Intermediate/high-energy heavy-ion collisions and nuclear matter equation of state

ZHANG Yapeng; SUN Zhiyu; YONG Gaochan; FENG Zhaoqing

doi:10.7498/aps.74.20241650

Abstract

The equation of state (EoS) of nuclear matter is a description of the macroscopic properties of nuclear matter under different thermodynamic conditions or external fields, which is critical for understanding the theory of the strong interaction—quantum chromodynamics (QCD), the nature of nuclei, the dynamics of heavy-ion collisions (HICs), the internal structure of compact stars, the merger of binary neutron stars, and other physical phenomena. Heavy-ion collisions (HICs) are the only method in laboratories to create nuclear matter with extreme conditions such as high temperatures and high densities. HICs at different energy levels offer the possibility to quantitatively study the properties of nuclear matter under diverse thermodynamic conditions. This paper mainly presents the current research status of the EoS of nuclear matter and introduces the fundamental observables in HICs that are sensitive to the EoS, as well as the typical experiments and results used to explore the EoS. The progress in studying the EoS containing strangeness is also described and its possible research directions in the future are also discussed. The status and progress of worldwide heavy-ion accelerators and experimental spectrometers in the high-baryon density region are introduced, including China’s large-scale scientific facilities, i.e HIRFL-CSR and HIAF, as well as the CEE experiment. Additionally, the opportunities and challenges for experimental research on the EoS of nuclear matter in China are discussed.

Keywords:

Authors and contacts

1.
State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2.
School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641, China

Corresponding author: SUN Zhiyu, sunzhy@impcas.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12475133, 11927901, 12311540139), the Youth Team Program in Basic Research Fields Stably Supported by Chinese Academy of Sciences (Grant No. YSBR-088), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB34030000), and the Western Light Project of Chinese Academy of Sciences.

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图 1 用温度、重子密度和同位旋不对称度表示的核物质相图. 图片更新自文献[8]

Figure 1. Nuclear matter phase diagram represented by temperature, baryon density and isospin asymmetry. Figure taken from Ref. [8]

DownLoad: Full-Size Img PowerPoint

图 2 对称核物质和中子核物质状态方程随密度的变化, 图片更新自文献[29]

Figure 2. EoS of isospin symmetric nuclear matter and neutron matter as a function of the density, figure taken and updated from Ref. [29].

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图 3 地面重离子碰撞实验和天文观测提取到$ E_\text{sym}(\rho_0) $(a)和$ L_\text{sym}(\rho_0) $(b)的结果. 图(a)和图(b)均取自文献[24]

Figure 3. $ E_\text{sym}(\rho_0) $ (a) and $ L_\text{sym}(\rho_0) $ (b) extracted from terrestrial heavy-ion experiments and astrophysical observations respectively. Panel (a) and panel (b) both are taken from Ref. [24].

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图 4 重离子碰撞中的碰撞参数和反应平面示意图

Figure 4. Sketch of impact parameter and reaction plane in Heavy-ion collisions.

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图 5 UrQMD模型在仅考虑强子相情况下, 模拟0.2—12.8 GeV/u的对心Au+Au碰撞中的温度和密度关联图, 实线和虚线分别表示硬和软的状态方程. 图片取自文献[34]

Figure 5. Diagram of temperature and maximum density in central Au+Au collisions at 0.2–12.8 GeV/u simulated by the UrQMD model with hadron phase only. Figure taken from Ref. [34].

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图 6 直接流$ v_1 $和快度在$ y_{{\mathrm{cm}}} = 0 $的斜率与碰撞能量的关联图. 图片取自文献[36]

Figure 6. Slope of $ v_1 $ as a function of rapidity at $ y_{{\mathrm{cm}}} = 0 $ of proton versus collision energies. Figure taken from Ref. [36].

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图 7 质子椭圆流与碰撞能量的依赖关系. 图片取自文献[37]

Figure 7. Elliptic flow of proton as a function of collision energies, figure taken from Ref. [37].

