The number of nucleon (NN) scaling of the directed flow $v_1$ and elliptic flow ($v_{2}$) as well as the nuclear modification factor ($R_{cp}$) are tested for light nuclei which are produced in 0.4$A$ GeV $^{197}Au + ^{197}Au$ collisions at different impact parameters with two different in-medium nucleon-nucleon cross sections in the framework of an isospin-dependent quantum molecular dynamics (IQMD) model. In that energy domain, the emission of light nuclei can be well described by the squeeze-out phenonomenon. The results show a nice NN scaling behavior for flow parameters $v_{1}$, $v_{2}$ and ${R_{cp}}$. These results demonstrate that the nucleon coalescence mechanism is responsible for nucleon-number scaling of above physical observables in squeeze-out region in heavy-ion collisions at intermediate energy.
Within a transport model it is shown that the neutron/proton ratio of squeezed-out nucleons perpendicular to the reaction plane, especially at high transverse momenta, in heavy-ion reactions induced by high energy neutron-rich nuclei can be a useful tool for studying the high density behavior of the nuclear symmetry energy.
By involving the constraints of the slope of nuclear symmetry energy $L$ into the question of determination of the high-density symmetry energy, one needs to probe the curvature of nuclear symmetry energy $K_{\rm{sym}}$. Based on the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, effects of the curvature of nuclear symmetry energy on the squeezed-out nucleons are demonstrated in the semi-central Au+Au reaction at 400 and 600 MeV/nucleon. It is shown that the squeezed-out isospin-dependent nucleon emissions at high transverse momenta are sensitive to the curvature of nucl…
The squeeze-out flow in reactions of $^{124}$Sn + $^{124}$Sn and $^{124}$Ba + $^{124}$Ba at different incident energies for different impact parameters is investigated by means of an isospin-dependent quantum molecular dynamics model. For the first time, it is found that the more neutron-rich system ($% ^{124}$Sn + $^{124}$Sn) exhibits weaker squeeze-out flow. This isospin dependence of the squeeze-out flow is shown to mainly result from the isospin dependence of nucleon-nucleon cross section and the symmetry energy.
We present a detailed analysis of the beam energy dependence of the mechanisms for the generation of directed and elliptic flows in Au+Au collisions focusing on the role of hadronic rescattering and spectator shadowing within a microscopic transport model JAM with different equation of state. A systematic study of the beam energy dependence is performed for Au+Au collisions at $\sqrt{s_{NN}} =2.3 - 62.4$ GeV. The transition of the dynamical origin of the directed flow is observed. We find that the initial Glauber type nucleon-nucleon collisions generate negative $v_1$ for nucleons at midrapidi…
Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till the mass number 4 as a function of rapidity have been studied for 25 MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum Molecular Dynamics model. A phenomenological scaling behavior of rapidity dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps almost independent of rapidity and remains a rough constant of 1/2 for all light fragmen…
We perform a systematic study of in-plane and out-of-plane proton and neutron flow from nucleus-nucleus collisions within the BUU transport approach employing different parameter sets for the mean-field potentials that can be characterized by the nuclear incompressibility and the stiffness of the momentum-dependent potential. We find that a simultaneous description of the experimental data from the BEVALAC and the SIS on both the nucleon squeeze-out $v_2$ and the in-plane flow $F$ at beam energies $E_{lab} = 0.15 ÷2$ AGeV requires a mean field with strong momentum dependence, i.e. an effective…
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on $\frac{dN}{d(<Cos2ϕ>)}$ and $\frac{dN}{p_tdp_t}$. Simulations have been carried out for the reactions of $^{124}X_{m}+^{124}X_{m}$, where m = (47, 50 and 59) and $^{40}S_{16}+^{40}S_{16}$. Our study shows that these parameters depend strongly on the isospin of cross-section and charge asymmetry. The distribution of nucleons and fragments is not symmetric around the beam axis.
