超相对论Au+Au碰撞中椭圆流的时间依赖

用相对论量子分子动力学(RQMD)模型模拟了质心系束能量为s_NN=200GeV的Au+Au非对心碰撞, 研究了椭圆流对末态粒子冻出时间的关系. 研究了在不同的阶段, 椭圆流对末态粒子位置的关系. 结果表明椭圆流随冻出时间的单调递减, 椭圆流对横向半径的关系随冻出时间发生变化. 用压力梯度对所得结果进行了分析. 径向速度用来表征压力梯度.     

System size dependence of the non-monotonous pion freeze-out volume excitation function

Hanburry-Brown-Twiss (HBT) correlation functions and radii of negatively charged pions from C+C, Si+Si, Cu+Cu, and In+In at lower RHIC/SPS energies are calculated with the UrQMD transport model and the CRAB analyzing program. We find a minimum in the excitation function of the pion freeze-out volume at low transverse momenta and around E _lab ?? 20?C30AGeV which can be related to the change from initial string emission to bulk emission from the created resonance matter. For small systems, we predict a local minimum in the excitation function of the HBT (freeze-out) volume which is explained by the competition of two mechanisms of the particle production, namely resonance decays and string formation/fragmentation.     

Hadronic expansion dynamics in central Pb+Pb collisions at 158 GeV per nucleon

Two-particle correlation functions of negative hadrons over wide phase space, and transverse mass spectra of negative hadrons and deuterons near mid-rapidity have been measured in central Pb+Pb collisions at 158 GeV per nucleon by the NA49 experiment at the CERN SPS. A novel Coulomb correction procedure for the negative two-particle correlations is employed making use of the measured oppositely charged particle correlation. Within an expanding source scenario these results are used to ext ract the dynamic characteristics of the hadronic source, resolving the ambiguities between the temperature and transverse expansion velocity of the source, that are unavoidable when single and two particle spectra are analysed separately. The source shape, the total duration of the source expansion, the duration of particle emission, the freeze-out temperature and the longitudinal and transverse expansion velocities are deduced. Received: 25 November 1997 / Published online: 24 March 1998     

相对论重离子碰撞中强子气体膨胀过程的蒙特卡罗研究

利用AMPT蒙特卡罗产生器中的强子化程序模块ART1.0, 得到了强子化过程的演化图形, 并基于强子在不同时刻的空间分布图, 估算出了不同时刻的反应区域半径. 将所得结果与根据HBT关联得到的结果相比较, 定出了冻结为强子气体的时刻, 得到了合理的结果.     

HBT with space- vs. time-like hydrodynamic freeze-out

Bose-Einstein correlations in relativistic heavy ion collisions and their dependence on the freeze-out condition in hydrodynamic models is examined. The Cooper & Fryespace-like freeze-out mechanism is compared totime-like freeze-out, where particles are emittedaway only from the surface, i.e. space- vs. time-like freeze-out. The corresponding HBT radii are calculated for the two models emphasizing the difference in the outward HBT radius.     

Search for collective transverse flow using particle transverse momentum spectra in relativistic heavy-ion collisions

The particle transverse momentum spectra recently measured in relativistic heavy-ion collisions at CERN and BNL are analysed within an expanding fireball model. All the particle spectra at a given beam energy can be reproduced simultaneously with a single set of intensive parameters for the initial state of the fireball. As typical freeze-out parameters in this beam energy region we find a freeze-out temperatureT _f?110 MeV for most hadrons, and an average transverse expansion velocity at freeze-out of 〈v/c〉?0.4–0.45. The striking enhancement at transverse momentap _T<200 MeV/c in the CERN pion data cannot be fully explained by the existence of transverse flow.     

Two-pion interferometry for viscous hydrodynamic sources

The space-time evolution of the (1+1)-dimensional viscous hydrodynamics with an initial quark-gluon plasma (QGP) produced in ultrarelativistic heavy ion collisions is studied numerically. The particle-emitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss (HBT) interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on the two-pion HBT results is small if only the shear viscosity is taken into consideration in the calculations. The bulk viscosity leads to a larger transverse freeze-out configuration of the pion-emitting sources, and thus increases the transverse HBT radii. The results of the longitudinal HBT radius for the source with Bjorken longitudinal scaling are consistent with the experimental data.     

RHIC能区Au+Au碰撞中HBT关联参数分析

利用相对论量子分子动力学模型RQMD,对RHIC能区s=200GeV/u Au+Au碰撞进行了2π干涉学分析,并讨论了HBT半径参数对横动量的依赖关系.研究表明,两粒子关联函数能够给出碰撞源在冻结时刻的时空拓扑信息,HBT半径参数能够较好地反映源的尺度和形状,但其对横动量的依赖关系并不能直接反映源的压缩性质,而是对粒子产生时源的空间–动量关联程度更为敏感.     

Reconstruction of hadronization stage in Pb+Pb collisions at 158 A GeV/c

Recent data on hadron multiplicities in central Pb+Pb collisions at 158 A GeV/c at mid-rapidity are analyzed within the concept of chemical freeze-out. A non-uniformity of the baryon chemical potential along the beam axis is taken into account. An approximate analytical solution of the hydrodynamic equations for a chemically frozen Boltzmann-like gas is found. The Cauchy conditions for hydrodynamic evolution of the hadron resonance gas are fixed at the thermal freeze-out hypersurface from analysis of one-particle momentum spectra and HBT correlations. The proper time of chemical freeze-out and physical conditions at the hadronization stage, such as energy density and averaged transverse velocity, are found.     

Study of Kinetic Freeze-Out Parameters as a Function of Rapidity in pp Collisions at CERN SPS Energies

We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were π+, π−, K+, K−, and p¯. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease.     

