Collective Flow In Heavy-ion Collisions Research Articles

Extracting the hyperon-nucleon interaction via collective flows in heavy-ion collisions

The 2-body hyperon-nucleon interaction softens the equation of state of neutron star matter and leads to the maximum mass of neutron star to be 1.3-1.6M⊙, which deviates from the recent observation with the masses of PSR J0348+0432 (2.01±0.04M⊙) and J0740+6620 (2.14−0.09+0.10M⊙). One attempt is to introduce the more repulsive hyperon-nucleon interaction above the saturation density. A phenomenological Λ potential by fitting the 3-body ΛNN results of chiral effective field theory is implemented into the quantum molecular dynamics transport model to solve the ‘hyperon puzzle’ in neutron stars. It is found that the directed and elliptic flows are sensitive to the high-density hyperon-nucleon potentials in collisions of 197Au + 197Au and 124Sn + 124Sn. The influence of the phenomenological potential on the Λ yields, rapidity distributions and transverse momentum spectra is negligible in comparison with the ones calculated by the well-known relativistic mean-field model. The inclusion of the ΛN, ΣN and ΞN potentials leads to the reduction of hyperon production in the midrapidity region. The Λ directed flows and the slope in the midrapidity region are enhanced with the phenomenological potential and more consistent with the STAR data in collisions of 197Au + 197Au at sNN=3 GeV.

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at Ebeam/A=1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. We find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

Jet drift and collective flow in heavy-ion collisions

We study the tomographic applications of a new phenomenon we dub "jet drift" -- the deflection of high-energy particles and jets toward the direction of a flowing medium -- to the quark-gluon plasma produced in heavy-ion collisions. While the physics of jet drift is quite general, for specificity we consider the case of photon-jet production at mid-rapidity. Beginning with the simplest possible model, a large slab of uniformly flowing plasma, we systematically introduce the geometrical elements of a heavy-ion collision in a simple optical Glauber model. We find that the moving medium causes the jet to drift in the direction of the flow, bending its trajectory and leaving detailed signatures of the flow pattern in the distribution of $\gamma + \: \mathrm{jet}$ acoplanarities. In the elliptical geometries produced in non-central collisions, this drift effect leads to a strong geometry coupling which persists despite the addition of event-by-event fluctuations in the jet production point, impact parameter, and acoplanarity. We propose a new observable to measure the jet drift effect through the correlation of $\gamma + \: \mathrm{jet}$ acoplanarities with the elliptic flow of soft particles. Preliminary estimates suggest this correlation may be studied at sPHENIX and the LHC.

Influence of differential elastic nucleon-nucleon cross section on stopping and collective flow in heavy-ion collisions at intermediate energies

By considering three different Nucleon-Nucleon (NN) elastic differential cross sections: the Cugnon \emph{et al.} parameterized differential cross section [Nucl. Instrum. Methods Phys. Res., Sect. \textbf{B111}, 215 (1996)], and the differential cross section derived from the collision term of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation proposed by Mao \emph{et al.} [Z.\ Phys.\ A {\bf 347}, 173 (1994)], as well as the isotropic differential cross section, within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the influence of the differential elastic NN cross section on various observables (e.g., nuclear stopping, both the rapidity and transverse-velocity dependence of the directed and elliptic flows) in Au+Au collisions at beam energies 150, 250, 400, and 800 MeV$/$nucleon is investigated. By comparing calculations with those three differential cross sections, it is found that the nuclear stopping power, the directed and elliptic flows are affected to some extent by the differential cross sections, and the impact of differential cross section on those observables becomes more visible as the beam energy increases. The effect on the elliptic flow difference $v_{2}^{n}$-$v_{2}^{H}$ and ratio $v_{2}^{n}$/$v_{2}^{H}$ of neutrons versus hydrogen isotopes ($Z=1$), which have been used as sensitive observables for probing nuclear symmetry energy at high densities, is weak.