Anisotropic flows ($v_2$ and $v_4$) of light nuclear clusters are studied by Isospin-Dependent Quantum Molecular Dynamics model for the system of $^{86}$Kr + $^{124}$Sn at intermediate energy and large impact parameters. Number-of-nucleon scaling of the elliptic flow ($v_2$) are demonstrated for the light fragments up to $A$ = 4, and the ratio of $v_4/v_2^2$ shows a constant value of 1/2. In addition, the momentum-space densities of different clusters are also surveyed as functions of transverse momentum, in-plane transverse momentum and azimuth angle relative to the reaction plane. The result…
It is shown that under changing density or temperature a nucleon Fermi superfluid can undergo a phase transition to an anisotropic superfluid state, characterized by nonvanishing gaps in pairing channels with singlet-singlet (SS) and triplet-singlet (TS) pairing of nucleons (in spin and isospin spaces). In the SS pairing channel nucleons are paired with nonzero orbital angular momentum. Such two-gap states can arise as a result of branching from the one-gap solution of the self-consistent equations, describing SS or TS pairing of nucleons, that depends on the relationship between SS and TS cou…
By using the Nikiforov-Uvarov method, the hyper-radial Schrodinger equation is analytically solved, in which the real modified potential is employed at finite temperature and baryon chemical potential. The eigenvalue of energy and corresponding wave function are obtained in the isotropic and anisotropic media in hot and dense media. The present results show that the binding energy of nucleon and some heavy baryon decrease strongly in hot medium and decreases slightly with increasing baryon chemical potential. In addition, binding energy for each baryon is more bound in an anisotropic medium in…
Decorrelation of the elliptic flow in rapidity is calculated within a hybrid approach which includes event-by-event viscous fluid dynamics and final state hadronic cascade model. The simulations are performed for Au+Au collisions at center-of-mass collision energies of 27 and 200 GeV per nucleon pair, as well as various colliding systems at 72 GeV per nucleon pair. Initial conditions determined by an extended Monte Carlo Glauber model show better agreement with experimental data than initial conditions from the UrQMD transport model. We show how the observed decorrelation is connected with the…
Anisotropic flows ($v_2$ and $v_4$) of hadrons and light nuclear clusters are studied by a partonic transport model and nucleonic transport model, respectively, in ultra-relativistic and intermediate energy heavy ion collisions. Both number-of-constituent-quark scaling of hadrons, especially for $ϕ$ meson which is composed of strange quarks, and number-of-nucleon scaling of light nuclear clusters are discussed and explored for the elliptic flow ($v_2$). The ratios of $v_4/v_2^2$ of hadrons and nuclear clusters are, respectively, calculated and they show different constant values which are inde…
The scaling behaviors of anisotropic flows of light charged particles are studied for 25 \,MeV/nucleon $^{40}$Ca+$^{40}$Ca collisions at different impact parameters by the isospin-dependent quantum molecular dynamics model. The number of nucleons scaling of elliptic flow is existed and the scaling of the ratios of $v_{4}/v_{2}^{2}$ and $v_{3}/(v_{1}v_{2})$ are applicable for collisions at almost all impact parameters except for peripheral collisions.
Anisotropic flow can offer significant information of evolution dynamics in heavy-ion collisions. A systematic study of the directed flow $v_1$ and elliptic flow $v_2$ of hard photons and free nucleons is performed for $^{40}$Ca+$^{40}$Ca collisions in a framework of isospin dependent quantum molecular dynamics (IQMD) model. The study firstly reveals that thermal photons emitted in intermediate-energy heavy-ion collisions have the behaviors of directed and elliptic flows. The interesting phenomena of incident energy dependence of $v_1$ and $v_2$ for thermal photons in central collisions also c…
A systemical analysis of the initial fluctuation effect on the collective flows for Au+Au at 1$A$ GeV has been presented in the framework of Isospin-dependent Quantum Molecular Dynamics model (IQMD), and a special focus on the initial fluctuation effect on the squeeze-out is emphasized. The flows calculated by the participant plane reconstructedby the initial geometry in coordinate space are compared with those calculated by both the ideal reaction plane and event plane methods. It is found that initial fluctuation weakens squeeze-out effect, and somediscrepancies between the flows extracted b…
Anisotropic flow coefficients v_1-v_5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The glasma dynamics, as realized in the IP-Glasma model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic sub-nucleon scale color charge fluctuations; the pre-equilibrium flow of matter is then matched to the MUSIC algorithm describing viscous hydrodynamic flow and particle p…
We apply a well tested hybrid transport model, which couples viscous hydrodynamics to a hadronic afterburner, to describe bulk observables in proton-lead and lead-lead collisions at $\sqrt{s_{NN}}=5.02$ TeV. The quark-gluon plasma (QGP) initial conditions are modeled using the parametric TRENTO model with additional nucleon substructure parameters to vary the number and size of hot spots inside each nucleon, followed by a pre-equilibrium free streaming stage to match the full energy-momentum tensor of the initial state onto viscous hydrodynamics. Initial condition and QGP medium parameters, su…
