净质子和奇异粒子集体流特性的研究
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摘要
随着相对论重离子对撞机(RHIC)的大量有重要研究意义实验数据的发表和公布,和更高能量的大强子对撞机(LHC)即将运行,相对论重离子碰撞研究已经成为21世纪一个有重大研究意义的前沿研究领域之一。RHIC和LHC要解决的重大问题之一是:碰撞所产生的物质热化到什么程度?RHIC和LHC能产生极端高温高密的物质以及数目巨大的粒子数,这种极端高温高密的物质有许多问题需要我们去探索,在什么情况下这种物质处于局部或者整体热平衡?能否用一些热力学量,例如温度、压强和能量来表征它们的特征和怎样表征它们的特征?这些高温高密物质相空间分布具有怎样的特征?如何更详细讨论这种热物质的状态方程以及状态之间的转化?核几何对这些碰撞特征有什么影响?
近期,许多理论和实验物理学家注意到:集体流特性研究已成为研究相对论重离子碰撞的多强子产生的一个重要研究工具,这是由于高能重离子碰撞所产生的纵向和横向流有丰富的物理内涵,它与系统的早期演化和核阻止特性有紧密的联系。可以用集体流来研究相对论重离子碰撞产生的核阻止和一些集体运动特征,通过分别对热解冻时,净质子和奇异粒子的相空间特征的研究,将会加深我们对重离子碰撞动力学机制的了解和认识。
非均匀集体流模型(Non-Uniform Flow Model NUFM)认为:净重子快度分布出现中心下凹现象可能与纵向相空间非均匀分布特性有关,也即是:随着碰撞能量的升高,不仅会出现较强的纵向(与横向比较),导致有圆柱状的相空间分布特征,而且,由于末态产生粒子还带有母核的运动学特征,在纵向分布的发射源会集中分布在大快度区间.集体流分布在纵向会出现非均匀分布特征,在纵向出现的非均匀分布将导致中心下凹现象。
本文的主要工作是利用NUFM,并考虑重子数守恒的修正,系统分析了A GS、SPS和RHIC能区的净质子分布特征.我们发现:对于RHIC能区,考虑到重子数守恒修正后,分布特征与不考虑分布完全不同。考虑重子数守恒,很显然是对原NUFM理论一个重要且合理的一个修正.原来没有考虑重子数守恒的NUFM在考虑RHIC能区上是有缺陷的,特别是在远离中心快度区间的区间,实验上还没有给出该快度区间的分布结果,且RHIC能区的动力学区间比A GS和SPS要宽许多,这一点已被实验所证实.文章预言该区域呈现峰状,这样的结论将有待更新的实验结果验证。并在此基础上分析了从AGS到RHIC能区的核阻止特性随入射粒子快度关系。
本文最为重要的一项工作,通过系统分析A GS、SPS和RHIC能区的净质子分布特征和核阻止特性,在此工作基础上,预言LHC能区的净质子分布和核阻止本领。当然,这项研究还需等待LHC实验结果的检验。
本文还根据非均匀流理论系统分析了SPS能区的奇异粒子分布特征,以及纵向流平均速度βγ随入射能量变化关系。
With the running of Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider(LHC) , relativistic heavy ion collisions have been one of the most important research area. Several of the most important questions that RHIC and LHC should be answered are: what is the degree of thermalization of that LHC can reach? What is the situation of the produced matter to reach local equilibrium? How to express the thermalization feature of the system by using the thermalization quantity such as temperature, pressure and energy? What is the feature of the phase space of the material of high temperature and high density? How to investigate the equation of state and the transition between the hadron and QGP?and how to study the effect of collision on nuclear geometry ?
The study of collective flow in high energy nuclear collisions has attracted increasing attentions from both experimental and theoretical points of view. The physics of longitudinal and transverse flows is due to their system evolution at early time and nuclear stopping. In general, the collective evolution of the hot and dense matter leaves a distinct imprint on the phase space distribution of the fireball at freeze-out. To disentangle such information from features generated during freeze-out, a refined understanding of the decoupling process is needed.
