Abstract
The Heavy Ion Research Facility in Lanzhou-Cooling Storage Ring (HIRFL-CSR) external-target experiment (CEE) under construction is expected to provide novel opportunities for the studies of the thermodynamic properties of nuclear matter, in particular the nuclear matter equation of state (nEOS), with heavy ion collisions at a few hundreds MeV/u beam energies. Based on Geant 4 packages, the simulations of the detector responses to the collision events generated using transport model are conducted. The overall performance of CEE, including the geometric coverage, the momentum resolution of tracks and the particle identification ability has been investigated. Various observables proposed to probe the nEOS, such as the production of light clusters, \({}^3\textrm{H}/^3\textrm{He}\) yield ratio, radial flow, \(\pi ^{-}/\pi ^{+}\) yield ratio and neutral kaon yields, have been reconstructed. The feasibility of studying nEOS beyond the saturation density via the aforementioned observables to be measured with CEE has been demonstrated by using the ultra relativistic quantum molecular dynamics (UrQMD) simulation data.
Similar content being viewed by others
Data Availability Statement
This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.]
References
I. Arsene et al., Quark gluon plasma and color glass condensate at rhic? The perspective from the Brahms experiment. Nucl. Phys. A 757(1), 1–27 (2005)
B.B. Back et al., The phobos perspective on discoveries at rhic. Nucl. Phys. A 757(1), 28–101 (2005)
J. Adams et al., Experimental and theoretical challenges in the search for the quark-gluon plasma: The star collaboration’s critical assessment of the evidence from rhic collisions (2005)
K. Adcox et al., Formation of dense partonic matter in relativistic nucleus-nucleus collisions at rhic: experimental evaluation by the phenix collaboration. Nucl. Phys. A 757(1–2 SPEC ISS), 184–283 (2005)
P. Braun-Munzinger et al., The quest for the quark-gluon plasma. Nature 448(7151), 302–309 (2007)
X.F. Luo et al., Search for the qcd critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at rhic: an overview. Nucl. Sci. Tech. 28(8), 40 (2017)
B.A. Li et al. Topical issue on nuclear symmetry energy. Eur. Phys. J. A. Hadrons Nucl 50(2) (2014)
H.H. Gutbrod et al., Squeeze-out of nuclear matter as a function of projectile energy and mass. Phys. Rev. C 42, 640–651 (1990)
W. Reisdorf et al., Systematics of azimuthal asymmetries in heavy ion collisions in the 1a gev regime. Nucl. Phys. A 876, 1–60 (2012)
P. Danielewicz et al., Determination of the equation of state of dense matter. Science 298(5598), 1592–1596 (2002)
Y.J. Wang et al., Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies. Front. Phys. 15, 44302 (2020)
P. Hillmann et al., Directed, elliptic and triangular flow of protons in au+au reactions at 1.23 a gev: a theoretical analysis of the recent hades data. J. Phys. G Nucl. Part. Phys. 45(8), 085101 (2018)
J. Aichelin et al., Subthreshold kaon production as a probe of the nuclear equation of state. Phys. Rev. Lett. 55, 2661–2663 (1985)
C. Fuchs et al., Probing the nuclear equation of state by \({{k}}^{+}\) production in heavy-ion collisions. Phys. Rev. Lett. 86, 1974–1977 (2001)
C. Sturm et al., Evidence for a soft nuclear equation-of-state from kaon production in heavy-ion collisions. Phys. Rev. Lett. 86, 39–42 (2001)
Ch. Hartnack et al., Hadronic matter is soft. Phys. Rev. Lett. 96, 012302 (2006)
A. Sorensen et al., Dense nuclear matter equation of state from heavy-ion collisions. white paper for 2023 LPR (2023). arXiv:2301.13253
B.A. Li et al., Equation of state of asymmetric nuclear matter and collisions of neutron-rich nuclei. Phys. Rev. Lett. 78, 1644–1647 (1997)
H.S. Xu et al., Isospin fractionation in nuclear multifragmentation. Phys. Rev. Lett. 85, 716–719 (2000)
W.P. Tan et al., Fragment isotope distributions and the isospin dependent equation of state. Phys. Rev. C 64, 051901 (2001)
M.B. Tsang et al., Isotopic scaling in nuclear reactions. Phys. Rev. Lett. 86, 5023–5026 (2001)
B.A. Li et al., Proton differential elliptic flow and the isospin dependence of the nuclear equation of state. Phys. Rev. C 64, 054604 (2001)