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图 8 STAR实验测量的组分夸克数约化强子集体流与约化横能量的依赖关系. 图片取自文献[46]

Figure 8. Constitute quark number scaled elliptic flow of hadrons as a function of quark number scaled transverse energy measured by the STAR experiment. Figure taken from Ref. [46].

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图 9 对称核物质压强随密度变化的实验限制. 图片取自文献[34]

Figure 9. Pressure of the symmetric nuclear matter as a function of density constrained by experimental measurements. Figure taken from Ref. [34]

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图 10 KaoS实验测量$ {\mathrm{K}}^+ $介子在Au+Au和Cu+Cu碰撞中产额比随碰撞能量的变化, 来自输运模型IQMD和RQMD的硬EoS和软EoS分别用短线和点线表示. 图片取自文献[50]

Figure 10. Yield ratio of $ {\mathrm{K}}^+ $ in Au+Au and Cu+Cu collisions as a function of collision energy measured by the KaoS experiment. The hard and soft EoS from the transport models IQMD and RQMD are represented by dashed and dotted lines, respectively. Figure taken from Ref. [50].

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图 11 FOPI实验测量0.4, 1.0和1.5 GeV/u的Au+Au碰撞中质子和氘核的椭圆流随快度的变化, 基于IQMD模型硬EoS和软EoS理论计算结果分别用虚线和实线表示. 图片取自文献[56]

Figure 11. Elliptic flow of proton and deuteron as a function of rapidity in Au+Au collisions at 0.4, 1.0, and 1.5 GeV/u mesured by the FOPI experiment, red dashed line and black line represent the IQMD predictions with hard EoS and soft EoS respectively. Figure taken from Ref. [56].

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图 12 对称能$ E_{\text{sym}} $与密度的依赖关系, 其中不同的点来自不同的实验. 图片取自文献[34]

Figure 12. The symmetric energy $ E_{\text{sym}} $ as a function of nuclear matter density, symbols represent results obtained from different experiments. Figure taken from Ref. [34]

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图 13 (a) 30 MeV/u的Ar+Au反应中, 轻带电粒子的约化中子丰度随实验室角度的变化关系, 曲线为理论模型计算结果; (b)轻核约化中子丰度小角度区的下降斜率(红色区域)与理论计算(空心圆圈)的比较. 图片取自文献[58]

Figure 13. (a) In 30 meV/u Ar+Au reactions, $ Y_{{\mathrm{n, ex}}}/Y_{{\mathrm{p, CL}}} $ as a function of polar angle, curves are theoretical calculations; (b) comparison the slope of $ Y_{{\mathrm{n, ex}}}/Y_{{\mathrm{p, CL}}} $ in $ \theta_{{\mathrm{lab}}}<100^{\circ} $ from experiment (red band) and theoretical predictions (open circles). Figure taken from Ref. [58]

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图 14 PREX实验装置示意图. 图片取自文献[60]

Figure 14. Schematic draw of PREX-II experiment. Figure taken from Ref. [60]

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图 15 不同的实验和理论给出的对称能参数$ L_\text{sym}-J_\text{sym} $的限制, 黑色空心圈为PREX-II测量结果, 红色实线和虚线表示其他实验中提取的$ L_\text{sym} = (58.9\pm16 )$ MeV的中心值和误差. 图片更新自文献[63]

Figure 15. Constraints on symmetry energy parameters $ L_\text{sym}-J_\text{sym} $, open circle presents the results of PREX-II experiment, solid and dashed horizontal lines represent the central value and error of $ L_\text{sym} = (58.9\pm16 )$ MeV, respectively. Figure was taken and updated from Ref. [63].

