GeV和MeV能区AA碰撞中末态产物的各向异性分布
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摘要
本文应用多源热模型模拟计算了质心系能量为22.4A、62.4A、200A GeV的Cu-Cu碰撞中,在0-6%、6-15%中心度范围内的事例中,末态带电粒子的赝快度分布,以及入射能量为25MeV/N的Kr-Sn碰撞中,末态核碎片的方位角分布,及椭圆流对横动量的依赖关系。结果表明,多源热模型仅利用几个简单的参数,就较好地重现了中高能重离子碰撞中的纵向赝快度分布和横向方位角分布、及椭圆流对横动量依赖的实验数据,或其他模型的计算结果。本文得到的主要结果可概括为以下两方面：
(1)从RHIC能区Cu-Cu碰撞中末态粒子的赝快度分布可以看出,随着碰撞能量的提高,赝快度分布宽度变宽,密度增高,且.在两中心度比较下其变化趋势一致,但中心度为6-15%的事例中的粒子产额比中心度为0-6%的事例中的粒子产额稍低。另外从模拟曲线看,最后的赝快度分布是由对称分布的两组四个近似高斯曲线叠加而成的。很明显单个的高斯分布不能描写赝快度的这种双峰分布,这也就否定了利用单一静止热源模型继续分析碰撞系统的可能性。无论采用那种模型,都认为赝快度分布宽度变宽是系统纵向扩散产生纵向流的表现。再联系到粒子产额,说明次级碰撞对赝快度分布宽度有绝对影响。而赝快度分布宽度随能量变宽,说明随着能量提高,核阻止度下降,系统越来越透明。
(2)从MeV能区Kr-Sn碰撞中产生的核碎片的方位角分布可以看出,由于空间各向异性,核碎片的方位角分布不再各向同性,而是出现与方位角关联的振荡,表现为一条上下起伏的曲线。且质量越大的核碎片,方位角分布的振荡越大,说明质量越大的核碎片各向异性分布越明显。从MeV能区Kr-Sn碰撞中产生的核碎片的椭圆流对横动量的依赖关系可以看出,在横动量空间,核碎片的分布不再为各向同性的圆,而是椭圆,且随着核碎片横动量的增加,各向异性程度增强,椭圆流变大。核碎片质量越大椭圆流也越大,说明椭圆流与系统碰撞形成的压力强度相关,质量对椭圆流影响明显。
The pseudorapidity distributions of final-state charged particles produced in Cu-Cu collisions with centralities0-6%and6-15%at22.4A,62.4A, and200A GeV are calculated by using the multi-source thermal model. Meanwhile, the azimuthal distributions and the dependences of elliptic flows on transverse momentum for nuclear fragments produced in Kr-Sn collisions at25Me V/N are calculated by the model. It is shown that the model with a few simple parameters is successful in the descriptions of longitudinal pseudorapidity distributions, transverse azimuthal distributions, and the dependences of elliptic flows on transverse momentum. Our results calculated by the model are in agreement with the experimental data or other modeling results. The main results obtained in the present work can be summarized as two parts given in the following.
(1) From the pseudorapidity distributions of final-state particles in Cu-Cu collisions at the RHIC energies, one can see that the distribution width and density increase with increasing the impact energy. These situations are the same for the two centralities. However, the density for centrality6-16%is slightly lower than that for centrality0-6%. The final-state pseudorapidity distribution is described by a sum of four Gaussian-like functions. A single Gaussian function does not describe the two-peak structure of pseudorapidity distribution. As representations of longitudinal flow effect and secondary collisions, the width of pseudorapidity distribution becomes wider.
(2) From the azimuthal distributions of nuclear fragments produced in25MeV/N Kr-Sn collisions, one can see that the emission of fragments is anisotropic. There are fluctuations in the azimuthal range. The heavy fragments have large fluctuation and anisotropy. From the dependences of elliptic flows on transverse momentum, one can see that the fragments distribute in a ellipse in the space of transverse momentum. A large transverse momentum corresponds to a large elliptic flow. On the other hand, the heavy fragments have large elliptic flow.