B.A. Li, Neutron-proton differential flow as a probe of isospin-dependence of the nuclear equation of state. Phys. Rev. Lett. 85, 4221–4224 (2000)
Z.G. Xiao et al., Probing nuclear symmetry energy at high densities using pion, kaon, eta and photon productions in heavy-ion collisions. Eur. Phys. J. A 50, 37 (2014)
B.A. Li, Isospin dependence of the \({\pi }^{-}/{\pi }^{+}\) ratio and density dependence of the nuclear symmetry energy. Phys. Rev. C 67, 017601 (2003)
D. Adhikari et al., Accurate determination of the neutron skin thickness of \(^{208}\rm Pb \) through parity-violation in electron scattering. Phys. Rev. Lett. 126, 172502 (2021)
T.R. Brendan et al., Implications of prex-2 on the equation of state of neutron-rich matter. Phys. Rev. Lett. 126, 172503 (2021)
Y. Zhang et al., Long-time drift of the isospin degree of freedom in heavy ion collisions. Phys. Rev. C 95, 041602 (2017)
Y.J. Wang et al., Observing the ping-pong modality of the isospin degree of freedom in cluster emission from heavy-ion reactions. Phys. Rev. C 107, L041601 (2023)
J. Estee et al., Probing the symmetry energy with the spectral pion ratio. Phys. Rev. Lett. 126, 162701 (2021)
Y. Zhou et al., Equation of state of dense matter in the multimessenger era. Phys. Rev. D 99, 121301 (2019)
N.B. Zhang et al., Constraints on the muon fraction and density profile in neutron stars. Astrophys. J. 893(1), 61 (2020)
Y.Y. Liu et al., Insights into the pion production mechanism and the symmetry energy at high density. Phys. Rev. C 103, 014616 (2021)
S. Huth et al., Constraining neutron-star matter with microscopic and macroscopic collisions. Nature 606, 276–280 (2022)
C. Y. Tsang, M. Y. Betty Tsang, W. G. Lynch, R. Kumar, C. J. Horowitz, Determination of the equation of state from nuclear experiments and neutron star observations (2023)
W. Reisdorf et al., Systematics of pion emission in heavy ion collisions in the 1a gev regime. Nucl. Phys. A 781(3), 459–508 (2007)
Z.G. Xiao et al., Circumstantial evidence for a soft nuclear symmetry energy at suprasaturation densities. Phys. Rev. Lett. 102, 062502 (2009)
W.J. Xie et al., Symmetry energy and pion production in the Boltzmann-Langevin approach. Phys. Lett. B 718(4), 1510–1514 (2013)
P. Russotto et al., Symmetry energy from elliptic flow in 197au+197au. Phys. Lett. B 697(5), 471–476 (2011)
X.F Luo et al. Properties of QCD Matter at High Baryon Density. Springer, Singapore (Science Press Beijing) (2022) (ISBN:978-981-19-4440-6)
L.M. Lyu et al., Conceptual design of the hirfl-csr external-target experiment. Sci. China Phys. Mech. Astron. 60, 012021 (2016)
Y.J. Yuan et al., Present status of hirfl complex in lanzhou. J. Phys. Conf. Ser. 1401(1), 012003 (2020)
Z.Y. Sun et al., Huizhou accelerator complex facility and its future development. Sci. Sinica Phys. Mech. Astron. 50, 112006 (2020)
Q.F. Li et al., Nonequilibrium dynamics in heavy-ion collisions at low energies available at the gsi schwerionen synchrotron. Phys. Rev. C 83, 044617 (2011)
Y.J. Wang et al., Study of the nuclear symmetry energy from the rapidity-dependent elliptic flow in heavy-ion collisions around 1 GeV/nucleon regime. Phys. Lett. B 802, 135249 (2020)
Y.J. Wang et al., Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies. Front. Phys. 15, 44302 (2020)
Li. He et al., Simulation of momentum resolution of the cee-tpc in hirfl. Nucl. Tech. 39, 070401 (2016)
X. Wang et al., Cee inner tof prototype design and preliminary test results. J. Instrument. 17(09), P09023 (2022)
B. Wang et al., The cee-etof wall constructed with new sealed mrpc. J. Instrument. 15(08), C08022 (2020)
S.H. Zhu et al., Prototype design of readout electronics for zero degree calorimeter in the hirfl-csr external-target experiment. J. Instrum. 16(08), P08014 (2021)
D. Hu et al., A t0/trigger detector for the external target experiment at csr. J. Instrum. 12(06), C06010 (2017)
D.D. Hu et al., Extensive beam test study of prototype mrpcs for the t0 detector at the csr external-target experiment. Eur. Phys. J. C 80, 282 (2020)
H.L. Wang et al., Design and tests of the prototype beam monitor of the csr external target experiment. Nucl. Sci. Tech. 33, 36 (2022)