Non-Uniform Flow Model (NUFM) realized that central dip of net proton distribution is closely related to the non-uniform feature of longitudinal phase space. As the incident energy increase, the transparency/stopping of relativistic heavy-ion collisions should be taken into account more carefully. A more reasonable assumption is that the fireballs keep some memory on the motion of the incident nuclei, and therefore the distribution of fireballs, instead of being uniform in the longitudinal direction, is more concentrated in the direction of motion of the incident nuclei, i.e. more dense at large absolute value of rapidity. It will not only lead to anisotropy in longitudinal-transverse directions, but also render the fireballs (especially for those baryons) distributing non-uniformly in the longitudinal direction. NUFM may analyze the central dip of baryon rapidity distribution by assuming that the centers of fireballs are distributed non-uniformly in the longitudinal phase space.
We have ever used NUFM to study the net proton rapidity among AGS, SPS and RHIC energy regions. But for the RHIC energy regions, we made a mistake before to predict the distributions of net proton distributions since we neglected the effects of the baryon number conservation. Therefore, it is necessary to reanalyze the features of net proton rapidity distributions among AGS to RHIC by taking into account the baryon number conservation. It is found that when we consider the baryon number conservation, the features of the distributions at RHIC are completely different from the results given before , especially at large absolute rapidity region.
With the run of forthcoming LHC, the predictions of the features of net proton rapidity distributions at LHC are also important. We will restudy the features of net proton rapidity distributions among AGS to RHIC by using NUFM, and make prediction for the features of forthcoming LHC in this paper.
The strange particle distributions are also investigated by using NUFM during the SPS energy region. The dependence of the number of strange particles and the velocity of longitudinal flow on incident energies is also studied in this paper.
近期,许多理论和实验物理学家注意到:集体流特性研究已成为研究相对论重离子碰撞的多强子产生的一个重要研究工具,这是由于高能重离子碰撞所产生的纵向和横向流有丰富的物理内涵,它与系统的早期演化和核阻止特性有紧密的联系。可以用集体流来研究相对论重离子碰撞产生的核阻止和一些集体运动特征,通过分别对热解冻时,净质子和奇异粒子的相空间特征的研究,将会加深我们对重离子碰撞动力学机制的了解和认识。
非均匀集体流模型(Non-Uniform Flow Model NUFM)认为:净重子快度分布出现中心下凹现象可能与纵向相空间非均匀分布特性有关,也即是:随着碰撞能量的升高,不仅会出现较强的纵向(与横向比较),导致有圆柱状的相空间分布特征,而且,由于末态产生粒子还带有母核的运动学特征,在纵向分布的发射源会集中分布在大快度区间.集体流分布在纵向会出现非均匀分布特征,在纵向出现的非均匀分布将导致中心下凹现象。
本文的主要工作是利用NUFM,并考虑重子数守恒的修正,系统分析了A GS、SPS和RHIC能区的净质子分布特征.我们发现:对于RHIC能区,考虑到重子数守恒修正后,分布特征与不考虑分布完全不同。考虑重子数守恒,很显然是对原NUFM理论一个重要且合理的一个修正.原来没有考虑重子数守恒的NUFM在考虑RHIC能区上是有缺陷的,特别是在远离中心快度区间的区间,实验上还没有给出该快度区间的分布结果,且RHIC能区的动力学区间比A GS和SPS要宽许多,这一点已被实验所证实.文章预言该区域呈现峰状,这样的结论将有待更新的实验结果验证。并在此基础上分析了从AGS到RHIC能区的核阻止特性随入射粒子快度关系。
本文最为重要的一项工作,通过系统分析A GS、SPS和RHIC能区的净质子分布特征和核阻止特性,在此工作基础上,预言LHC能区的净质子分布和核阻止本领。当然,这项研究还需等待LHC实验结果的检验。
本文还根据非均匀流理论系统分析了SPS能区的奇异粒子分布特征,以及纵向流平均速度βγ随入射能量变化关系。
With the running of Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider(LHC) , relativistic heavy ion collisions have been one of the most important research area. Several of the most important questions that RHIC and LHC should be answered are: what is the degree of thermalization of that LHC can reach? What is the situation of the produced matter to reach local equilibrium? How to express the thermalization feature of the system by using the thermalization quantity such as temperature, pressure and energy? What is the feature of the phase space of the material of high temperature and high density? How to investigate the equation of state and the transition between the hadron and QGP?and how to study the effect of collision on nuclear geometry ?