Centrality dependence of particle yields and their ratios at RHIC experiments

The collision centrality dependence of the yields per unit rapidity dN/dy along with their ratios for various hadrons produced in Au+Au collisions at different collision energies have been studied within the framework of unified statistical thermal freeze-out model (USTFM) taking into account both longitudinal and transverse hydrodynamic flows. Bulk freeze-out properties in terms of the thermal parameters, temperature and mid-rapidity baryon chemical potential at chemical freeze-out, obtained within the proposed model, which are in agreement with experimental data. The extracted chemical freeze-out temperature is found to depend weakly on the collision centrality. It is also found that this temperature is almost independent of the collision energies considered in this work. The closeness of the freeze-out temperature to the predicted phase-transition temperature suggests that the chemical freeze-out happens near hadronization. Furthermore, the dependence of the mid-rapidity chemical potential on the collision energy at different centralities, as well as the centrality dependence of the mid-rapidity size of the system in terms of the transverse size of the system, has been studied at the RHIC. The effect of resonance decay contributions has also been taken into account.     

Transverse momentum spectra of the produced hadrons at SPS energy and a random walk model

The transverse momentum spectra of the produced hadrons have been compared to a model, which is based on the assumption that a nucleus–nucleus collision is a superposition of isotropically decaying thermal sources at a given freeze-out temperature. The freeze-out temperature in nucleus–nucleus collisions is fixed from the inverse slope of the transverse momentum spectra of hadrons in nucleon–nucleon collision. The successive collisions in thessss nuclear reactions leads to gain in transverse momentum, as the nucleons propagate in the nucleus following a random walk pattern. The average transverse rapidity shift per collision is determined from the nucleon–nucleus collision data. Using this information, we obtain parameter-free result for the transverse momentum distribution of produced hadrons in nucleus–nucleus collisions. It is observed that such a model is able to explain the transverse mass spectra of the produced pions at SPS energies. However, it fails to satisfactorily explain the transverse mass spectra of kaons and protons. This indicates the presence of collective effect which cannot be accounted for, by the initial state collision broadening of transverse momentum of produced hadrons, the basis of random walk model.     

Hydrodynamic description of spectra at high transverse mass in ultrarelativistic heavy ion collisions

Transverse mass spectra of pions and protons measured in central collisions of heavy ions at the SPS and at RHIC are compared to a hydrodynamic parameterization. While the chemical temperature needed at RHIC is significantly higher compared to SPS, the spectra may be described using kinetic freeze-out parameters which are similar for both beam energies. At RHIC either the temperature or the flow velocity is higher, but the data provide no unambiguous proof for much stronger transverse flow. The contribution of such hydrodynamic emission at high transverse momenta is investigated in detail. It is shown that hydrodynamics may be relevant up to relatively high transverse momenta. The importance of the velocity profile used in this context is highlighted. Received: 4 July 2002 / Revised version: 6 November 2002 / Published online: 20 December 2002     

Size of the freeze-out source in high energy heavy ion collisions

Based on a hydro-inspired azimuthally symmetric emission function, we analyze the HBT radius Rs and the single-particle transverse momentum spectra in Au+Au collisions measured by the STAR Collaboration at SNN = 200 GeV. The results show that consistent assumptions about transverse density (and/or flow profile) in the calculation of the HBT radius Rs and single-particle spectral analyses play an important role for understanding the size of the freeze-out source.     

玻色─爱因斯坦关联半径和源半径对实验窗口的依赖及它们的差异

研究了１６０ＡＧｅＶＰｂ＋Ｐｂ反应中π源的玻色─爱因斯坦关联半径和源半径（均方根半径）的关系，以及它们对实验窗口的依赖。模型冗源由ＵＲＡＳｉＭＡ生成器产生。研究表明关联半径和源半径不仅数值不等，而且变化行为也不同。     

Excitation Functions of Tsallis-Like Parameters in High-Energy Nucleus–Nucleus Collisions

The transverse momentum spectra of charged pions, kaons, and protons produced at mid-rapidity in central nucleus–nucleus (AA) collisions at high energies are analyzed by considering particles to be created from two participant partons, which are assumed to be contributors from the collision system. Each participant (contributor) parton is assumed to contribute to the transverse momentum by a Tsallis-like function. The contributions of the two participant partons are regarded as the two components of transverse momentum of the identified particle. The experimental data measured in high-energy AA collisions by international collaborations are studied. The excitation functions of kinetic freeze-out temperature and transverse flow velocity are extracted. The two parameters increase quickly from ≈3 to ≈10 GeV (exactly from 2.7 to 7.7 GeV) and then slowly at above 10 GeV with the increase of collision energy. In particular, there is a plateau from near 10 GeV to 200 GeV in the excitation function of kinetic freeze-out temperature.     

Two-dimensional analysis of Bose-Einstein correlationsin hadronic Z decays at LEP

Bose-Einstein correlations are studied in pairs of charged pions from hadronic Z decays, collected by the ALEPH detector. The correlation function, measured using either the unlike-sign or the mixed reference sample, is studied in terms of the Lorentz-invariant four-momentum difference and its transverse, Q _T, and longitudinal, Q _L, components with respect to the longitudinal centre-of-mass system. Values for the correlation radii, R _T and R _L, are obtained from the fit of the Goldhaber parametrisation. The results indicate that the correlation radii values depend on the chosen kind of reference sample and on the two-jet purity.Received: 23 April 2004, Revised: 11 May 2004, Published online: 9 July 2004     

Chiral condensate and chemical freeze-out

We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T, μ)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion decay constant while preserving the GMOR relation. We demonstrate within a schematic resonance gas model consisting of a variable number of pionic and nucleonic degrees of freedom that within the above model a quantitative explanation of the hadonic freeze-out curve and its phenomenological conditions can be given.