J. Liu et al., Design and preliminary characterization of a novel silicon charge sensor for the gaseous beam monitor at the csr external-target experiment. Nucl. Instrum. Methods Phys. Res. Sect. A Accelerat. Spectromet. Detect. Assoc. Equip. 1047, 167786 (2023)
J. Adolfsson et al., Sampa chip: the new 32 channels asic for the alice tpc and mch upgrades. J. Instrum. 12(04), C04008 (2017)
J. Y. Yuan et al., Development of multichannel readout electronics prototype system for tpc detector of csr external-target experiment. Nucl. Instrum. Methods Phys. Res. Sect. A Accelerat. Spectromet. Detect. Assoc. Equip. 1052:168281 (2023)
F. Anghinolfi et al., Nino, an ultra-fast, low-power, front-end amplifier discriminator for the time-of-flight detector in alice experiment. In 2003 IEEE Nuclear Science Symposium. In: Conference Record (IEEE Cat. No. 03CH37515) 1, 375–379 (2003)
J.M. Lu et al., Readout electronics prototype of tof detectors in cee of hirfl. IEEE Trans. Nucl. Sci. 68(8), 1976–1983 (2021)
W.J. Xie et al., Bayesian inference of high-density nuclear symmetry energy from radii of canonical neutron stars. Astrophys. J. 883(2), 174 (2019)
I. Legred et al., Impact of the psr \({\rm J} 0740+6620\) radius constraint on the properties of high-density matter. Phys. Rev. D 104, 063003 (2021)
D. Oliinychenko et al., Sensitivity of \({\rm Au} + {\rm Au}\) collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities. Phys. Rev. C 108, 034908 (2023)
P. Morfouace et al., Constraining the symmetry energy with heavy-ion collisions and bayesian analyses. Phys. Lett. B 799, 135045 (2019)
J. Xu et al., Constraining isovector nuclear interactions with giant resonances within a bayesian approach. Phys. Lett. B 810, 135820 (2020)
M.O. Kuttan et al., The qcd eos of dense nuclear matter from bayesian analysis of heavy ion collision data (2022)
S.A. Bass et al., Microscopic models for ultrarelativistic heavy ion collisions. Prog. Part. Nucl. Phys. 41, 255–369 (1998)
M. Bleicher et al., Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model. J. Phys. G Nucl. Part. Phys. 25(9), 1859 (1999)
Y.J. Wang et al., Collective flows of light particles in the Au+Au collisions at intermediate energies. Phys. Rev. C 89(3), 034606 (2014)
Y.J. Wang et al., Constraining the high-density nuclear symmetry energy with the transverse-momentum dependent elliptic flow. Phys. Rev. C 89(4), 044603 (2014)
Q.F. Li et al., Medium modifications of the nucleon-nucleon elastic cross section in neutron-rich intermediate energy HICs. J. Phys. G 32, 407–416 (2006)
Pengcheng Li, Yongjia Wang, Qingfeng Li, Chenchen Guo, Hongfei Zhang, Effects of the in-medium nucleon-nucleon cross section on collective flow and nuclear stopping in heavy-ion collisions in the Fermi-energy domain. Phys. Rev. C 97(4), 044620 (2018)
P.C. Li et al., Accessing the in-medium effects on nucleon-nucleon elastic cross section with collective flows and nuclear stopping. Phys. Lett. B 828, 137019 (2022)
Y. Zhang, Z. Li, C. Zhou, M.B. Tsang, Effect of isospin dependent cluster recognition on the observables in heavy ion collisions. Phys. Rev. C 85, 051602 (2012)
Y.S. Du et al., The effect of Lorentz-like force on collective flows of K\(^{+}\) in Au+Au collisions at 1.5 GeV/nucleon. Sci. China Phys. Mech. Astron. 61(6), 062011 (2018)
Y.Y. Liu et al., Collective flows of pions in Au+Au collisions at energies 1.0 and 1.5 GeV/nucleon. Phys. Rev. C 97(3), 034602 (2018)
Y.Y. Liu et al., Insights into the pion production mechanism and the symmetry energy at high density. Phys. Rev. C 103(1), 014616 (2021)
Y.X. Zhang et al., Progress of quantum molecular dynamics model and its applications in heavy ion collisions. Front. Phys. 15, 54301 (2020)
W. Klempt, Review of particle identification by time of flight techniques. Nucl. Instrum. Methods Phys. Res. Sect. A Accelerat. Spectrom. Detect. Assoc. Equip. 433(1), 542–553 (1999)
Y. Kim. Study of nuclear stopping in isospin-asymmetric nuclear collisions at 0.4 and 1.5 GeV. Dr., Seoul, Korea, Univ., Seoul, p.2004 (Univ., Diss, Korea, 2004)
T. Kobayashi et al. Samurai spectrometer for ri beam experiments. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 317:294–304, 2013. XVIth International Conference on ElectroMagnetic Isotope Separators and Techniques Related to their Applications, December 2-7, 2012 at Matsue, Japan