(1)从RHIC能区Cu-Cu碰撞中末态粒子的赝快度分布可以看出,随着碰撞能量的提高,赝快度分布宽度变宽,密度增高,且.在两中心度比较下其变化趋势一致,但中心度为6-15%的事例中的粒子产额比中心度为0-6%的事例中的粒子产额稍低。另外从模拟曲线看,最后的赝快度分布是由对称分布的两组四个近似高斯曲线叠加而成的。很明显单个的高斯分布不能描写赝快度的这种双峰分布,这也就否定了利用单一静止热源模型继续分析碰撞系统的可能性。无论采用那种模型,都认为赝快度分布宽度变宽是系统纵向扩散产生纵向流的表现。再联系到粒子产额,说明次级碰撞对赝快度分布宽度有绝对影响。而赝快度分布宽度随能量变宽,说明随着能量提高,核阻止度下降,系统越来越透明。
(2)从MeV能区Kr-Sn碰撞中产生的核碎片的方位角分布可以看出,由于空间各向异性,核碎片的方位角分布不再各向同性,而是出现与方位角关联的振荡,表现为一条上下起伏的曲线。且质量越大的核碎片,方位角分布的振荡越大,说明质量越大的核碎片各向异性分布越明显。从MeV能区Kr-Sn碰撞中产生的核碎片的椭圆流对横动量的依赖关系可以看出,在横动量空间,核碎片的分布不再为各向同性的圆,而是椭圆,且随着核碎片横动量的增加,各向异性程度增强,椭圆流变大。核碎片质量越大椭圆流也越大,说明椭圆流与系统碰撞形成的压力强度相关,质量对椭圆流影响明显。
The pseudorapidity distributions of final-state charged particles produced in Cu-Cu collisions with centralities0-6%and6-15%at22.4A,62.4A, and200A GeV are calculated by using the multi-source thermal model. Meanwhile, the azimuthal distributions and the dependences of elliptic flows on transverse momentum for nuclear fragments produced in Kr-Sn collisions at25Me V/N are calculated by the model. It is shown that the model with a few simple parameters is successful in the descriptions of longitudinal pseudorapidity distributions, transverse azimuthal distributions, and the dependences of elliptic flows on transverse momentum. Our results calculated by the model are in agreement with the experimental data or other modeling results. The main results obtained in the present work can be summarized as two parts given in the following.
(1) From the pseudorapidity distributions of final-state particles in Cu-Cu collisions at the RHIC energies, one can see that the distribution width and density increase with increasing the impact energy. These situations are the same for the two centralities. However, the density for centrality6-16%is slightly lower than that for centrality0-6%. The final-state pseudorapidity distribution is described by a sum of four Gaussian-like functions. A single Gaussian function does not describe the two-peak structure of pseudorapidity distribution. As representations of longitudinal flow effect and secondary collisions, the width of pseudorapidity distribution becomes wider.
(2) From the azimuthal distributions of nuclear fragments produced in25MeV/N Kr-Sn collisions, one can see that the emission of fragments is anisotropic. There are fluctuations in the azimuthal range. The heavy fragments have large fluctuation and anisotropy. From the dependences of elliptic flows on transverse momentum, one can see that the fragments distribute in a ellipse in the space of transverse momentum. A large transverse momentum corresponds to a large elliptic flow. On the other hand, the heavy fragments have large elliptic flow.
引文
[1]Hirano T., Kolk N., Bilandzic A. Hydrodynamics and flow. arXiv:0808.2684vl [nucl-th];及其中所引文献.
[2]宁平治.原子核物理基础—核子与核.北京：高等教育出版社,2003：10-12.
[3]李庆峰,李祝霞,Bleicher M.,等.大入射能量范围内重离子输运过程的动力学性质研究.原子核物理评论.2011,2(28)：142-155.
[4]Goldhaber G, Pais A. Influence of Bose-Einstein statistics on the antiproton-proton annihilation process. Phys. Rev. 1960, 120(2): 300-312.
[5]Lisa M. A., Ajitanand N. N., Alexander J. M. et al. Azimuthal dependence of pion interferometry at the AGS. Phys. Lett. B, 2000, 496(1-2):1-8..