The study of collective flow in high energy nuclear collisions has attracted increasing attentions from both experimental and theoretical points of view. The physics of longitudinal and transverse flows is due to their system evolution at early time and nuclear stopping. In general, the collective evolution of the hot and dense matter leaves a distinct imprint on the phase space distribution of the fireball at freeze-out. To disentangle such information from features generated during freeze-out, a refined understanding of the decoupling process is needed.
Non-Uniform Flow Model (NUFM) realized that central dip of net proton distribution is closely related to the non-uniform feature of longitudinal phase space. As the incident energy increase, the transparency/stopping of relativistic heavy-ion collisions should be taken into account more carefully. A more reasonable assumption is that the fireballs keep some memory on the motion of the incident nuclei, and therefore the distribution of fireballs, instead of being uniform in the longitudinal direction, is more concentrated in the direction of motion of the incident nuclei, i.e. more dense at large absolute value of rapidity. It will not only lead to anisotropy in longitudinal-transverse directions, but also render the fireballs (especially for those baryons) distributing non-uniformly in the longitudinal direction. NUFM may analyze the central dip of baryon rapidity distribution by assuming that the centers of fireballs are distributed non-uniformly in the longitudinal phase space.
We have ever used NUFM to study the net proton rapidity among AGS, SPS and RHIC energy regions. But for the RHIC energy regions, we made a mistake before to predict the distributions of net proton distributions since we neglected the effects of the baryon number conservation. Therefore, it is necessary to reanalyze the features of net proton rapidity distributions among AGS to RHIC by taking into account the baryon number conservation. It is found that when we consider the baryon number conservation, the features of the distributions at RHIC are completely different from the results given before , especially at large absolute rapidity region.
With the run of forthcoming LHC, the predictions of the features of net proton rapidity distributions at LHC are also important. We will restudy the features of net proton rapidity distributions among AGS to RHIC by using NUFM, and make prediction for the features of forthcoming LHC in this paper.
The strange particle distributions are also investigated by using NUFM during the SPS energy region. The dependence of the number of strange particles and the velocity of longitudinal flow on incident energies is also studied in this paper.
引文
[1]黄卓然(Cheuk-Yin Wong),《高能重离子碰撞导论》张卫宁译,哈尔滨工业大学出版社,2002
[2]冯笙琴著,《高能多强子产生物理导论》,北京:北京理工大学出版社,2005: 3-7,186-192
[3]Bjorken J D. Highly relativistic nucleus-nucleus collisions: the central rapidity region. Phys Rev D,1983,27(1):140—151
[4]Lee T D. Missing symmetries, unseen quarks and the physical vacuum. Nucl. Phys, 1992, A25(1):3c-13c
[5]Schukraft J. Heavy-ion physics at the LHC. 2nd Latin American School of High-Energy Physics, San Miguel Regla, Mexico, 1-14 Jun 2003
[6]Wiedemamn U A. Opportunities for heavy-ion physics at the large hadron collider LHC, J. Phys.2007, G34:503-509
[7]Jacobs P, Wang X N. Matter in extremis: ultrarelativistic nuclear collisions at RHIC. Progress in Particle and Nuclear Physics. 2005. 54(2): 443~534
[8]Xu N. Collective Dynamics at RHIC. Proceedings of CCAST,Beijing,2002
[9]CERN Yellow Report on“Hard probes in heavy collisions at LHC”, 2003
[10]Lisa M, Pratt S, Soltz R, and Wiedemann U. Femtoscopy in relativistic heavy ion collisions .Ann Rev Nucl Part Sci,2005, 55:357-402
