RHIC能区椭圆流的演化分析
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摘要
高能重离子碰撞研究的目的是探索高温度高密度条件下核物质的性质,期望获得核物质的状态方程。理论和实验研究均表明,椭圆流对于核―核碰撞的演化过程较为敏感,是提取早期碰撞体系信息的重要实验观测量。本文利用两个唯象模型即相对论量子分子动力学(RQMD)模型和相对论流体动力学模型对RHIC能区Au+Au碰撞中椭圆流的产生机制及时空演化进行分析。
计算了RQMD模型中冻出粒子的平均横向速度。分析了反应平面内外横向速度的时间和空间依赖关系,并与相对论流体动力学模型给出的源的膨胀速度进行了比较。结果显示,反应中存在明显的空间―动量关联。横向速度的时空依赖表明,对于早期的冻出粒子,在横向半径小于初始表面平均半径的范围内,反应平面内的横向速度大于反应平面外的横向速度,在横向半径大于初始表面平均半径的范围内,情况则相反;对于晚期的冻出粒子,在横向半径较大时,反应平面内外的横向速度一致。HBT关联是一种特殊的空间―动量关联,可以反映碰撞体系的时空结构。利用RQMD模型计算了质子的HBT关联函数。
分别用RQMD模型和相对论流体动力学模型分析了椭圆流的时间和空间依赖关系。RQMD模型结果表明,对于冻出粒子,椭圆流随冻出时间增大而减小;相对论流体动力学模型结果表明,对于参与者区全部物质,椭圆流随时间增大而增大。研究了在不同的时间段椭圆流随横向半径的变化,RQMD模型和相对论流体动力学模型得到了类似的结果,即在早期阶段,椭圆流在初始表面平均半径附近出现峰值;在晚期阶段,椭圆流在初始表面平均半径附近达到了饱和,这一结果反映了粒子的坐标空间分布的演化。
讨论了一级相变对椭圆流演化的影响。分析表明:在碰撞体系的演化过程中,当QGP相几乎完全转化为混合相时,混合相物质处于演化的主导地位,椭圆流可看作平均能量密度的增函数,参与者区的膨胀尤其是纵向膨胀导致的能量密度降低可能是出现一级相变时,椭圆流下降的重要原因。进一步研究了不同物质相对参与者区椭圆流的贡献,在半对心碰撞中,末态的椭圆流主要产生于QGP和混合相,而边缘碰撞中椭圆流受强子气体相的影响较大。
在流体动力学模型中,当声速为定值时,椭圆流存在坐标空间离心率标度不变性。当态方程包含一级相变时,不同物质相中声速不同,分析了相互作用区扰动的传播规律,对于不同碰撞参数的系统,演化存在明显的差别。引入扰动传播的特征距离,并用碰撞系统的初始尺寸做标度,除边缘碰撞外,表现出了一致的规律。在此基础上,进一步讨论了椭圆流的空间离心率标度,对√sNN = 200GeV的Au+Au碰撞体系,流体动力学的计算表明,除了边缘碰撞外,椭圆流在演化过程中具有离心率标度不变性,而扰动的传播可以表征椭圆流的演化。
The goal of high energy heavy-ion collisions is to extract information about prop-erties of nuclear matter at high density and high temperature and to obtain the nuclearequation of state. Both the theoretical and experimental results demonstrate that the ellip-tic ?ow is sensitive to the evolution of the collision system and it is a important observableto extract the information of the early stage of the source. In this thesis, using the rela-tivistic quantum molecule dynamics(RQMD) model and relativistic hydrodynamic modelwhich are phenomenological models we study the mechanism of the generation of elliptic?ow and its space-time evolution for Au+Au collisions at RHIC energy.
The average transverse velocity of the freeze out particles in the RQMD model iscalculated, and the time and space dependence of the transverse velocity in and out ofreaction plane is analyzed. The average transverse velocity of freeze out particles is com-pared with the expansion speed of the source calculated by the hydrodynamical model,the results show that the correlation between space and momentum exists in the processof interaction. The time and space dependence of transverse velocity demonstrates that atthe early stage, if the transverse radius of freeze-out particles are smaller than the averageradius of initial surface of the source, the transverse velocity is bigger in in-plane than thatin out-of-plane; if the transverse radius of freeze-out particles are more than the averageradius of initial surface of the source, the transverse velocity is bigger in out-of-plane.At lately stage, if the transverse radius is bigger than the initial surface, the transversevelocity of particles are nearly same for in-plane and out-of-plane. HBT is one kind ofspecial correlation and can re?ect the structure of space-time. We calculate the HBT ofprotons using RQMD model.