Dynamics of strangeness and collective flows in heavy-ion collisions near threshold energies

Strangeness (K$^{0,+}$, $\Lambda$ and $\Sigma^{-,0,+}$) production in heavy-ion collisions near threshold energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. The kaon (anti-kaon)-nucleon and hyperon-nucleon potentials in dense nuclear matter are implemented in the model, which are computed from the chiral perturbation approach and the relativistic mean-field model, respectively. It is found that the in-medium potentials change the structure of transverse flow, and also affect the rapidity distributions and the inclusive spectra for strangeness production. The local temperature of the fire ball extracted from the kaon spectra of inclusive invariant cross sections is influenced by the kaon-nucleon potential. The stiffness of nuclear symmetry energy and the kaon-nucleon potential by distinguishing isospin effect play a significant role on the ratio of K$^{0}$/K$^{+}$, in particular at the subthreshold energies. The ratio of $\Sigma^{-}/\Sigma^{+}$ depends on the high-density symmetry energy, in which the $\Sigma$-nucleon potential has a neglectable contribution on the isospin ratio.

Shear viscosities from the Chapman-Enskog and the relaxation time approaches

The interpretation of the measured elliptic and higher order collective flows in heavy-ion collisions in terms of viscous hydrodynamics depends sensitively on the ratio of shear viscosity to entropy density. Here we perform a quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods for selected test cases with specified elastic differential cross sections: (i) the nonrelativistic, relativistic and ultrarelativistic hard sphere gas with angle and energy independent differential cross section, (ii) the Maxwell gas, (iii) chiral pions, and (iv) massive pions for which the differential elastic cross section is taken from experiments. Our quantitative results (i) reveal that the extent of agreement (or disagreement) depends sensitively on the energy dependence of the differential cross sections employed, and (ii) stress the need to perform quantum molecular dynamical (URQMD) simulations that employ Green-Kubo techniques with similar cross sections to validate the codes employed and to test the accuracy of other methods.

Nuclear in-medium effects and collective flows in heavy-ion collisions at intermediate energies

A recent updated version of the Lanzhou quantum molecular dynamics is reviewed, in which the momentum dependence of symmetry potential and the effective mass splitting of proton and neutron in nuclear medium are included in the model. The in-medium nucleon-nucleon (NN) elastic cross sections are evaluated with the scaling approach according to the effective mass and their influence on collective flows in heavy-ion collisions are discussed. The inelastic cross sections, in particular for the process of the channel N$\Delta\rightarrow$NN, are parameterized in accordance with the available experimental data. It is found that the in-medium cross sections play a significant role on isospin emissions and result in a flat distribution for transverse flows and elliptic flows of free nucleons comparing with the in-vacuum ones. The rapidity distribution of the difference between neutron and proton transverse flows is sensitive to the stiffness of nuclear symmetry energy as a promising observable, which can not be influenced by the in-medium effect and collision centrality. Furthermore, the elliptic flow of free energetic nucleons in the case of the mass splitting of $m_{n}^{\ast}>m_{p}^{\ast}$ is also related to the symmetry energy. However, the pion flows weakly depend on the symmetry energy and the mass splitting.

Collective flows in high-energy heavy-ion collisions at AGS and SPS energies

Proton collective flows in heavy-ion collisions from AGS ((2–11) A GeV) to SPS ((40,158) A GeV) energies are investigated in a nonequilibrium transport model with nuclear mean-field (MF). Sideward (p x), directedv 1, and ellipticv 2 flows are systematically studied with different assumptions on the nuclear equation of state (EoS). We find that momentum dependence in the nuclear MF is important for understanding the proton collective flows at AGS and SPS energies. Calculated results with momentum-dependent MF qualitatively reproduce the experimental data of proton sideward, directed, and elliptic flows in an incident energy range of (2–158) A GeV

Mean-field effects on collective flow in high-energy heavy-ion collisions at 2–158AGeV energies

Collective flows in heavy-ion collisions from AGS ($(2-11)A$ GeV) to SPS ($(40,158)A$ GeV) energies are investigated in a nonequilibrium transport model with nuclear mean-field (MF). Sideward $<p_x>$, directed $v_1$, and elliptic flows $v_2$ are systematically studied with different assumptions on the nuclear equation of state (EOS). We find that momentum dependence in the nuclear MF is important for the understanding of the proton collective flows at AGS and SPS energies. Calculated results with momentum dependent MF qualitatively reproduce the experimental data of proton sideward, directed, and elliptic flows in a incident energy range of $(2-158)A$ GeV.