[11]Busza W and Goldhaber A S. Nuclear Stopping Power. Phys.Lett.1984, B139:235
[12]Bialas A and W.Czyz. Moments of the particle phase-space density at freeze-out and coincidence probabilities. Acta Phys Polon,2005,B36: 3109-3114
[13]Bearden I G, Beavis D, Besliu C, et al. Charged Meson Rapidity Distributions in Central Au+Au Collisions at s NN=200 GeV. Phys. Rev. Lett, 2005, 94: 162301(1)~162301(4)
[14]Back B B, Betts R R, Chang J et al. Baryon rapidity loss in relativistic Au+Au collisions. Phys Rev Lett, 2001,86:1970–1973
[15]Bearden I G, Beavis D, Besliu C et al. Nuclear stopping in Au+Au collisions at s NN=200 GeV. Phys Rev Lett, 2004, 93:102301(1) ~102301(5)
[16]Klay J L, Ajitanand N N, Alexander J M et al. Longitudinal flow of protons from (2–8) A GeV central Au + Au collisions. Phys Rev Lett, 2002, 88:102301(1)—102301(5)
[17]Ahle L, Akiba Y,Ashktorab1 K.,et al. Proton and deuteron production in Au + Au reactions at 11.6/A-Gev/c. Phys Rev C, 1999, 60(6):064901
[18]Barrette J, Bellweid R,Bennett S,et al. Proton and pion production in Au + Au collisions at 10.8A-GeV/c. Phys Rev C, 2000. 62(2):024901
[19]Appelshauser H, Bachler H,Bailey S J, et al. Baryon stopping and charged particle distributions in central Pb+Pb collisions at 158 GeV per nucleon. Phys Rev Lett, 1999, 82(12):2471-2475
[20]Videbeck F et al. Recent results from E866. Nucl Phys A, 1995, 590(7):249c-258c
[21]Wienold T et al. Stopping and collective effects at SPS energies. Nucl Phys A, 1996, A610(11):76c-87c
[22]Huovinen P. Hydrodynamic description of collective flow. World Scientific Singapore, 2003
[23]Kolb P F, Huovinen P, Heinz U and Heiselberg H . Elliptic flow at SPS and RHIC: From kinetic transport to hydrodynamics. Phys.Lett,2001, B500:232-240
[24]Huovinen P, Kolb P F, Heinz U W, Ruuskanen P V and Voloshin S A. Radial and elliptic flow at RHIC: Further predictions. Phys. Lett. 2001, B503: 58-64
[25]Kolb P F, Heinz U W, Huovinen P, Eskola K J and Tuominen K. Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics. Nucl.Phys, 2001, A696:197-215
[26]Bleicher M and Stocker H. Anisotropic flow in ultrarelativistic heavy ion collisions. Phys.Lett, 2002, B526:309-314
[27]Hirano T and Nara Y. Energy loss in high-energy heavy ion collisions from the Hydro + Jet model. Phys. Rev C, 2002, 66:041901
[28]Hirano T and Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freeze-out. Phys.Rev,2002, C66:054905
[29]Hirano T and Nara Y. Back-to-back correlations of high p(T) hadrons in relativistic heavy ion collisions. Phys.Rev.Lett, 2003, 91:082301
[30]Hirano T and Nara Y , Pseudorapidity dependence of parton energy loss in relativisticheavy ion collisions. Phys.Rev, 2003, C68:064902
[31]Hirano T and Nara Y , Hydrodynamic afterburner for the color glass condensate and the parton energy loss, Nucl. Phys, 2004, A743:305-328, nucl-th/0404039
[32]Cooper F, Frye G. Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multi-particle production. Phys Rev, 1974. D10(1):186～189
[33]Hirano T, Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freeze-out. Phys. Rev. 2002, C 66 : 054905. nucl-th/0205043
[34]Bass S.A. et al., Hadronic freezeout following a first order hadronization phase transition in ultrarelativistic heavy ion collisions Phys. Rev. 1999, C 60 : 021902. nucl-th/9902062
[35]Adler S S. et al., Identified charged particle spectra and yields in Au+Au collisions at s NN = 200-GeV. Phys. Rev. 2004, C 69: 034909. nucl-ex/0307022
[36]Adcox K. et al., Centrality dependence of pi+ / pi-, K+ / K-, p and anti-p production from s NN = 130GeV Au+Au collisions at RHIC. Phys. Rev. Lett,2002, 88:242301. nucl-ex/0112006
[37]Adler C. et al., Measurement of inclusive anti-protons from Au+Au collisions at ( s NN = 130-GeV. Phys. Rev. Lett, 2001, 87 :262302, nucl-ex/0110009.