[6]Odyniec G. J.. Strangeness production in relativistic nuclear collisions. Nucl. Phys.A, 1998,638:135c-146c.
[7]Afanasiev S. V., et al. (NA49 Collaboration). Energy dependence of pion and kaon production in central Pb+Pb collisions. Phys. Rev. C, 2002,66(5):054902.
[8]蔡励,周代梅.超高能诱发核反应的国际合作实验研究进展.高能物理与核物理,2002,26(9)：971-990.
[9]Wurm P. for NA45/CERES. New results from NA45/CERES. Proc. Quark Matter'95, Nucl. Phys. A,1995,590(1-2):103c-116c.
[10]Agakichiev G., et al. (CERES Collaboration). Enhanced production of Low-Mass electron pairs in 200 GeV/Nucleon S-Au collisions at the CERN Super Proton Synchrotron. Phys. Rev. Lett.,1995,75(7):1272-1275.
[11]Masera M. for HELIOS/3 Collaboration. Dimuon production below mass 3.1 GeV/c/Z in p-W and S-W interactions at 200A GeV/c Proc. Quark Matter t95. Nucl. Phys. A,1995,590:93c-102c.
[12]Falco D. for NA35 Collaboration. Antibaryon production in 32S+nucleus collisions at 200 GeV/nucleon. Proc. Quark Matter'97, Nucl. Phys. A,1998,638:487c-490c.
[13]Abreu M. C, et al. (NA50 Collaboration). Evidence for deconfinement of quarks and gluons from the J/W suppression pattern measured in Pb-Pb collisions at the CERN-SPS. Phys. Lett. B, 2000, 477(1-2):28-36.
[14]http://www.bnl.gov/rhic/
[15]Adcox K., et al. (PHENIX Collaboration). Suppression of hadrons with large transverse momentum in central Au+Au collisions at 130 GeV. Phys. Rev. Lett., 2002, 88(2):022301.
[16]Adler S. S., et al. (PHENIX Collaboration). Absence of suppression in particle production at large transverse momentum in ?=200GeV d+Au collisions. Phys. Rev. Lett.,2003,91(7):072303; Adams J., et al. (STAR Collaboration). Evidence from d+Au measurements in Au+Au collisions at RHIC. Phys. Rev. Lett.,2003,91(7): 072304.
[17]Cronin J. W., Frisch H. J., Shochet M. J. Production of hadron at large transverse momentum at 200,300 and 400 GeV. Phys. Rev. D, 1975,11(11):2105-3123.
[18]Adler S. S., et al. (PHENIX Collaboration). Elliptic flow of identified hadrons in Au+Au collisions at ?=200 GeV. Phys. Rev. Lett., 2003, 91(18):182301.
[19]周铀.相对论重离子碰撞中带电粒子比率起伏与净重子数分布的高阶矩起伏研究.华中师范大学硕士论文,2010.
[20]张东海.相对论性重离子诱发乳胶核反应研究.中国原子能科学院博士论文,1999.
[21]刘福虎.中能原子核碎裂中的方位角关联-高能物理与核物理.1995,19(3)：217-222.
[22]李娜.相对论重离子碰撞中方位角的各向异性和电荷平衡函数的纵向性质,华中师范大学博士论文,2010.
[23]李俊生.重离子反应中的分形行为和椭圆流效应,山西大学博士论文,2009.
[24]Gyulassy M, Vitev I., Wang X. N., Zhang B. W. Jet quenching and radiative energy loss in dense nuclear matter. arXiv:nucl-th/0302077.
[25]Kovner A., Wiedemann U. A. Gluon radiation and parton energy loss. arXiv:hep-ph/0304151.
[26]http://www.bnl.goe/bnlweb/pubaf/pr/pR-display.asp?prad=05-38
[27]http://tupian.hudong.com/a2-23-15-jpg.html
[28]Teaney D., Shuryak E. V., An unusual space-time evolution for heavy ion collisions at high energies due to the QCD phase transition. Phys. Rev. Lett.,1999,83:4951-4954. arXiv:nucl-th/9904006.
[29]Voloshin S. A., Poskanzer A. M., Snellings R. Collective phenomena in non-central nuclear collisions. arXiv:0809.2949v2 [nucl-ex].