The time and space dependence of the elliptic ?ow is analyzed by using both theRQMD model and the relativistic hydrodynamical model. The results from RQMD showthat the elliptic ?ow of particles which freeze-out decreases with time. The results fromthe hydrodynamical model shows that the elliptic ?ow of the whole source increases withtime. The transverse radius dependence of the elliptic ?ow is analyzed at different stageand the results from RQMD model and hydrodynamical model are similar. The resultsshow that the elliptic ?ow reaches the peak value at the average radius of initial surface in the early stage, the elliptic ?ow reaches the saturation at the average radius of initialsurface in the lately stage. The results are related with the evolution of distribution ofparticles in coordinate space.
The effect of first order phase transition on the evolution of the elliptic ?ow is dis-cussed. The analysis demonstrates that when the QGP phase nearly transform to themixed phase completely, the evolution of the source is mainly dominated by the mixedphase, the elliptic ?ow can be seen as the function of the energy density and increase withthe energy density. The decrease of the energy density from the expansion of the sourceespecially the longitudinal expansion maybe the main cause of that the elliptic ?ow de-crease with time. Further, we analyze the contribution of different matter phase to thetotal momentum anisotropy. The results demonstrate that the final elliptic ?ow is mainlygenerated by the QGP phase and mixed phase for semi-central collisions and by hadrongas phase for peripheral collisions.
In the hydrodynamical model, if the speed of sound is a constant the eccentricityscaling invariance of elliptic ?ow can be seen. If the EoS contains the first order transitionthe speed of sound varies with the different phase. The transmission of the perturbation inthe source is analyzed, and the difference of the evolutions are distinct for collisions withdifferent impact parameters. The characteristic distance of the transmission of the pertur-bation is introduced and scaled by the initial size of the source. The eccentricity scalinginvariance of the characteristic distance can be seen except for peripheral collisions. Onthis basis, the eccentricity scaled elliptic ?ow is also analyzed. For√sNN =200 GeVAu+Au collisions, the results from the hydrodynamical model show the eccentricity scal-ing invariance of the elliptic ?ow, and the transmission of the perturbation can characterizethe evolution of the elliptic ?ow.
计算了RQMD模型中冻出粒子的平均横向速度。分析了反应平面内外横向速度的时间和空间依赖关系,并与相对论流体动力学模型给出的源的膨胀速度进行了比较。结果显示,反应中存在明显的空间―动量关联。横向速度的时空依赖表明,对于早期的冻出粒子,在横向半径小于初始表面平均半径的范围内,反应平面内的横向速度大于反应平面外的横向速度,在横向半径大于初始表面平均半径的范围内,情况则相反;对于晚期的冻出粒子,在横向半径较大时,反应平面内外的横向速度一致。HBT关联是一种特殊的空间―动量关联,可以反映碰撞体系的时空结构。利用RQMD模型计算了质子的HBT关联函数。
分别用RQMD模型和相对论流体动力学模型分析了椭圆流的时间和空间依赖关系。RQMD模型结果表明,对于冻出粒子,椭圆流随冻出时间增大而减小;相对论流体动力学模型结果表明,对于参与者区全部物质,椭圆流随时间增大而增大。研究了在不同的时间段椭圆流随横向半径的变化,RQMD模型和相对论流体动力学模型得到了类似的结果,即在早期阶段,椭圆流在初始表面平均半径附近出现峰值;在晚期阶段,椭圆流在初始表面平均半径附近达到了饱和,这一结果反映了粒子的坐标空间分布的演化。
讨论了一级相变对椭圆流演化的影响。分析表明:在碰撞体系的演化过程中,当QGP相几乎完全转化为混合相时,混合相物质处于演化的主导地位,椭圆流可看作平均能量密度的增函数,参与者区的膨胀尤其是纵向膨胀导致的能量密度降低可能是出现一级相变时,椭圆流下降的重要原因。进一步研究了不同物质相对参与者区椭圆流的贡献,在半对心碰撞中,末态的椭圆流主要产生于QGP和混合相,而边缘碰撞中椭圆流受强子气体相的影响较大。
在流体动力学模型中,当声速为定值时,椭圆流存在坐标空间离心率标度不变性。当态方程包含一级相变时,不同物质相中声速不同,分析了相互作用区扰动的传播规律,对于不同碰撞参数的系统,演化存在明显的差别。引入扰动传播的特征距离,并用碰撞系统的初始尺寸做标度,除边缘碰撞外,表现出了一致的规律。在此基础上,进一步讨论了椭圆流的空间离心率标度,对√sNN = 200GeV的Au+Au碰撞体系,流体动力学的计算表明,除了边缘碰撞外,椭圆流在演化过程中具有离心率标度不变性,而扰动的传播可以表征椭圆流的演化。
The goal of high energy heavy-ion collisions is to extract information about prop-erties of nuclear matter at high density and high temperature and to obtain the nuclearequation of state. Both the theoretical and experimental results demonstrate that the ellip-tic ?ow is sensitive to the evolution of the collision system and it is a important observableto extract the information of the early stage of the source. In this thesis, using the rela-tivistic quantum molecule dynamics(RQMD) model and relativistic hydrodynamic modelwhich are phenomenological models we study the mechanism of the generation of elliptic?ow and its space-time evolution for Au+Au collisions at RHIC energy.