[38]M. Calderon de la Barca Sanchez, Charged hadron spectra in Au+Au collisions at s NN= 130-GeV. Ph.D. Thesis, Yale University, 2001, nucl-ex/0111004
[39]Kolb P F, Heinz U W. Hydrodynamic description of ultra-relativistic heavy ion collisions, Invited review for 'Quark Gluon Plasma 3'. Editors: R.C. Hwa and X.N. Wang, World Scientific, Singapore, nucl-th/0305084
[40]Huovinen P, Kolb P F, Heinz W. Is there elliptic flow without transverse flow? Nucl Phys, 2002,A698(5):475—478
[41]Schnedermann E, Sollfrank J and Heinz U. Thermal phenomenology of hadrons from 200-A/GeV S+S collisions. Phys Rev C,1993. 48(5):2462—2475
[42]Braun-Munzinger P, Stachel J, Wessels J P, Xu N. Thermal and hadrochemical equilibration in nucleus-nucleus collisions at the SPS. Phys Lett B,1996,365:1-6
[43]Heinz U W, Kolb P F. Two RHIC puzzles: Early thermalization and the HBT problem.Published in Proceedings of the 18th Winter Workshop on Nuclear Dynamics. Edited by R. Bellwied, J. Harris, and W. Bauer. EP Systema, Debrecen, Hungary, 2002. pp. 205-216
[44]Kolb P F, Rapp R. Transverse flow and hadrochemistry in Au + Au collisions at s NN= 200 GeV. Phys Rev, 2003,C67:044903
[45]Becattini F, Gazdzicki M, Sollfrank J. On chemical equilibrium in nuclear collisions. Eur Phys J, 1998. C5(10):143-153
[46]Braun-Munzinger P, Redlich K, Stachel J. Particle Production in Heavy Ion Collisions. World Scientific Publishing, 2003
[47]Koch P. Some remarks on the statistical model of heavy ion collisions. Nucl Phys, 2003. A715(10):108-117
[48]Feng S Q,Liu F,Liu L S. Thermal equilibrium and nouniform logitudinal flow in relativistic heavy ion collision. Phys Rev C, 2000, 63:014901(1)~014901(6)
[49]Feng S Q, Yuan X B, Shi Y F. Collective flow distributions and nuclear stopping in heavy ion collisions at AGS,SPS and RHIC. Modern Phys Lett A, 2006, 21:663-673.
[50]Feng Shengqin, Xiong Wei. Thermalization component model of multiplicity distributions of charged hadrons measured at the BNL( E lNabN=2-11.6GeV), the CERN( El NabN=20-200GeV) , and the BNL( s NN=19.6-200GeV). Phys. Rev. C, 2008, 77:044906
[51]袁显宝,冯笙琴. RHIC能区的纵向流分布特性和核阻止特性,高能物理与核物理,2005,29(4):44-48
[52]袁显宝,冯笙琴. AGS、SPS和RHIC三个能区中的π介子和质子的快度分布特征的研究.中国科学,2008,G39:28-36
[53]冯笙琴,刘峰,刘连寿.相对论重离子碰撞中的热解冻和纵向非均匀膨胀集体流.高能物理与核物理,2002,26(12):1277-1284
[54]钟洋,冯笙琴.重子数守恒对净质子快度分布的影响.三峡大学学报,2009,39:110-112
[55]Zhong Yang, Feng Shengqin. Rapidity distributions of net proton from AGS to LHC energy regions.已经被Chinese Physics C接收,即将发表
[56]J. Rafelski and B. Muller. Strangeness production in the Quark - Gluon Plasma. Phys. Rev. Lett. 1982,48:1066.
[57]P. Koch, B. Muller, and J. Rafelski, Strangeness in relativistic heavy ion vollisions Phys. Rep. 1986, 142: 167.
[58]J. Bartke et al. (NA35 Collaboration), Neutral strange particle production in sulphur sulphur and proton sulphur collisions at 200-Gev/nucleon. Z. Phys. C. 1990,48:191.
[59]L. Ahle et al. (E802 Collaboration), Phys. Rev. C 60, 044904(1999).
[60]P.Chung et al. (E895 Collaboration), Phys. Rev. Lett. 91, 202301(2003).
[61]T. Anticic et al. (NA49 Collaboration), Phys. Rev. Lett. 93, 022302 (2004).
