some recent data of projectile fragmentation of Ni on Ta and Be at beam energy 140 MeV/nucleon and some older data of Xe on Al at beam energy 790 MeV/nucleon. Reasonable values of cross-sections for various composites populated in the reactions are obtaine…
A model for projectile fragmentation is developed whose origin can be traced back to the Bevalac era. The model positions itself between the phenomenological EPAX parametrization and transport models like "Heavy Ion Phase Space Exploration" (HIPSE) model and antisymmetrised molecular dynamics (AMD) model. A very simple impact parameter dependence of input temperature is incorporated in the model which helps to analyze the more peripheral collisions. The model is applied to calculate the charge, isotopic distributions, average number of intermediate mass fragments and the average size of larges…
The formation of the projectile spectator and the fragmentation processes in 107,124Sn + 120Sn collisions at 600 MeV/nucleon are studied with the isospin-dependent quantum molecular dynamics (IQMD) model. The minimum spanning tree algorithm and the ratio of parallel to transverse kinetic quantities are applied to identify the equilibrated projectile spectator during the dynamical evolution. The influence of secondary decay on fragmentation observables is investigated by performing calculations with and without the statistical code GEMINI. The validity of the theoretical approach is examined by…
A new empirical parametrization for the estimation of cross-sections of projectile fragments has been prescribed for studying the advantages and limitations of high energy RI beams for the production of new exotic nuclei. The parametrization reproduces the experimental data for the production of fragments from neutron rich projectiles accurately in contrast to the existing parametrization which tends to overestimate the cross-section of neutron rich fragments in most cases. The modified formalism has been used to compute the cross-sections of neutron-rich species produced by fragmentation of r…
A remarkably simple dependence of fragmentation cross-section on average binding energy has been established in experimental data. This dependence was empirically parametrised leading to a very useful formula for extrapolation. We find that the canonical thermodynamic model, which has been used in the past for successful computations of many observables resulting from multifragmentation, reproduces the salient fetures of fragmentation cross-sections of very neutron rich nuclei very well. This helps towards a theoretical understanding of the observed data.
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 …
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…
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…
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…
Spectroscopic properties of nuclei are accessible with projectile fragmentation reactions, but approximations made in the reaction theory can limit the accuracy of the determinations. We examine here two models that have rather different approximations for the nucleon wave function, the target interaction, and the treatment of the finite duration of the reaction. The nucleon-target interaction is treated differently in the eikonal and the transfer-to-continuum model, but the differences are more significant for light targets. We propose a new parameterization with that in mind. We also propose…
The isospin effect and isoscaling behavior in projectile fragmentation have been systematically investigated by a modified statistical abrasion-ablation (SAA) model. The normalized peak differences and reduced isoscaling parameters are found to decrease with ($Z_{proj}-Z$)/$Z_{proj}$ or the excitation energy per nucleon and have no significant dependence on the size of reaction systems. Assuming a Fermi-gas behavior, the excitation energy dependence of the symmetry energy coefficients are tentatively extracted from $α$ and $β$ which looks consistent with the experimental data. It is pointed ou…
The collisions in four different reaction systems using $^{40,48}$Ca and $^{58,64}$Ni isotope beams and a Be target have been simulated using the Heavy Ion Phase Space Exploration and the Antisymmetrized Molecular Dynamics models. The present study mainly focuses on the model predictions for the excitation energies of the hot fragments and the cross sections of the final fragments produced in these reactions. The effects of various factors influencing the final fragment cross sections, such as the choice of the statistical decay code and its parameters have been explored. The predicted fragmen…
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…
We present a simple time dependent model for the excitation of a nucleon from a bound state to a continuum resonant state in a neutron-core complex potential which acts as a final state interaction. The final state is described by an optical model S-matrix so that both resonant and non resonant states of any continuum energy can be studied as well as deeply bound initial states. It is shown that, due to the coupling between the initial and final states, the neutron-core free particle phase shifts are modified, in the exit channel, by an additional phase. The effect of the additional phase on t…
The fragmentation of projectile and spectator matter is studied at different incident energies using an isospin-dependent QMD model with reduced isospin dependent cross-section. The sensitivity of the production of fragments is analyzed using different parametrizations of density dependence of symmetry energy. We shall also highlight the collective response of the momentum dependent interactions(MDI) and symmetry energy towards the fragmentation of colliding nuclei at intermediate energies.
