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核物质状态方程是核物质体系在不同热力学或者外场条件下对其宏观性质的描述，它对理解微观强相互作用的理论-量子色动力学（QCD）、原子核性质、重离子碰撞动力学、致密天体内部结构、双中子星合并等具有重要意义。重离子碰撞（HICs）是在实验室产生极端条件（如高温、高密、强磁场、强涡旋等）核物质的唯一手段。不同碰撞能量的HICs为定量研究核物质在不同热力学条件下的性质提供了可能。本文主要介绍当前核物质状态方程的研究现状，并介绍HICs中对核物质状态方程敏感的基本可观测量、探索核物质状态的典型实验和结果。展现包含有奇异强子核物质状态方程的研究进展，并探讨未来可能的研究方向。介绍国际上在建和正在运行的重离子加速器和实验谱仪的最新进展，包括我国已经建成的兰州重离子加速器装置(HIRFL)和兰州重离子加速器装置-冷却储存环(HIRFL-CSR)、在建的强流重离子加速器装置（HIAF）和在建的低温高密核物质测量谱仪的研制进展，并讨论未来基于我国大科学装置开展核物质状态方程实验研究的机遇与挑战。
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关键词:
- 核物质状态方程 /
- 重离子碰撞 /
- 兰州重离子加速器装置-冷却储存环（HIRFL-CSR） /
- 强流重离子加速器装置（HIAF）
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 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 also discussed. The status and progress of world-wide heavy-ion accelerators and experimental spectrometers in 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:
- Equation of State (EoS) /
- Heavy-ion Collisions /
- HIRFL-CSR /
- HIAF
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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) $(上)和$ L_\text{sym}(\rho_0) $(下)的结果. (a)和(b)均取自[24]
Fig. 3. $ E_\text{sym}(\rho_0) $ (upper panel) and $ L_\text{sym}(\rho_0) $ (lower panel) extracted from terrestrial heavy-ion experiments and astrophysical observations respectively. Panel (a) and Panel (b) both are taken from[24].
图 4 重离子碰撞中的碰撞参数和反应平面示意图
Fig. 4. Sketch of impact parameter and reaction plane in Heavy-ion collisions.
图 10 KaoS实验测量$ 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. 图片取得自[50]
Fig. 10. Yield ratio of $ 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[50].
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依赖, 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. 图片取得自[56]
Fig. 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[56].
图 13 (左)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; (右)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[58]
Fig. 13. (Left) In 30 meV/u Ar+Au reactions, $ Y_{n, ex}/Y_{p, CL} $ as a function of polar angle, curves are theoretical calculations. (Right) Comparison the slope of $ Y_{n, ex}/Y_{p, CL} $ in $ \theta_{lab}<100^{\circ} $ from experiment (red band) and theoretical predictions (open circles). Figure taken from[58]
图 15 不同的实验和理论给出的对称能参数$ L_\text{sym}-J_\text{sym} $的限制, 黑色空心圈为PREX-II测量结果, 红色实线和虚线表示其它实验中提取的$ L_\text{sym} = 58.9\pm16 $ MeV的中心值和误差. 图片更新自[63]
Fig. 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[63].
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^n/v_2^{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 $)对称能时计算结果, 实线是对理论计算结果做线性延拓, 得到与实验数据最佳符合时$ \gamma = 0.75\pm0.1 $, 图片取自[68]
Fig. 18. Elliptic flow ratio of neutron and charged particle as a function of transverse momentum, in semi-central Au+Au collisions (b<7.5 fm) at 400 MeV/u measured by ASY-EoS experiment. Triangles and squares are UrQMD predictions with hard ($ \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 $. Figure taken from[68]
图 19 FOPI实验测量400 MeV/u的核核中心碰撞中$ \pi^-/\pi^+ $产额比与碰撞系统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[72]
Fig. 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[72]
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$ <\text{A}_\text{part}> $的关系. 图片取自[81]
Fig. 20. π multiplicity measured by HADES(squares), FOPI(filled circles), Stream chamber (triangles) and E895 experiment (star) as a function of $ <\text{A}_\text{part}> $. Figure taken from[81]
图 23 (左)SπRIT实验测量270 MeV/u时, 不同Sn+Sn碰撞系统$ \pi^-/\pi^+ $产额比; (右)系统132Sn+124Sn和108Sn+112Sn系统双$ \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[88]
Fig. 23. (Left) $ \pi^-/\pi^+ $ yield ratio measured by the SπRIT experiment in Sn+Sn collisions with different N/Z ratio; (Right) 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[88]
图 24 中子星质量(M)和半径(R)的关系, 其中绿区域为核物质, 红色区域代表在核物质基础上再加入$ {\Lambda}N $相互作用后中子星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[96]
Fig. 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[96]
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[108]
Facility $ \sqrt{s_{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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