[62]C. Alt et al. (NA49 Collaboration), Phys. Rev. Lett. 94, 192301(2005).
[63]F. Becattini, J. Cleymans, A. Keranen, E. Suhonen, and K. Redlich, Phys. Rev. C 64, 024901 (2001).
[64]P. Braun-Munzinger, J. Cleymans, H. Oeschler, and K. Redlich, Nucl. Phys. A697, 902 (2002).
[65]C. Greiner and S. Leupold, J. Phys. G 27, L95 (2001).
[66]P. Braun-Munzinger, J. Stachel, and C. Wetterich, Phys. Lett. B596, 61 (2004).
[67]F. Becattini, M. Ga′zdzicki, and J. Sollfrank, Eur. Phys. J. C 5, 143 (1998).
[68]F. Becattini, M. Ga′zdzicki, A. Keranen, J. Manninen, and R. Stock, Phys. Rev. C 69, 024905 (2004).
[69]Alt C, Anticic T, Baatar B. et al. Energy dependence ofΛandΞproduction in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV measured at the CERN Super Proton Synchrotron, PHYSICAL REVIEW C 78, 034918 (2008)
[2]冯笙琴著,《高能多强子产生物理导论》,北京:北京理工大学出版社,2005: 3-7,186-192
[3]Bjorken J D. Highly relativistic nucleus-nucleus collisions: the central rapidity region. Phys Rev D,1983,27(1):140—151
[4]Lee T D. Missing symmetries, unseen quarks and the physical vacuum. Nucl. Phys, 1992, A25(1):3c-13c
[5]Schukraft J. Heavy-ion physics at the LHC. 2nd Latin American School of High-Energy Physics, San Miguel Regla, Mexico, 1-14 Jun 2003
[6]Wiedemamn U A. Opportunities for heavy-ion physics at the large hadron collider LHC, J. Phys.2007, G34:503-509
[7]Jacobs P, Wang X N. Matter in extremis: ultrarelativistic nuclear collisions at RHIC. Progress in Particle and Nuclear Physics. 2005. 54(2): 443~534
[8]Xu N. Collective Dynamics at RHIC. Proceedings of CCAST,Beijing,2002
[9]CERN Yellow Report on“Hard probes in heavy collisions at LHC”, 2003
[10]Lisa M, Pratt S, Soltz R, and Wiedemann U. Femtoscopy in relativistic heavy ion collisions .Ann Rev Nucl Part Sci,2005, 55:357-402
[11]Busza W and Goldhaber A S. Nuclear Stopping Power. Phys.Lett.1984, B139:235
[12]Bialas A and W.Czyz. Moments of the particle phase-space density at freeze-out and coincidence probabilities. Acta Phys Polon,2005,B36: 3109-3114
[13]Bearden I G, Beavis D, Besliu C, et al. Charged Meson Rapidity Distributions in Central Au+Au Collisions at s NN=200 GeV. Phys. Rev. Lett, 2005, 94: 162301(1)~162301(4)
[14]Back B B, Betts R R, Chang J et al. Baryon rapidity loss in relativistic Au+Au collisions. Phys Rev Lett, 2001,86:1970–1973
[15]Bearden I G, Beavis D, Besliu C et al. Nuclear stopping in Au+Au collisions at s NN=200 GeV. Phys Rev Lett, 2004, 93:102301(1) ~102301(5)
[16]Klay J L, Ajitanand N N, Alexander J M et al. Longitudinal flow of protons from (2–8) A GeV central Au + Au collisions. Phys Rev Lett, 2002, 88:102301(1)—102301(5)
[17]Ahle L, Akiba Y,Ashktorab1 K.,et al. Proton and deuteron production in Au + Au reactions at 11.6/A-Gev/c. Phys Rev C, 1999, 60(6):064901
[18]Barrette J, Bellweid R,Bennett S,et al. Proton and pion production in Au + Au collisions at 10.8A-GeV/c. Phys Rev C, 2000. 62(2):024901
[19]Appelshauser H, Bachler H,Bailey S J, et al. Baryon stopping and charged particle distributions in central Pb+Pb collisions at 158 GeV per nucleon. Phys Rev Lett, 1999, 82(12):2471-2475
[20]Videbeck F et al. Recent results from E866. Nucl Phys A, 1995, 590(7):249c-258c
[21]Wienold T et al. Stopping and collective effects at SPS energies. Nucl Phys A, 1996, A610(11):76c-87c
[22]Huovinen P. Hydrodynamic description of collective flow. World Scientific Singapore, 2003
[23]Kolb P F, Huovinen P, Heinz U and Heiselberg H . Elliptic flow at SPS and RHIC: From kinetic transport to hydrodynamics. Phys.Lett,2001, B500:232-240
[24]Huovinen P, Kolb P F, Heinz U W, Ruuskanen P V and Voloshin S A. Radial and elliptic flow at RHIC: Further predictions. Phys. Lett. 2001, B503: 58-64