Correlation between Symmetry Energy and Collective Flow inHeavy-Ion Collisions Induced by High Energy Radioactive Beams

Using an isospin- and momentum-dependent hadronic transport model, weinvestigate effects of the symmetry energy on several collective flowsin heavy-ion collisions induced by radioactive beams at intermediateenergies. It is found that the neutron-proton differential directed flowand the neutron-proton differential elliptic flow are stronglycorrelated with the symmetry energy, while the position averaged radialflow is weakly correlated with the symmetry energy.

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling.

Medium effects on the flow of strange particles in heavy-ioncollisions

Strange particles such as the kaon and lambda are useful in probing theproperties of dense matter formed in heavy-ion collisions. Here we reviewthe theoretical understanding of their properties in a nuclearmedium based on both the effective chiral Lagrangian and thephenomenological hadronic model. We further review the effects due tochanges in their in-medium properties on their collective flow inheavy-ion collisions.

Microscopic study of energy and centrality dependence of transverse collective flow in heavy-ion collisions

The centrality dependence of directed and elliptic flow in light and heavy systems of colliding nuclei is studied within two microscopic transport models at energies from $1A$ GeV to $160A$ GeV. The pion-directed flow has negative slope in the midrapidity range irrespective of bombarding energy and mass number of the colliding ions. In contrast, the directed flow of nucleons vanishes and even develops antiflow in the midrapidity range in (semi)peripheral collisions at energies around $11.6A$ GeV and higher. The origin of the disappearance of flow is linked to nuclear shadowing. Since the effect is stronger for a light system, it can be distinguished from a similar phenomenon caused by quark-gluon plasma formation. In the latter case the disappearance of flow due to the softening of the equation of state should be most pronounced in collisions of heavy ions. The centrality dependence of the elliptic flow shows that the maximum in the $〈{v}_{2}(b)〉$ distribution is shifted to very peripheral events with rising incident energy, in accordance with experimental data. This is an indication of the transition from baryonic to mesonic degrees of freedom in hot hadronic matter.

Isospin dependence of collective flow

Nuclear collective flow in heavy-ion collisions at intermediate energies has been studied in an isospin-dependent transport model. It is found that both the sign and strength of collective flow are significantly affected by the isospin asymmetry of the colliding system. The predicted dependence of the balance energy, defined by the incident energy at which the collective flow disappears, on the isospin asymmetry is compared with recent experiments at NSCL/MSU.

Isospin dependence of collective flow in heavy-ion collisions at intermediate energies.

Within the framework of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (BUU) model using initial proton and neutron densities calculated from the nonlinear relativistic mean-field (RMF) theory, we compare the strength of transverse collective flow in reactions $^{48}Ca+^{58}Fe$ and $^{48}Cr+^{58}Ni$, which have the same mass number but different neutron/proton ratios. The neutron-rich system ($^{48}Ca+^{58}Fe$) is found to show significantly stronger negative deflection and consequently has a higher balance energy, especially in peripheral collisions. NOTE ADDED IN PROOF: The new phenomenon predicted in this work has just been confirmed by an experiment done by G.D. Westfall et al. using the NSCL/MSU radioactive beam facility and a spartan soccer. A paper by R. Pak et al. is submitted to PRL to report the experimental result.

Momentum-dependent nuclear mean fields and collective flow in heavy-ion collisions.

We use the Boltzmann-Uehling-Uhlenbeck model to simulate the dynamical evolution of heavy ion collisions and to compare the effects of two parametrizations of the momentum--dependent nuclear mean field that have identical properties in cold nuclear matter. We compare with recent data on nuclear flow, as characterized by transverse momentum distributions and flow ($F$) variables for symmetric and asymmetric systems. We find that the precise functional dependence of the nuclear mean field on the particle momentum is important. With our approach, we also confirm that the difference between symmetric and asymmetric systems can be used to pin down the density and momentum dependence of the nuclear self consistent one--body potential, independently. All the data can be reproduced very well with a momentum--dependent interaction with compressibility K = 210 MeV.

Measurement of collective flow in heavy-ion collisions using particle-pair correlations.

We present a new type of flow analysis, based on a particle-pair correlation function, in which there is no need for an event-by-event determination of the reaction plane. Consequently, the need to correct for dispersion in an estimated reaction plane does not arise. Our method also offers the option to avoid any influence from particle misidentification. Using this method, streamer chamber data for collisions of Ar+KCl and Ar+${\mathrm{BaI}}_{2}$ at 1.2 GeV/nucleon are compared with predictions of a nuclear transport model.