[30]Dobler H., Sollfrank J., Heinz U. Kinetic freeze-out and radial flow in 11.6 A GeV Au+Au collisions. Phys. Lett. B, 1999,457:353-358. arXiv:nucl-th/9904018.
[31]Kolb P. F., Sollfrank J., Heinz U. Anisotropic flow from AGS to LHC energies Phys.
Lett. B,1999,459:667-673. arXiv:nucl-th/9906003.
[32]Netrakanti P. K., Mohanty B. The width of the rapidity distribution in heavy ion collisions. Phys. Rev. C, 2005,71:047901. arXiv:nucl-ex/0504004.
[33]Back B. B., Betts R. R., Chang J., Chang W. C. Baryon rapidity loss in relativistic Au+ Au collisions. Phys. Rev. Lett.,2001,86(10):1970-1973.
[34]Voloshin S., Zhang Y. Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions. Z. Phys. C, 1996,70:665-672. arXiv: hep-ph/9407282.
[35]Ollitrault J. Y. Flow systematics from SIS to SPS energies. Nucl. Phys. A,1998,638: 195-206. arXiv:nucl-ex/9802005.
[36]Snellings R. J. M., Sorge H., Voloshin S. A. et al. Rapidity dependence of directed flow in high energy heavy ion collisions. Phys. Rev. Lett.,2000, 84:2803-2805. arXiv:nucl-ex/9908001.
[37]Brachmann J., Soff S., Dumitru A., Stocker H. et al. Antiflow of nucleons at the softest point of the EoS. Phys. Rev. C, 2000, 61:024909. arXiv:nucl-th/9908010.
[38]Csernai L. P., Roehrich D. Third flow component as QGP signal. Phys. Lett. B,1999, 458:454. arXiv:nucl-th/9908034.
[39]Magas V. K., Csernai L. P., Strottman D. D. The initial state of ultra-relativistic heavy ion collision. Phys. Rev. C, 2001,64:014901. arXiv:hep-ph/0010307.
[40]Sorge H.. Elliptical flow a signature for early pressure in ultrarelativistic nucleus-nucleuscollisions. Phys. Rev. Lett.,1997,78: 2309-2312.arXiv:nucl-th/9610026.
[41]Rischke D. H., Puersuen Y, Maruhn J. A., The phase transition to the Quark-Gluon Plasma and its effect on hydrodynamic flow. arXiv:nucl-th/9505014.
[42]Heinz U. W., Kolb P. F. Early thermalization at RHIC. Nucl. Phys. A,2002,702: 269-280. arXiv:hep-ph/0111075.
[43]Huovinen P. Hydrodynamical description of collective flow. arXiv:nucl-th/0305064.
[44]Ollitrault J. Y, in the Proceedings of the Second International Conference on Physics
and Astrophysics of Quark-Gluon Plasma (ICPA-QGP'93), Calcutta India, Jan.19-23,
1993. (World Scientific,1994):376.
[45]Denes M., Sergei A., Voloshin S. A. Elliptic flow at large transverse momenta from quark coalescence. Phys. Rev. Lett.,2003,91:092301. arXiv:nucl-th/0302014.
[46]Voloshin S. A. Anisotropic flow. Nucl. Phys. A,2003,715:379-388. arXiv:nucl-ex/0210014.
[47]Liu F. H. Dependence of charged particle pseudorapidity distributions on centrality and energy in p(d) A collisions at high energies. Phys. Rev. C, 2008,78(1):014902.
[48]Alver B., Back B., Baker M. et al. System size, energy, and centrality dependence of pseudorapidity distributions charged particles in relativistic heavy-ion collisions. Phys. Rev. Lett.,2009,102:142301.
[49]Liu F. H., Li J. S., Duan M. Y. Light fragment emission in86Kr-124Sn collisions at 25 Mev/nucleon. Phys. Rev. C, 2007,75:054613.
[50]Yan T. Z., Ma Y. G.., Cai X. Z., et al. Scaling of anisotropic flow and momentum-space densities for light particles in intermediate energy heavy ion collisions. Phys. Lett. B, 2006,638:50.
