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.
Within a dynamical description of nuclear fragmentation, based on the liquid-gas phase transition scenario, we explore the relation between neutron-proton density fluctuations and nuclear symmetry energy. We show that, along the fragmentation path, isovector fluctuations follow the evolution of the local density and approach an equilibrium value connected to the local symmetry energy. Higher density regions are characterized by smaller average asymmetry and narrower isotopic distributions. This dynamical analysis points out that fragment final state isospin fluctuations can probe the symmetry …
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 effect of the density dependence of symmetry energy on fragmentation is studied using isospin-dependent quantum molecular dynamics model(IQMD) Model. We have used the reduced isospin-dependent cross-section with soft equation of state to explain the experimental findings for the system 79_Au^197 + 79_Au^197 for the full colliding geometry. In addition to that we have tried to study the collective response of the momentum dependent interactions(MDI) and symmetry energy towards the multifragmentation
We extract values for the free symmetry energy as a function of the fragment size (the proton number Z) from antisymmetrized molecular dynamics (AMD) calculations of calcium collisions. Simple statistical physics describe well the distribution of hot nuclei at breakup, provided the surface symmetry term in the free energy is much smaller at high excitation than in ground state nuclei. This result may reflect the condition of low density and finite temperature when these systems disassemble.
We studied the influence of a momentum dependent interaction in the context of isopspin effects on fragmentation and dissipation in intermediate energy heavy ion collisions by using an isospin dependent quantum molecular dynamics model. It is shown that the nuclear stopping, the number of nucleons emitted ,and the multiplicity of intermediate mass fragments are larger with a momentum dependent interaction than without. In particular, the differences for these observables, when using an isospin dependent in-medium nucleon nucleon cross section versus an isospin independent one, are also larger …
Based on an isospin dependent quantum molecular dynamics model we studied the influence of a medium correction of an isospin dependent nucleon nucleon cross section on the fragmentation at the intermediate energy heavy ion collisions. We found that the medium correction from an isospin dependent nucleon nucleon cross section increases the dependence of the fragmentation on the isospin effect of in-medium nucleon nucleon cross section, at the same time, the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the medium correction on the isospin ef…
The influence of medium correction from an isospin dependent nucleon nucleon cross section on the fragmentation and nucleon emission in the intermediate energy heavy ion collisions was studied by using an isospin dependent quantum molecular dynamical model (IQMD). We found that the medium correction enhances the dependence of multiplicity of intermediate mass fragment $N_{imf}$ and the number of nucleon emission $N_{n}$ on the isospin effect of the nucleon nucleon cross section,while the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the med…
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…
We investigate the unpolarized pion and kaon fragmentation functions, employing the nonlocal chiral-quark model, which manifests the nonlocal interactions between the quarks and pseudoscalar mesons, considering the explicit flavor-SU(3)-symmetry breaking in terms of the current-quark masses. Moreover, we study the quark-distribution functions, derived from the fragmentation ones with the Drell-Yan-Levi relation. Numerical results are evaluated to higher Q^2 by the DGLAP evolution and compared with the empirical data. The ratios between the relevant valance quark-distribution functions are also…
The thermal and phase properties of a multifragmentation model which uses clusters as degrees of freedom, are explored as a function of isospin. A good qualitative agreement is found with the phase diagram of asymmetric nuclear matter as established by different mean-field models. In particular, from the convexity properties of the nuclear entropy, we show that uncharged finite nuclei display first and second order liquid-gas-like phase transitions. Different quantities are examined to connect the thermal properties of the system to cluster observables. In particular we show that fractionation…
We study the transverse momentum spectrum of hadrons in jets. By measuring the transverse momentum with respect to a judiciously chosen axis, we find that this observable is insensitive to (the recoil of) soft radiation. Furthermore, for small transverse momenta we show that the effects of the jet boundary factorize, leading to a new transverse-momentum-dependent (TMD) fragmentation function. In contrast to the usual TMD fragmentation functions, it does not involve rapidity divergences and is universal in the sense that it is independent of the type of process and number of jets. These results…
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.