The collective expansion of matter created in collisions of heavy-ions, ranging from collision energies of tens of MeV to a few TeV per nucleon pair, proved to be one of the best probes to study the detailed properties of these unknown states of matter. Collective expansion originates from the initial pressure gradients in the created hot and dense matter. These pressure gradients transform the initial spatial deformations and inhomogeneities of the created matter into momentum anisotropies of the final state particle production, which we call anisotropic flow. These momentum anisotropies are …
Anisotropic flow of hadrons is studied in heavy ion collisions at SPS and RHIC energies within the microscopic quark-gluon string model. The model was found to reproduce correctly many of the flow features, e.g., the wiggle structure of direct flow of nucleons at midrapidity, or centrality, rapidity, and transverse momentum dependences of elliptic flow. Further predictions are made. The differences in the development of the anisotropic flow components are linked to the freeze-out conditions, which are quite different for baryons and mesons.
We present an analysis of $Ξ^-$ baryon production in subthreshold proton--nucleus ($p+A$) collisions in the framework of a BUU type transport model. We propose a new mechanism for $Ξ$ production in the collision of a secondary $Λ$ or $Σ$ hyperon and a nucleon from the target nucleus. We find that the $Ξ^-$ multiplicity in $p+A$ collisions is sensitive to the angular distribution of hyperon production in the primary $N+N$ collision. Using reasonable assumptions on the unknown elementary cross sections we are able to reproduce the $Ξ^-$ multiplicity and the $Ξ^-/(Λ+Σ^0)$ ratio obtained in the HA…
Multicluster models consider that the nucleons can be moving around different centers in the nuclei. These models have been widely used to describe light nuclei but always considering that the mean field is composed of isotropic harmonic oscillators with different centers. In this work, we propose an extension of these models by using anisotropic harmonic oscillators. The strenghts of these oscillators, the distance among the different centers and the disposition of the nucleons inside every cluster are free parameters which have been fixed using the variational criterion. We have used a hamil…
Two important parametrizations of momentum-dependent nucleonic fields, proposed for the simulations of central heavy-ion collisions, one by Gale et al. and the other by Welke et al., suffer from practical limitations. The first gives rise to mean fields isotropic in momentum, even when underlying momentum distributions are anisotropic, making descriptions of early nonequilibrium stages of collisions unrealistic. The second parametrization gives rise to anisotropic mean fields, but is computationally expensive, because the mean field has to be computed separately for every location of a nucleon…
Some emerging concepts of nuclear structure are overviewed. (1) Background: the many-body quantum structure of atomic nucleus, a complex system comprising protons and neutrons (called nucleons collectively), has been studied largely based on the idea of the quantum liquid (a la Landau), where nucleons are quasiparticles moving in a (mean) potential well, with weak "residual" interactions between nucleons. The potential is rigid in general, although it can be anisotropic. While this view was a good starting point, it is time to look into kaleidoscopic aspects of the nuclear structure brought in…
The nuclear symmetry energy, which describes the energy difference of per proton and neutron in nuclear matter, has been extensively studied within the last two decades. Around saturation density, both the value and the slope of the nuclear symmetry energy have been roughly constrained, its high-density behavior is now still in argument. Probing high-density symmetry energy at terrestrial laboratories is being carried out at facilities that offer radioactive beams worldwide. While relevant experiments are being conducted, we theoretically developed more advanced isospin-dependent transport mod…
Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light clusters have been studied in details for 25 MeV/nucleon $^{86}$Kr + $^{124}$Sn at large impact parameters by Quantum Molecular Dynamics model with different potential parameters. Four parameter sets which include soft or hard equation of state (EOS) with/without symmetry energy term are used. Both number-of-nucleon ($A$) scaling of the elliptic flow versus transverse momentum ($p_t$) and the scaling of $v_4/A^{2}$ versus $(p_t/A)^2$ have been demonstrated for the light clusters in all above calculation conditions. It was also found …
Anisotropic flows ($v_1$, $v_2$ and $v_4$) of light nuclear clusters are studied by a nucleonic transport model in intermediate energy heavy ion collisions. The number-of-nucleon scalings of the directed flow ($v_1$) and elliptic flow ($v_2$) are demonstrated for light nuclear clusters. Moreover, the ratios of $v_4/v_2^2$ of nuclear clusters show a constant value of 1/2 regardless of the transverse momentum. The above phenomena can be understood by the coalescence mechanism in nucleonic level and are worthy to be explored in experiments.