[25]Kolb P F, Heinz U W, Huovinen P, Eskola K J and Tuominen K. Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics. Nucl.Phys, 2001, A696:197-215
[26]Bleicher M and Stocker H. Anisotropic flow in ultrarelativistic heavy ion collisions. Phys.Lett, 2002, B526:309-314
[27]Hirano T and Nara Y. Energy loss in high-energy heavy ion collisions from the Hydro + Jet model. Phys. Rev C, 2002, 66:041901
[28]Hirano T and Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freeze-out. Phys.Rev,2002, C66:054905
[29]Hirano T and Nara Y. Back-to-back correlations of high p(T) hadrons in relativistic heavy ion collisions. Phys.Rev.Lett, 2003, 91:082301
[30]Hirano T and Nara Y , Pseudorapidity dependence of parton energy loss in relativisticheavy ion collisions. Phys.Rev, 2003, C68:064902
[31]Hirano T and Nara Y , Hydrodynamic afterburner for the color glass condensate and the parton energy loss, Nucl. Phys, 2004, A743:305-328, nucl-th/0404039
[32]Cooper F, Frye G. Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multi-particle production. Phys Rev, 1974. D10(1):186～189
[33]Hirano T, Tsuda K. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freeze-out. Phys. Rev. 2002, C 66 : 054905. nucl-th/0205043
[34]Bass S.A. et al., Hadronic freezeout following a first order hadronization phase transition in ultrarelativistic heavy ion collisions Phys. Rev. 1999, C 60 : 021902. nucl-th/9902062
[35]Adler S S. et al., Identified charged particle spectra and yields in Au+Au collisions at s NN = 200-GeV. Phys. Rev. 2004, C 69: 034909. nucl-ex/0307022
[36]Adcox K. et al., Centrality dependence of pi+ / pi-, K+ / K-, p and anti-p production from s NN = 130GeV Au+Au collisions at RHIC. Phys. Rev. Lett,2002, 88:242301. nucl-ex/0112006
[37]Adler C. et al., Measurement of inclusive anti-protons from Au+Au collisions at ( s NN = 130-GeV. Phys. Rev. Lett, 2001, 87 :262302, nucl-ex/0110009.
[38]M. Calderon de la Barca Sanchez, Charged hadron spectra in Au+Au collisions at s NN= 130-GeV. Ph.D. Thesis, Yale University, 2001, nucl-ex/0111004
[39]Kolb P F, Heinz U W. Hydrodynamic description of ultra-relativistic heavy ion collisions, Invited review for 'Quark Gluon Plasma 3'. Editors: R.C. Hwa and X.N. Wang, World Scientific, Singapore, nucl-th/0305084
[40]Huovinen P, Kolb P F, Heinz W. Is there elliptic flow without transverse flow? Nucl Phys, 2002,A698(5):475—478
[41]Schnedermann E, Sollfrank J and Heinz U. Thermal phenomenology of hadrons from 200-A/GeV S+S collisions. Phys Rev C,1993. 48(5):2462—2475
[42]Braun-Munzinger P, Stachel J, Wessels J P, Xu N. Thermal and hadrochemical equilibration in nucleus-nucleus collisions at the SPS. Phys Lett B,1996,365:1-6
[43]Heinz U W, Kolb P F. Two RHIC puzzles: Early thermalization and the HBT problem.Published in Proceedings of the 18th Winter Workshop on Nuclear Dynamics. Edited by R. Bellwied, J. Harris, and W. Bauer. EP Systema, Debrecen, Hungary, 2002. pp. 205-216
[44]Kolb P F, Rapp R. Transverse flow and hadrochemistry in Au + Au collisions at s NN= 200 GeV. Phys Rev, 2003,C67:044903
[45]Becattini F, Gazdzicki M, Sollfrank J. On chemical equilibrium in nuclear collisions. Eur Phys J, 1998. C5(10):143-153
[46]Braun-Munzinger P, Redlich K, Stachel J. Particle Production in Heavy Ion Collisions. World Scientific Publishing, 2003
[47]Koch P. Some remarks on the statistical model of heavy ion collisions. Nucl Phys, 2003. A715(10):108-117
[48]Feng S Q,Liu F,Liu L S. Thermal equilibrium and nouniform logitudinal flow in relativistic heavy ion collision. Phys Rev C, 2000, 63:014901(1)~014901(6)
[49]Feng S Q, Yuan X B, Shi Y F. Collective flow distributions and nuclear stopping in heavy ion collisions at AGS,SPS and RHIC. Modern Phys Lett A, 2006, 21:663-673.
