Transverse radius dependence for transverse velocity and elliptic flow in intermediate energy HIC

The mean transverse velocity and elliptic flow of light fragments (A≤2) as a function of transverse radius are studied for 25 MeV/nucleon <'64>Cu+<'64>Cu collisions with impact parameters 3-5 fm by the isospin- dependent quantum molecular dynamics model. By comparison between the in-plane and the out-of-plane transverse velocities, the elliptic flow dependence on the transverse radius can be understood qualitatively, and variation of the direction of the resultant force on the fragments can be investigated qualitatively.     

Shadowing effects and transverse momentum dependence of particle emission in intermediate energy heavy ion collisions

Light particle emission was studied at Ganil for ³⁶ Ar +²⁷ Al between 55 and 95 MeV/u and for ⁶⁴ Zn+⁵⁸ Ni between 35 and 79 MeV/u. The correlation of these particles with the reaction plane was analyzed. In intermediate impact parameter events, the transverse momentum dependence of this correlation changes drastically with the energy for midrapidity particles. For both systems, at the upper incident energies, particles with highest transverse momenta are preferentially emitted perpendicular to the reaction plane. This can be qualitatively reproduced by simulations taking into account shadowing effects.     

System size, energy, pseudorapidity, and centrality dependence of elliptic flow

This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.     

Studying the energy dependence of elliptic and directed flow within a relativistic transport approach

The energy excitation functions of directed flow (v₁) and elliptic flow (v₂) from E_beam=90 A MeV to E_cm=200 A GeV are explored within the UrQMD framework and discussed in the context of the available data. The radial and the elliptic flow of the particles produced in a relativistic heavy-ion collision are intimately connected to the pressure and its gradients in the early stage of the reaction. Therefore, these observables should also be sensitive to changes in the equation of state. To prove this connection, the temporal evolution of the pressure, pressure gradients and elliptic flow are shown. For the flow excitation functions it is found that, in the energy regime below E_beam≤10 A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40 A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component (“antiflow”) and cannot be reproduced by the transport model. The difference between the data and the UrQMD model can possibly be explained by assuming a phase transition from hadron gas to quark–gluon plasma around E_lab=40 A GeV. This would be consistent with the model calculations, indicating a transition from hadronic matter to “string matter” in this energy range. Thus, we speculate that the missing pressure might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au + Au (Pb + Pb) collisions already at lower SPS energies. PACS 25.75.-q; 25.75.Ld; 25.75.Dw; 25.75.Gz; 24.10.Lx     

Energy dependence for directed and elliptic flow in in termediate-energy heavy ion collisions

Differential and integrated directed flow and elliptic flow of light charged particles （z≤2） are studied systematically for semi-central （b=5 fm）¹⁹⁷ Au+197 Au collisions at incident energies from 25 to 250 MeV/nucleon by the isospin-dependent quantum molecular dynamics model. The changes of directed and elliptic flow with incident energy reflect the dynamic competition between the mean field and nucleon-nucleon collisions and also between collective rotation and expansion.     

Energy dependence for directed and elliptic flow in in termediate-energy heavy ion collisions

Differential and integrated directed flow and elliptic flow of light charged particles (z ≤ 2) are studied systematically for semi-central (b = 5 fm) ¹⁹⁷Au+¹⁹⁷Au collisions at incident energies from 25 to 250 MeV/nucleon by the isospin-dependent quantum molecular dynamics model. The changes of directed and elliptic flow with incident energy reflect the dynamic competition between mean field and nucleon-nucleon collisions and also between collective rotation and expansion.     

Transverse energy dependence of neutron squeeze-out in relativistic heavy ion collisions

We present a microscopic calculation of neutronsqueeze-out in relativistic heavy ion collisions at beam energies betweeen 400 and 1000 MeV/nucleon. After demonstrating the importance of the correct isospin treatment for the neutron to proton ratio, our main emphasis is put on the investigation of the properties of neutronsqueeze-out. Thesqueeze-out ratio increases monotonously with the transverse momentum of the neutrons. This ratio is independent of the incident beam energy if plotted versusp _t /p _proj . Most importantly, we observe a strong dependence on the nuclear equation of state and momentum dependent interaction.Supported by GSI, BMFT and DFG     

Energy dependence of transverse quark flow in heavy ion collisions

Energy dependence of quark transverse flow carries information about dynamical properties (equation of state, initial conditions) of deconfined matter produced in heavy ion collisions. We assume quark-antiquark matter formation in Pb+Pb collisions at CERN SPS and Au+Au collisions at RHIC energies and determine quark transverse flow at the critical temperature of the quark-hadron phase transition. Coalescence of massive quarks is calculated in the MICOR hadronization model and hadronic final state effects are considered using the GROMIT cascade program. Comparing theoretical results to data, transverse flow values are determined and energy dependence is discussed.     