We present a new method to extract anisotropic flow in heavy ion collisions from the genuine correlation among a large number of particles. Anisotropic flow is obtained from the zeroes in the complex plane of a generating function of azimuthal correlations, in close analogy with the theory of phase transitions by Lee and Yang. Flow is first estimated globally, i.e., averaged over the phase space covered by the detector, and then differentially, as a function of transverse momentum and rapidity for identified particles. The corresponding estimates are less biased by nonflow correlations than wi…
Within the framework of an isospin and momentum dependent transport model, the emissions of isospin particles (nucleons and light clusters) squeezed out in heavy-ion collisions are investigated as probes of the poorly known symmetry energy at high baryon density. Two different mass splittings of neutrons and protons in nuclear medium as $m_{n}^{\ast}>m_{p}^{\ast}$ and $m_{n}^{\ast}<m_{p}^{\ast}$ are used in the model and their influence on the isospin emission in heavy-ion collisions is discussed thoroughly. The competition between the stiffness and the momentum dependence of the symmetry pote…
The notion of the "size" of nucleons and their constituents plays a pivotal role in the current paradigm of the formation and the fluctuations of the quark-gluon plasma produced in high-energy nuclear collision experiments. We report on state-of-the-art hydrodynamic results showing that the correlation between anisotropic flow, $v_n^2$, and the mean transverse momentum of hadrons, $[p_t]$, possesses a unique sensitivity to the nucleon size in off-central heavy-ion collisions. We argue that existing experimental measurements of this observable support a picture where the relevant length scale c…
Low-energy baryon-baryon interactions are calculated in a high-statistics lattice QCD study on a single ensemble of anisotropic clover gauge-field configurations at a pion mass of m_π~ 390 MeV, a spatial volume of L^3 ~ (2.5 fm)^3, and a spatial lattice spacing of b~0.123 fm. Lüscher's method is used to extract nucleon-nucleon, hyperon-nucleon and hyperon-hyperon scattering phase shifts at one momentum from the one- and two-baryon ground-state energies in the lattice volume. The isospin-3/2 NΣinteractions are found to be highly spin-dependent, and the interaction in the ^3S_1 channel is found …
The nuclear overlap zone in non-central relativistic heavy ion collisions is azimuthally very asymmetric. By varying the angle between the axes of deformation and the transverse direction of the pair momenta, the suppression of $J/Ψ$ and $Ψ'$ will oscillate in a characteristic way. Whereas the average suppression is mostly sensitive to the early and high density stages of the collision, the amplitude is more sensitive to the late stages. This effect provides additional information on the $J/Ψ$ suppression mechanisms such as direct absorption on participating nucleons, comover absorption or for…
Within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model, pion dynamics in heavy-ion collisions near threshold energies and the emission of preequilibrium particles (nucleons and light complex fragments) have been investigated. A density, momentum and isospin dependent pion-nucleon potential based on the $Δ$-hole model is implemented in the transport approach, which slightly leads to the increase of the $π^{-}/π^{+}$ ratio, but reduces the total pion yields. It is found that a bump structure of the $π^{-}/π^{+}$ ratio in the kinetic energy spectra appears at the pi…
Subthreshold kaon (K$^{0}$ and K$^{+}$) production in neutron-rich nuclear reactions to probe the kaon-nucleon interaction in nuclear medium and to extract the isospin dependent part of the nuclear equation of state at high-baryon densities, is investigated within an isospin and momentum dependent transport model. A repulsive kaon-nucleon potential is implemented in the model through fitting the flow data and inclusive spectra in heavy-ion collisions, which enhances the energetic kaon emission squeezed out in the reaction zone and leads to a variation of the high-momentum spectrum of the K$^{0…
We review recent studies about anisotropic flows ($v_1, v_2, v_3$) of charmonium in the quark-gluon plasma produced in relativistic heavy-ion collisions. Collective flows of the bulk medium are developed due to the anisotropic pressure gradient of the medium. Strongly coupled with the bulk medium, charm quarks carry collective flows from the expanding medium, which will be inherited by the regenerated charmonium via the coalescence process. In event-by-event collisions where nucleon positions fluctuate from the smooth distribution, there is triangularity in the medium initial energy density. T…