[2]宁平治.原子核物理基础—核子与核.北京：高等教育出版社,2003：10-12.
[3]李庆峰,李祝霞,Bleicher M.,等.大入射能量范围内重离子输运过程的动力学性质研究.原子核物理评论.2011,2(28)：142-155.
[4]Goldhaber G, Pais A. Influence of Bose-Einstein statistics on the antiproton-proton annihilation process. Phys. Rev. 1960, 120(2): 300-312.
[5]Lisa M. A., Ajitanand N. N., Alexander J. M. et al. Azimuthal dependence of pion interferometry at the AGS. Phys. Lett. B, 2000, 496(1-2):1-8..
[6]Odyniec G. J.. Strangeness production in relativistic nuclear collisions. Nucl. Phys.A, 1998,638:135c-146c.
[7]Afanasiev S. V., et al. (NA49 Collaboration). Energy dependence of pion and kaon production in central Pb+Pb collisions. Phys. Rev. C, 2002,66(5):054902.
[8]蔡励,周代梅.超高能诱发核反应的国际合作实验研究进展.高能物理与核物理,2002,26(9)：971-990.
[9]Wurm P. for NA45/CERES. New results from NA45/CERES. Proc. Quark Matter'95, Nucl. Phys. A,1995,590(1-2):103c-116c.
[10]Agakichiev G., et al. (CERES Collaboration). Enhanced production of Low-Mass electron pairs in 200 GeV/Nucleon S-Au collisions at the CERN Super Proton Synchrotron. Phys. Rev. Lett.,1995,75(7):1272-1275.
[11]Masera M. for HELIOS/3 Collaboration. Dimuon production below mass 3.1 GeV/c/Z in p-W and S-W interactions at 200A GeV/c Proc. Quark Matter t95. Nucl. Phys. A,1995,590:93c-102c.
[12]Falco D. for NA35 Collaboration. Antibaryon production in 32S+nucleus collisions at 200 GeV/nucleon. Proc. Quark Matter'97, Nucl. Phys. A,1998,638:487c-490c.
[13]Abreu M. C, et al. (NA50 Collaboration). Evidence for deconfinement of quarks and gluons from the J/W suppression pattern measured in Pb-Pb collisions at the CERN-SPS. Phys. Lett. B, 2000, 477(1-2):28-36.
[14]http://www.bnl.gov/rhic/
[15]Adcox K., et al. (PHENIX Collaboration). Suppression of hadrons with large transverse momentum in central Au+Au collisions at 130 GeV. Phys. Rev. Lett., 2002, 88(2):022301.
[16]Adler S. S., et al. (PHENIX Collaboration). Absence of suppression in particle production at large transverse momentum in ?=200GeV d+Au collisions. Phys. Rev. Lett.,2003,91(7):072303; Adams J., et al. (STAR Collaboration). Evidence from d+Au measurements in Au+Au collisions at RHIC. Phys. Rev. Lett.,2003,91(7): 072304.
[17]Cronin J. W., Frisch H. J., Shochet M. J. Production of hadron at large transverse momentum at 200,300 and 400 GeV. Phys. Rev. D, 1975,11(11):2105-3123.
[18]Adler S. S., et al. (PHENIX Collaboration). Elliptic flow of identified hadrons in Au+Au collisions at ?=200 GeV. Phys. Rev. Lett., 2003, 91(18):182301.
[19]周铀.相对论重离子碰撞中带电粒子比率起伏与净重子数分布的高阶矩起伏研究.华中师范大学硕士论文,2010.
[20]张东海.相对论性重离子诱发乳胶核反应研究.中国原子能科学院博士论文,1999.
[21]刘福虎.中能原子核碎裂中的方位角关联-高能物理与核物理.1995,19(3)：217-222.
[22]李娜.相对论重离子碰撞中方位角的各向异性和电荷平衡函数的纵向性质,华中师范大学博士论文,2010.
[23]李俊生.重离子反应中的分形行为和椭圆流效应,山西大学博士论文,2009.
[24]Gyulassy M, Vitev I., Wang X. N., Zhang B. W. Jet quenching and radiative energy loss in dense nuclear matter. arXiv:nucl-th/0302077.