Search for QCD critical point by transverse velocity dependence of anti-deuteron to deuteron ratio

We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system evolution trajectory in the QCD phase diagram,which is known as the focusing effect.To quantify this effect,we employ the thermal and hadronic transport model to simulate the dynamical particle emission along a hypothetical focusing trajectory near the critical point.We found that the focusing effect can lead to anomalous β_T dependence on ■/p,■/d and ■/~3 He ratios.We examined the β_T dependence of ■/p and ■/d ratios of central Au+Au collisions at ■=7.7 to 200 GeV measured by the STAR experiment at RHIC.Surprisingly,we only observe a negative slope in β_T dependence of ■/d ratio at ■=19.6 GeV,which indicates the trajectory evolution has passed through the critical region.In the future,we could constrain the location of the critical point and/or width of the critical region by conducting precise measurements on the β_T dependence of the ■/d ratio at different energies and rapidity.     

Directed and elliptic flow in 197Au+197Au at intermediate energies

Directed and elliptic flow for the ¹⁹⁷Au+¹⁹⁷Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ _NN and demonstrate the importance of angular momentum conservation in transport codes at low energies.     

Effect of the momentum dependence of nuclear symmetry potential on the transverse and elliptic flows

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, the effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction ¹³²Sn+¹²⁴Sn at a beam energy of 400MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transverse flow more evidently than the difference of neutron and proton transverse flows as well as the difference of proton and neutron elliptic flows. It is thus better to probe the symmetry energy by using the difference of neutron and proton flows since the momentum dependence of nuclear symmetry potential is still an open question. And it is better to probe the momentum dependence of nuclear symmetry potential by using the neutron-proton differential transverse flow the rapidity distribution of the free neutron to proton ratio.     

Intensity dependence of flow signal in slice selective velocity measurements

The quantitative determination of flow velocities using inflow-outflow techniques require slice selective excitation pulses. The intensity-velocity relationship for such methods is shown to be such that flow velocities estimated using techniques which rely on an absolute calibration of the measured intensity are sensitive to the details of the slice profile of the excited material. This can cause errors when the estimation of flow velocities is made from the image intensity. A method which provides a measure of the flow velocities and which relies only on relative variations in intensity is examined and shown to be insensitive to details of the slice profile.     

Transverse energy flow in lepton and hadron induced reactions at high energies

We show that correlations betweenx- andy-components of the secondary particle momenta together with an amount of stochasticity and coherency account for the transverse energy (momentum) spectra observed recently in high energy collisions of leptons and hadrons. Relations obtained within the framework of quantum statistics involving the coherent state expansions are applied to e⁺e^– (at s 14 GeV), pp (26 GeV), ¯pp (900 GeV) and p + Au (200 GeV proton beam) collisions. The comparison of theoretical relations with data leads to sufficiently accurate conclusions. However, more experimental results of the same collision are needed as far as the values of the parameters involved should be determined uniquely.One of the authors (M. B.) acknowledges with pleasure the fruitful discussions with Drs. J. Peina, L. Kubáek, D. Krupa, J. Piút and M. Seman.     

Measurements of transverse energy flow in deep-inelastic scattering at HERA

Measurements of transverse energy flow are presented for neutral current deep-inelastic scattering events produced in positron-proton collisions at HERA. The kinematic range covers squared momentum transfers from 3.2 to 2 200 GeV, the Bjorken scaling variable x from to 0.11 and the hadronic mass W from 66 to 233 GeV. The transverse energy flow is measured in the hadronic centre of mass frame and is studied as a function of , x, W and pseudorapidity. A comparison is made with QCD-based models. The behaviour of the mean transverse energy in the central pseudorapidity region and an interval corresponding to the photon fragmentation region are analysed as a function of and W. Received: 15 July 1999 / Published online: 27 January 2000     

Impact parameter and beam energy dependence for azimuthal asymmetry of direct photons and free protons in intermediate energy heavy-ion collisions

Hard photon emitted from energetic heavy ion collisions is of very interesting since it does not experience the late-stage nuclear interaction, therefore it is useful to explore the early-stage information of matter phase. In this work, we have calculated the impact parameter and beam energy dependence for azimuthal asymmetry, characterized by directed transverse flow parameter F and elliptic asymmetry coeffcient v2, of direct photons and the corresponding free protons in intermediate energy heavy-ion collisions. It is further shown the anti-correlated azimuthal asymmetry between direct photons and free protons.