The isotopic and isotonic distributions of the projectile fragmentation products have been simulated by a modified statistical abrasion-ablation (SAA) model and the isoscaling behavior of projectile-like fragments has been discussed. The isoscaling parameters $α$ and $β$ for hot fragments before evaporation and cold fragments after evaporation have been extracted, respectively. It looks that the evaporation has strong effect on $α$. For cold fragments, a monotonic increase of $α$ and $|β|$ with the increasing of $Z$ and $N$ is observed. The relation between isoscaling parameter and the change …
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 projectile fragmentation reactions using $^{58}Ni$ $\&$ $^{64}Ni$ beams at 140 MeV/n on targets$^{9}Be$ $\&$ $^{181}Ta$ 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…
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 …
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 present our recent results on the fragmentation by varying the mass asymmetry of the reaction between 0.2 and 0.7 at an incident energy of 250 MeV/nucleon. For the present study, the total mass of the system is kept constant (ATOT = 152) and mass asymmetry of the reaction is defined by the asymmetry parameter (? = | (AT - AP)/(AT + AP) |). The measured distributions are shown as a function of the total charge of all projectile fragments, Zbound. We see an interesting outcome for rise and fall in the production of intermediate mass fragments (IMFs) for large asymmetric colliding nuclei. This…
Halo nuclei projectiles can undergo into a fragmentation process when scattered by a nucleus target. The corresponding core from exotic nuclei is usually observed while the others fragments of the reaction are not. We use the recently proposed theory by [Phys. Lett. B767, 53 (2017)] with a four-body description of the inclusive breakup reaction where the projectile is 20C described like a two-neutron halo nucleus. The momentum of both neutrons are integrated out giving a generic description of the core angular distribution. In this preliminary study we perform an analysis of the inclusive inel…
Exploiting the idea that the fast partons of an energetic projectile can be treated as sources of color radiation interpreted as wee partons, it is shown that the recently observed property of extended limiting fragmentation implies a scaling law for the rapidity distribution of fast partons. This leads to a picture of a self-similar process where, for fixed total rapidity Y, the sources merge with probability varying as 1/y.
Theoretical calculations are performed to investigate the angular momentum and Coulomb effects on fragmentation and multifragmentation in peripheral heavy-ion collisions at Fermi energies. Inhomogeneous distributions of hot fragments in the freeze-out volume are taken into account by microcanonical Markov chain calculations within the Statistical Multifragmentation Model (SMM). Including an angular momentum and a long-range Coulomb interaction between projectile and target residues leads to new features in the statistical fragmentation picture. In this case, one can obtain specific correlation…
We consider semi-inclusive diphoton+jet and inclusive diphoton production in high-energy proton-nucleus collisions, treating the target nucleus as a Color-Glass-Condensate and the projectile proton in the parton model. We obtain the prompt diphoton production cross-section in terms of fragmentation and direct contributions. The fragmentation part is given in terms of single-photon and double-photon fragmentation functions. We study prompt, direct and fragmentation diphoton correlations in p+p and p+A collisions at the LHC, and show that at low values of transverse momenta of the produced photo…
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.
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…
We review studies of vortical motion and the resulting global polarization of $Λ$ and $\barΛ$ hyperons in heavy-ion collisions, in particular, within 3FD model. 3FD predictions for the global midrapidity polarization in the FAIR-NICA energy range are presented. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pu…
The equation of state (EOS) of infinite nuclear matter with a small proton/neutron fraction is a crucial input to determine the properties of neutron stars and compare model predictions to astronomical observations. The so-called `symmetry energy' is the part of the EOS accounting for the difference in the number of neutrons and protons. Numerous experiments have been devised to assess the symmetry energy and constrain its functional dependence with the nucleon density. Further constraints follow from a stellar modeling using the EOS to reproduce astronomical observations such as neutron star …
Within the statistical multifragmentation model we study modifications of the surface and symmetry energy of primary fragments in the freeze-out volume. The ALADIN experimental data on multifragmentation obtained in reactions induced by high-energy projectiles with different neutron richness are analyzed. We have extracted the isospin dependence of the surface energy coefficient at different degrees of fragmentation. We conclude that the surface energy of hot fragments produced in multifragmentation reactions differs from the values extracted for isolated nuclei at low excitation. At high frag…
We consider production of prompt photons in high energy gold-gold and deuteron-gold collisions in the forward rapidity region of RHIC ($y \sim 3.8$). In this kinematics, the projectile partons typically have large $x_{bj}$ while the target partons are mostly at very small $x_{bj}$ so that the primary partonic collisions involve valence quarks from the projectile and gluons from the target. We take the target nucleus to be a Color Glass Condensate while the projectile deuteron or nucleus is treated as a dilute system of partons. We show that the photon production cross section can be written as…
The reaction mechanism of nucleus-nucleus collisions at projectile energies around the Fermi energy is investigated with emphasis on the production of fragmentation-like residues. The results of simulations are compared to experimental mass distributions of elements with Z = 21 - 29 observed in the reactions 86Kr+124,112Sn at 25 AMeV. The model of incomplete fusion is modified and a component of excitation energy of the cold fragment dependent on isospin asymmetry is introduced. The modifications in the model of incomplete fusion appear consistent with both overall model framework and availabl…
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-…
A method is proposed for the experimental measurement of neutron separation energies for nuclei far from stability. The procedure is based on determining cross sections for the production of nuclei, by projectile fragmentation, for which only protons are removed but for which the number of neutrons is left unchanged. A simple Abrasion-Ablation analysis leads to a cross section prediction which is sensitive to the neutron separation energy after a single parameter is adjusted in comparison with data. Examples which illustrate the method are presented.
The proton and neutron inclusive distributions in the projectile fragmentation region of $pA$ collisions are studied in the valon model. Momentum degradation and flavor changes due to the nuclear medium are described at the valon level using two parameters. Particle production is treated by means of the recombination subprocess. The centrality dependences of the net proton and neutron spectra of the NA49 data are satisfactorily reproduced. The effective degradation length is determined to be 17 fm. Pion inclusive distributions can be calculated without any adjustable parameters.