The average transverse velocity of the freeze out particles in the RQMD model iscalculated, and the time and space dependence of the transverse velocity in and out ofreaction plane is analyzed. The average transverse velocity of freeze out particles is com-pared with the expansion speed of the source calculated by the hydrodynamical model,the results show that the correlation between space and momentum exists in the processof interaction. The time and space dependence of transverse velocity demonstrates that atthe early stage, if the transverse radius of freeze-out particles are smaller than the averageradius of initial surface of the source, the transverse velocity is bigger in in-plane than thatin out-of-plane; if the transverse radius of freeze-out particles are more than the averageradius of initial surface of the source, the transverse velocity is bigger in out-of-plane.At lately stage, if the transverse radius is bigger than the initial surface, the transversevelocity of particles are nearly same for in-plane and out-of-plane. HBT is one kind ofspecial correlation and can re?ect the structure of space-time. We calculate the HBT ofprotons using RQMD model.
The time and space dependence of the elliptic ?ow is analyzed by using both theRQMD model and the relativistic hydrodynamical model. The results from RQMD showthat the elliptic ?ow of particles which freeze-out decreases with time. The results fromthe hydrodynamical model shows that the elliptic ?ow of the whole source increases withtime. The transverse radius dependence of the elliptic ?ow is analyzed at different stageand the results from RQMD model and hydrodynamical model are similar. The resultsshow that the elliptic ?ow reaches the peak value at the average radius of initial surface in the early stage, the elliptic ?ow reaches the saturation at the average radius of initialsurface in the lately stage. The results are related with the evolution of distribution ofparticles in coordinate space.
The effect of first order phase transition on the evolution of the elliptic ?ow is dis-cussed. The analysis demonstrates that when the QGP phase nearly transform to themixed phase completely, the evolution of the source is mainly dominated by the mixedphase, the elliptic ?ow can be seen as the function of the energy density and increase withthe energy density. The decrease of the energy density from the expansion of the sourceespecially the longitudinal expansion maybe the main cause of that the elliptic ?ow de-crease with time. Further, we analyze the contribution of different matter phase to thetotal momentum anisotropy. The results demonstrate that the final elliptic ?ow is mainlygenerated by the QGP phase and mixed phase for semi-central collisions and by hadrongas phase for peripheral collisions.
In the hydrodynamical model, if the speed of sound is a constant the eccentricityscaling invariance of elliptic ?ow can be seen. If the EoS contains the first order transitionthe speed of sound varies with the different phase. The transmission of the perturbation inthe source is analyzed, and the difference of the evolutions are distinct for collisions withdifferent impact parameters. The characteristic distance of the transmission of the pertur-bation is introduced and scaled by the initial size of the source. The eccentricity scalinginvariance of the characteristic distance can be seen except for peripheral collisions. Onthis basis, the eccentricity scaled elliptic ?ow is also analyzed. For√sNN =200 GeVAu+Au collisions, the results from the hydrodynamical model show the eccentricity scal-ing invariance of the elliptic ?ow, and the transmission of the perturbation can characterizethe evolution of the elliptic ?ow.
引文
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