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图 16 FOPI-LAND实验探测器布局图. 图片取自文献[64]

Figure 16. Detector layout of the FOPI-LAND experiment. Figure taken from Ref. [64]

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图 17 ASY-EOS实验探测器布局图, 图片取自文献[68]

Figure 17. ASY-EOS experiment detector layout, figure were taken from Ref. [68]

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图 18 400 MeV/u的Au+Au半中心碰撞(b < 7.5 fm)中ASY-EOS实验测量到的中子和带电粒子椭圆流的比值$ v_2^{\mathrm{n}}/v_2^{{\mathrm{ch}}} $和横动量的关联(黑色方框), 三角和圆分别代表UrQMD在硬($ \gamma = 1.5 $)和软($ \gamma = 0.5 $)对称能时计算结果, 实线是对理论计算结果做线性延拓, 得到与实验数据符合得最好时$ \gamma = 0.75\pm0.1 $. 图片取自文献[68]

Figure 18. Elliptic flow ratio of neutron and charged particle as a function of transverse momentum, in semi-central Au+Au collisions (b < 7.5 fm) at 400 MeV/u measured by ASY-EoS experiment. Triangles and squares are UrQMD predictions with hard ($ \gamma = 1.5 $) and soft ($ \gamma = 0.5 $) symmetry energy, solid line is the linear interpolation of predictions which can describe the data best, correspond to $ \gamma = 0.75\pm0.1 $. Figure taken from Ref. [68]

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图 19 FOPI实验测量400 MeV/u的核核中心碰撞中$ {\pi}^-/{\pi}^+ $产额比对碰撞系统N/Z的依赖(空心菱形)和IBUU04模型在x = 1.0 (软EoS)、0.5 (中等EoS)和0 (硬EoS)模拟结果比较, 图片取自文献[72]

Figure 19. $ {\pi}^-/{\pi}^+ $ yield ratio measured the FOPI experiment in central nucleus-nucleus collisions at 400 MeV/u as a function of N/Z ratio of the colliding systems (open diamonds), and compared simulation results from the IBUU04 model for x = 1.0 (soft EoS), 0.5 (medium EoS), and 0 (hard EoS). Figure taken from Ref. [72]

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图 20 HADES实验(方框)、FOPI实验(圆点)、Stream chamber(三角)和E895(五角星)测量到的约化π多重数与$ \langle {A}_\text{part}\rangle $的关系. 图片取自文献[81]

Figure 20. π multiplicity measured by HADES (squares), FOPI (filled circles), Stream chamber (triangles), and E895 experiment (star) as a function of $ \langle {A}_\text{part} \rangle $. Figure taken from Ref. [81]

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图 21 SπRIT实验装置图. 图片取自文献[84]

Figure 21. SπRIT experiment setup. Figure taken from Ref. [84]

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图 22 SπRIT实验中Tyoto-Array和前角区触发探测器 (KATANA)实物照片. 图片取自文献[87]

Figure 22. Photo of the Tyoto-Array and the KATANA detector of the SπRIT experiment. Figure taken from Ref. [87]

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图 23 (a) SπRIT实验测量270 MeV/u时, 不同Sn+Sn碰撞系统$ {\pi}^-/{\pi}^+ $产额比; (b)系统¹³²Sn+¹²⁴Sn和¹⁰⁸Sn+¹¹²Sn系统双$ \pi^-/\pi^+ $产额比; 7个输运模型计算结果用不同颜色标记. 图片取自文献[88]

Figure 23. (a) $ \pi^-/\pi^+ $ yield ratio measured by the SπRIT experiment in Sn+Sn collisions with different N/Z ratio; (b) double ${\pi}^-/{\pi}^+ $ yield ratio in ¹³²Sn+¹²⁴Sn and ¹⁰⁸Sn+¹¹²Sn, results from 7 transport models are marked by bands with different color. Figure taken from Ref. [88]

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图 24 中子星质量(M)和半径(R)的关系, 其中绿色区域为核物质, 红色区域代表在核物质基础上再加入$ {\Lambda}{\mathrm{N}} $相互作用后中子星的M-R关系, 其中考虑了两种都可以描述超核数据的YNN相互作用. 图片取自文献[96]

Figure 24. The relationship between the mass (M) and radius (R) of a neutron star, where the green region represents pure nuclear matter, and the red region shows the M-R relationship of neutron stars after incorporating ΛN interactions on top of the nuclear matter, considering two types of YNN interactions that can both describe hyper-nuclear data. Figure taken from Ref. [96]

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图 25 对称核物质(a)和中子核物质(b)中, 超子-核子(YN)和超子-核子-核子(YNN) 三体相互作用随密度的函数关系. 图片取自文献[99]