[25]Kovner A., Wiedemann U. A. Gluon radiation and parton energy loss. arXiv:hep-ph/0304151.
[26]http://www.bnl.goe/bnlweb/pubaf/pr/pR-display.asp?prad=05-38
[27]http://tupian.hudong.com/a2-23-15-jpg.html
[28]Teaney D., Shuryak E. V., An unusual space-time evolution for heavy ion collisions at high energies due to the QCD phase transition. Phys. Rev. Lett.,1999,83:4951-4954. arXiv:nucl-th/9904006.
[29]Voloshin S. A., Poskanzer A. M., Snellings R. Collective phenomena in non-central nuclear collisions. arXiv:0809.2949v2 [nucl-ex].
[30]Dobler H., Sollfrank J., Heinz U. Kinetic freeze-out and radial flow in 11.6 A GeV Au+Au collisions. Phys. Lett. B, 1999,457:353-358. arXiv:nucl-th/9904018.
[31]Kolb P. F., Sollfrank J., Heinz U. Anisotropic flow from AGS to LHC energies Phys.
Lett. B,1999,459:667-673. arXiv:nucl-th/9906003.
[32]Netrakanti P. K., Mohanty B. The width of the rapidity distribution in heavy ion collisions. Phys. Rev. C, 2005,71:047901. arXiv:nucl-ex/0504004.
[33]Back B. B., Betts R. R., Chang J., Chang W. C. Baryon rapidity loss in relativistic Au+ Au collisions. Phys. Rev. Lett.,2001,86(10):1970-1973.
[34]Voloshin S., Zhang Y. Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions. Z. Phys. C, 1996,70:665-672. arXiv: hep-ph/9407282.
[35]Ollitrault J. Y. Flow systematics from SIS to SPS energies. Nucl. Phys. A,1998,638: 195-206. arXiv:nucl-ex/9802005.
[36]Snellings R. J. M., Sorge H., Voloshin S. A. et al. Rapidity dependence of directed flow in high energy heavy ion collisions. Phys. Rev. Lett.,2000, 84:2803-2805. arXiv:nucl-ex/9908001.
[37]Brachmann J., Soff S., Dumitru A., Stocker H. et al. Antiflow of nucleons at the softest point of the EoS. Phys. Rev. C, 2000, 61:024909. arXiv:nucl-th/9908010.
[38]Csernai L. P., Roehrich D. Third flow component as QGP signal. Phys. Lett. B,1999, 458:454. arXiv:nucl-th/9908034.
[39]Magas V. K., Csernai L. P., Strottman D. D. The initial state of ultra-relativistic heavy ion collision. Phys. Rev. C, 2001,64:014901. arXiv:hep-ph/0010307.
[40]Sorge H.. Elliptical flow a signature for early pressure in ultrarelativistic nucleus-nucleuscollisions. Phys. Rev. Lett.,1997,78: 2309-2312.arXiv:nucl-th/9610026.
[41]Rischke D. H., Puersuen Y, Maruhn J. A., The phase transition to the Quark-Gluon Plasma and its effect on hydrodynamic flow. arXiv:nucl-th/9505014.
[42]Heinz U. W., Kolb P. F. Early thermalization at RHIC. Nucl. Phys. A,2002,702: 269-280. arXiv:hep-ph/0111075.
[43]Huovinen P. Hydrodynamical description of collective flow. arXiv:nucl-th/0305064.
[44]Ollitrault J. Y, in the Proceedings of the Second International Conference on Physics
and Astrophysics of Quark-Gluon Plasma (ICPA-QGP'93), Calcutta India, Jan.19-23,
1993. (World Scientific,1994):376.
[45]Denes M., Sergei A., Voloshin S. A. Elliptic flow at large transverse momenta from quark coalescence. Phys. Rev. Lett.,2003,91:092301. arXiv:nucl-th/0302014.
[46]Voloshin S. A. Anisotropic flow. Nucl. Phys. A,2003,715:379-388. arXiv:nucl-ex/0210014.
[47]Liu F. H. Dependence of charged particle pseudorapidity distributions on centrality and energy in p(d) A collisions at high energies. Phys. Rev. C, 2008,78(1):014902.
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