[50]Feng Shengqin, Xiong Wei. Thermalization component model of multiplicity distributions of charged hadrons measured at the BNL( E lNabN=2-11.6GeV), the CERN( El NabN=20-200GeV) , and the BNL( s NN=19.6-200GeV). Phys. Rev. C, 2008, 77:044906
[51]袁显宝,冯笙琴. RHIC能区的纵向流分布特性和核阻止特性,高能物理与核物理,2005,29(4):44-48
[52]袁显宝,冯笙琴. AGS、SPS和RHIC三个能区中的π介子和质子的快度分布特征的研究.中国科学,2008,G39:28-36
[53]冯笙琴,刘峰,刘连寿.相对论重离子碰撞中的热解冻和纵向非均匀膨胀集体流.高能物理与核物理,2002,26(12):1277-1284
[54]钟洋,冯笙琴.重子数守恒对净质子快度分布的影响.三峡大学学报,2009,39:110-112
[55]Zhong Yang, Feng Shengqin. Rapidity distributions of net proton from AGS to LHC energy regions.已经被Chinese Physics C接收,即将发表
[56]J. Rafelski and B. Muller. Strangeness production in the Quark - Gluon Plasma. Phys. Rev. Lett. 1982,48:1066.
[57]P. Koch, B. Muller, and J. Rafelski, Strangeness in relativistic heavy ion vollisions Phys. Rep. 1986, 142: 167.
[58]J. Bartke et al. (NA35 Collaboration), Neutral strange particle production in sulphur sulphur and proton sulphur collisions at 200-Gev/nucleon. Z. Phys. C. 1990,48:191.
[59]L. Ahle et al. (E802 Collaboration), Phys. Rev. C 60, 044904(1999).
[60]P.Chung et al. (E895 Collaboration), Phys. Rev. Lett. 91, 202301(2003).
[61]T. Anticic et al. (NA49 Collaboration), Phys. Rev. Lett. 93, 022302 (2004).
[62]C. Alt et al. (NA49 Collaboration), Phys. Rev. Lett. 94, 192301(2005).
[63]F. Becattini, J. Cleymans, A. Keranen, E. Suhonen, and K. Redlich, Phys. Rev. C 64, 024901 (2001).
[64]P. Braun-Munzinger, J. Cleymans, H. Oeschler, and K. Redlich, Nucl. Phys. A697, 902 (2002).
[65]C. Greiner and S. Leupold, J. Phys. G 27, L95 (2001).
[66]P. Braun-Munzinger, J. Stachel, and C. Wetterich, Phys. Lett. B596, 61 (2004).
[67]F. Becattini, M. Ga′zdzicki, and J. Sollfrank, Eur. Phys. J. C 5, 143 (1998).
[68]F. Becattini, M. Ga′zdzicki, A. Keranen, J. Manninen, and R. Stock, Phys. Rev. C 69, 024905 (2004).
[69]Alt C, Anticic T, Baatar B. et al. Energy dependence ofΛandΞproduction in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV measured at the CERN Super Proton Synchrotron, PHYSICAL REVIEW C 78, 034918 (2008)