Predicting Quadrupole deformation via anisotropic flow and transverse momentum spectra in isotopic $\mathbf{\prescript{128-135}{54}{\mathrm{Xe}}}$ collisions at LHC
Anisotropic Flow of light (anti-)(hyper-)nuclei in Pb+Pb Collision at $\sqrt{s_{NN}}=5.36$ TeV
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（复旦大学理论核物理上海研究中心）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；Heavy lon Science and Technology Key Laboratory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子科学和技术重点实验室）；Cyclotron Institute and Department of Physics and Astronomy, Texas A&M University（德州农工大学回旋加速器研究所及物理与天文学系）；School of Physics, East China Normal University（华东师范大学物理系）
The LHC data on event-by-event harmonic flow coefficients measured in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted within the HYDJET++ model. To compare the model results with the experimental data the unfolding procedure is employed. The essentially dynamical origin of the flow fluctuations in hydro-inspired freeze-out approach has been established. It is shown that the simple modification of the model via introducing the distribution over spatial anisotropy parameters permits HYDJET++ to reproduce both elliptic and triangular flow fluctuatio…
In nuclear physics a magic number is defined as the nucleon number, which is separated by a significantly large single-particle energy gap from the next nucleon. Magic numbers define the nuclear shells, which are considered to be active, only if they are partially occupied by nucleons. As a consequence the single particle interactions of the valence nucleons lead to the description of the collective properties of the whole nucleus in the shell model theory. But phenomena as the island of inversion, the shape coexistence and the break down of the N=20 magic number reveal that the above definiti…
The transverse momentum dependence of the anisotropic flow $v_2$ for $π$, $K$, nucleon, $Λ$, $Ξ$ and $Ω$ is studied for Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV within two independent string-hadron transport approaches (RQMD and UrQMD). Although both models reach only 60% of the absolute magnitude of the measured $v_2$, they both predict the particle type dependence of $v_2$, as observed by the RHIC experiments: $v_2$ exhibits a hadron-mass hierarchy (HMH) in the low $p_T$ region and a number-of-constituent-quark (NCQ) dependence in the intermediate $p_T$ region. The failure of the ha…
We demonstrate the consistency of the quark deconfinement phase transition parameters in the beta-stable neutron star matter and in the nearly symmetric nuclear matter formed in heavy-ion collisions (HICs). We investigate the proton and $Λ$ flow in Au+Au collisions at 3 and 4.5 GeV/nucleon incident beam energies with the pure hadron cascade version of a multi-phase transport model. The phase transition in HICs and neutron stars is described based on a class of hybrid equations of state from the quark mean-field model for the hadronic phase and a constant-speed-of-sound parametrization for the …
Using the quantum molecular dynamics model, we aim to investigate the emis- sion of light complex particles, and degree of stopping reached in heavy-ion colli- sions. We took incident energies between 50 and 1000 MeV/nucleon. In addition, central and peripheral collisions and different masses are also considered. We ob- serve that the light complex particles act in almost similar manner as anisotropic ratio. In other words, multiplicity of light complex particles is an indicator of global stopping in heavy-ion collisions. We see that maximum light complex particles and stopping is obtained for…
A framework combining Yang-Mills dynamics of the pre-equilibrium glasma with relativistic viscous hydrodynamic evolution of the quark-gluon plasma and hadron gas phases is presented. Event-by-event fluctuations of nucleon positions and color charges are taken into account, leading to negative binomial fluctuations of gluon multiplicities. Experimental anisotropic flow coefficients v2-v5 of charged hadron distributions in heavy-ion collisions at the Large Hadron Collider are well described. Furthermore, event-by-event distributions of v2, v3 and v4 measured by the ATLAS collaboration are reprod…