We show the possibility of extracting important information on the symmetry term of the Equation of State ($EOS$) directly from multifragmentation reactions using stable isotopes with different charge asymmetries. We study n-rich and n-poor $Sn + Sn$ collisions at $50AMeV$ using a new stochastic transport approach with all isospin effects suitably accounted for. For central collisions a chemical component in the spinodal instabilities is clearly seen. This effect is reduced in the neck fragmentation observed for semiperipheral collisions, pointing to a different nature of the instability. In s…
In order to describe the hadronization of polarized quarks, we discuss an extension of the quark-jet model to transverse momentum dependent fragmentation functions. The description is based on a product ansatz, where each factor in the product represents one of the transverse momentum dependent splitting functions, which can be calculated by using effective quark theories. The resulting integral equations and sum rules are discussed in detail for the case of inclusive pion production. In particular, we demonstrate that the 3-dimensional momentum sum rules are satisfied naturally in this transv…
Isospin equilibration in multi-fragmentation processes is studied for the system $^{40}Cl+^{28}Si$ at 40 MeV/nucleon. The investigation is performed through semiclassical microscopic many-body calculations based on the CoMD-II model. The study has been developed to describe isospin equilibration processes involving the gas and liquid "phases" of the total system formed in the collision processes. The investigation of the behavior of this observable in terms of the repulsive/attractive action of the symmetry term, highlights many-body correlations which are absent in semiclassical mean-field ap…
We perform the first global QCD analysis of polarized inclusive and semi-inclusive deep-inelastic scattering and single-inclusive $e^+e^-$ annihilation data, fitting simultaneously the parton distribution and fragmentation functions using the iterative Monte Carlo method. Without imposing SU(3) symmetry relations, we find the strange polarization to be very small, consistent with zero for both inclusive and semi-inclusive data, which provides a resolution to the strange quark polarization puzzle. The combined analysis also allows the direct extraction from data of the isovector and octet axial…
We investigate properties of the symmetry term in the equation-of-state (EOS) of nuclear matter (NM) from the analysis of simulations of fragmentation events in intermediate energy heavy ion collisions. For charge asymmetric systems a qualitative new feature in the liquid-gas phase transition is predicted: the onset of chemical instabilities with a mixture of isoscalar and isovector components. This leads to a separation into a higher density (``liquid'') symmetric and a low density (``gas'') neutron-rich phase, the so-called neutron distillation effect. We analyse the simulations with respect…
Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\…
Based on the isospin-dependent quantum molecular dynamics (IQMD) model, we aim to understand the effect of target fragmentation on various quantities i.e. collision rate, fragments multiplicity etc by simulating the collision between $Au^{197}$ projectile and $C^{12}$, $Al^{26}$, $Cu^{63}$, and $Pb^{208}$ as targets at incident energy 600 MeV/nucleon. The collision geometry is varied from central to peripheral. Our results indicate the rise and fall in the production of intermediate mass fragments with ${Z_{bound}}$ which is in agreement with the experimental data of Aladin collaboration at lo…
The asymptotic time derivative of the total dipole signal is proposed as an useful observable to study Isospin equilibration phenomenon in multi-fragmentation processes. The study proceeds through the investigation of the $^{40}Cl+^{28}Si$ system at 40 MeV/nucleon by means of semiclassical microscopic many-body calculations based on the CoMD-II model. In particular, the study has been developed to describe charge/mass equilibration processes involving the gas and liquid "phases" of the total system formed during the early stage of a collision. Through the investigation of dynamical many-body c…
Dynamics of the nuclear fragmentations and the charge exchange reactions in pion-nucleus collisions near the $Δ$(1232) resonance energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. An isospin, momentum and density-dependent pion-nucleon potential is implemented in the model, which influences the pion dynamics, in particular the kinetic energy spectra, but weakly impacts the fragmentation mechanism. The absorption process in pion-nucleon collisions to form the $Δ$(1232) resonance dominates the heating mechanism of target nucleus. The excitation e…
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…
For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = …
We demonstrate that spontaneous transverse polarization of Lambda baryon ($Λ$) production in $e^+e^-$ annihilation can be described using the transverse momentum dependent polarizing fragmentation functions (TMD PFFs). Using a simple Gaussian model, we perform an extraction of the TMD PFFs by fitting the BELLE collaboration's recent measurement of the $Λ$ transverse polarization in back-to-back $Λ+h$ production in $e^+ e^-$ collisions, $e^{-} + e^{+} \rightarrow Λ^{\uparrow}+h+X$. We find that this simple model accurately describes the experimental data for $Λ$ production associated with pions…
We present new features of the transition from nuclear multifragmentation to neck fragmentation in semi-central heavy-ion collisions at Fermi energies as obtained within a microscopic transport model, Stochastic Mean Field (SMF). We show that along this transition specific hierarchy phenomena of some kinematic observables associated with the intermediate mass fragments develop. Their correlations with the dynamics of isospin degree of freedom, predicted by our calculations, open new possibilities to learn about the density dependence of nuclear symmetry energy below saturation, as well as abou…
Transverse-spin dependent energy-energy correlators in proton-proton collisions within the dihadron fragmentation framework
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·布海米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（纽约州立大学石溪分校核科学前沿中心）；Temple University（天普大学）；Lebanon Valley College（黎巴嫩谷学院）
Jets in the vacuum correspond to multi-parton configurations that form via a branching process sensitive to the soft and collinear divergences of QCD. In heavy-ion collisions, energy loss processes that are stimulated via interactions with the medium, affect jet observables in a profound way. Jet fragmentation factorizes into a three-stage process, involving vacuum-like emissions above the medium scale, induced emissions enhanced by the medium length and, finally, long-distance vacuum-like fragmentation. This formalism leads to a novel, non-linear resummation of jet energy loss. In this talk w…
The ratio of symmetry energy coefficient to temperature $C_{sym}/T$ 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 t…
We undertake a quantitative comparison of multi-fragmentation reactions, as modeled by two different approaches: the Antisymmetrized Molecular Dynamics (AMD) and the momentum-dependent stochastic mean-field (SMF) model. Fragment observables and pre-equilibrium (nucleon and light cluster) emission are analyzed, in connection to the underlying compression-expansion dynamics in each model. Considering reactions between neutron-rich systems, observables related to the isotopic properties of emitted particles and fragments are also discussed, as a function of the parametrization employed for the is…
The hypothesis of limiting fragmentation (LF) or it is called otherwise recently, as extended longitudinal scaling, is an interesting phenomena in high energy multiparticle production process. This paper discusses about different regions of phase space and their importance in hadron production, giving special emphasis on the fragmentation region. Although it was conjectured as a universal phenomenon in high energy physics, with the advent of higher center-of-mass energies, it has become prudent to analyse and understand the validity of such hypothesis in view of the increasing inelastic nucleo…