Figure 25. In symmetric nuclear matter (a) and pure neutron matter (b), the hyperon-nucleon (YN) and three-body hyperon-nucleon-nucleon (YNN) interactions as a function of the density. Figure taken from Ref. [99]

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图 26 超氚$ ^3_{\Lambda}\text{H} $产额随重离子碰撞能量的变化. 图片取自文献[101]

Figure 26. Production yields of hyper-triton $ ^3_{\Lambda}\text{H} $ as a function of colliding energies in HICs. Figure taken from Ref. [101]

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图 27 3 GeV Au+Au碰撞5%—40%碰撞中心度中$ ^3_{\Lambda}\text{H} $和$ ^4_{\Lambda}\text{H} $直接流与快度依赖关系. 图片取自文献[102]

Figure 27. Directed flow of $ ^3_{\Lambda}\text{H} $ and $ ^4_{\Lambda}\text{H} $ as a function of the rapidity at 3 GeV Au+Au collisions in 5%–40% centrality. Figure taken from Ref. [102]

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图 28 从能量为$ \sqrt{s_{{\mathrm{NN}}}} = 2—5020 $ GeV重离子碰撞数据中提取到的化学冻出温度(T)和重子化学势($ \mu_{\mathrm{B}} $). 图片取自文献[108]

Figure 28. Chemical freeze-out temperature (T) and baryon chemical potential ($ \mu_{\mathrm{B}} $) extracted from HICs with colliding energy $ \sqrt{s_{{\mathrm{NN}}}} = 2-5020 $ GeV. Figure taken from Ref. [108]

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图 29 FAIR装置上的CBM实验和HADES实验的探测器布局示意图. 图片取自文献[40]

Figure 29. Schematic diagram of the detector layout of the CBM experiment and the HADES experiment at the FAIR facility. Figure taken from Ref. [40]

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图 30 NICA装置上的MPD实验探测器布局示意图. 图片取自文献[41]

Figure 30. Schematic diagram of the detector layout of the MPD experiment at the NICA facility. Figure taken from Ref. [41]

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图 31 韩国RAON装置上的LAMPS实验探测器布局示意图. 图片取自文献[45]

Figure 31. Schematic diagram of the LAMPS experiment at the RAON facility. Figure taken from Ref. [45].

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图 32 HIRFL-CSR加速器布局示意图. 图片取自文献[119]

Figure 32. Schematic diagram of the HIRFL-CSR facility. Figure taken from Ref. [119]

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图 33 低温高密核物质测量谱仪探测器布局示意图

Figure 33. Schematic diagram of the CEE experiment.

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图 34 强流重离子加速器装置(HIAF)布局示意图. 图片取自文献[121]

Figure 34. Schematic diagram of the HIAF facility. Figure taken from Ref. [121].

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表 1 世界上重离子加速器与其典型实验, 基于文献[108]数据扩充

Table 1. Heavy-ion accelerator in the world and its typical Experiments, expanded based on data listed in Ref. [108]

Facility	$ \sqrt{s_{{\mathrm{NN}}}} $/GeV	Period	Experiments
Bevalac	2.0—2.7	1975-1993	EOS/et al.
SIS18	2.4—2.7	1990—now	FOPI/Hades/et al.
FRIB	1.9—2.1	>2025	AT-TPC$ ^* $
RIBF	1.9—2.1	1986—now	SπRIT
RAON	1.9—2.0	>2030	LAMPS
HIRFL	2.0—2.4	2008—now	CEE/ETE
Nuclotron	2.0—3.5	2000—now	BM@N
JPARC-HI	2.0—6.2	>2030	DHS
SIS100	2.7—5.0	>2029	CBM/Hades
NICA	2.7—11.0	>2025	BM@N/MPD
RHIC	3.0—200	2000—2025	STAR
SPS	4.5—17.3	1981—now	NA49/NA61/SHINE
AGS	2.7—4.8	2022—now	E895/et al.
HIAF	2.2—3.5	>2027	CEE+/CHNS
LHC	2760	2018—now	ALICE
LHC	72	>2027	LHCb/ALICE-FT

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