D. Guo et al., An fpga-based trigger system for cshine. Nucl. Sci. Tech. 33, 162 (2022)
M. Zhang et al., Systematic study of the \({\pi }^{-}/{\pi }^{+}\) ratio in heavy-ion collisions with the same neutron/proton ratio but different masses. Phys. Rev. C 80, 034616 (2009)
F. Fen et al., Nuclear stopping and compression in heavy-ion collisions at intermediate energies. Phys. Lett. B 666(4), 359–363 (2008)
L.W. Chen et al., Effects of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei. Phys. Rev. Lett. 90, 162701 (2003)
L.W. Chen et al., Effects of momentum-dependent nuclear potential on two-nucleon correlation functions and light cluster production in intermediate energy heavy-ion collisions. Phys. Rev. C 69, 054606 (2004)
Q.F. Li et al., Probing the density dependence of the symmetry potential at low and high densities. Phys. Rev. C 72, 034613 (2005)
Y.X. Zhang et al., Probing the density dependence of the symmetry potential with peripheral heavy-ion collisions. Phys. Rev. C 71, 024604 (2005)
Y.J. Wang et al., 3h/3he ratio as a probe of the nuclear symmetry energy at sub-saturation densities. Eur. Phys. J. A 51, 37 (2015)
C.C. Guo et al., Influence of the symmetry energy on the balance energy of the directed flow. Sci. China Phys. Mech. Astron. 55, 252–259 (2012)
K. Hagel et al., Light particle probes of expansion and temperature evolution: coalescence model analyses of heavy ion collisions at \(47a \rm MeV \). Phys. Rev. C 62, 034607 (2000)
L.W. Chen et al., Light clusters production as a probe to nuclear symmetry energy. Phys. Rev. C 68, 017601 (2003)
W. Reisdorf et al., Systematics of central heavy ion collisions in the 1a gev regime. Nucl. Phys. A 848(3), 366–427 (2010)
J.F. Dempsey et al., Isospin dependence of intermediate mass fragment production in heavy-ion collisions at e/a=55 mev. Phys. Rev. C 54, 1710–1719 (1996)
M. Veselsky et al., Isospin dependence of isobaric ratio y(3(h)/y(3he) and its relation to temperature. Phys. Lett. B 497(1), 1–7 (2001)
B.A. Li et al. Progress in constraining nuclear symmetry energy using neutron star observables since gw170817. Universe 7(6) (2021)
J.Y. Ollitrault, Flow systematics from sis to sps energies. Nucl. Phys. A 638(1), 195c–206c (1998)
W. Bauer et al., Large radial flow in nucleus-nucleus collisions. Phys. Rev. C 47, R1838–R1841 (1993)
G. Poggi et al., Evidence for collective expansion in light-particle emission following au+au collisions at 100, 150 and 250 a.mev. Nucl. Phys. A, 586(4), 755–776 (1995)
W. Reisdorf et al., Nuclear stopping from \(0.09a\) to \(1.93a {\rm GeV} \) and its correlation to flow. Phys. Rev. Lett. 92, 232301 (2004)
G. Stoicea et al., Azimuthal dependence of collective expansion for symmetric heavy-ion collisions. Phys. Rev. Lett. 92, 072303 (2004)
J. Stachel, Tests of thermalization in relativistic nucleus-nucleus collisions. Nucl. Phys. A 610, 509–522 (1996)
B.A. Li et al., Pion flow and antiflow in relativistic heavy-ion collisions. Phys. Rev. C 53, R22–R24 (1996)
J.Y. Ollitrault, Determination of the reaction plane in ultrarelativistic nuclear collisions. Phys. Rev. D 48, 1132–1139 (1993)
J.P. Alard et al., Midrapidity source of intermediate-mass fragments in highly central collisions of au + au at 150a mev. Phys. Rev. Lett. 69, 889–892 (1992)
Ch. Hartnack et al., Transverse flow of nuclear matter in collisions of heavy nuclei atintermediate energies. Phys. Lett. B 506(3), 261–266 (2001)
P.J. Siemens et al., Evidence for a blast wave from compressed nuclear matter. Phys. Rev. Lett. 42, 880–883 (1979)
H.A. Gustafsson et al., Collective flow observed in relativistic nuclear collisions. Phys. Rev. Lett. 52, 1590–1593 (1984)
M.A. Lisa et al. Radial flow in \({\rm Au}+{\rm Au}\) collisions at \({E}=(0.25{-}1.15){A}{\rm GeV}\). Phys. Rev. Lett. 75, 2662–2665 (1995)
S. Wang et al., In-plane retardation of collective expansion in \({\rm Au}+{\rm Au}\) collisions. Phys. Rev. Lett. 76, 3911–3914 (1996)
B.A. Li et al., Near-threshold pion production with radioactive beams. Phys. Rev. C 71, 014608 (2005)
B. Hong et al., Charged pion production in \({}_{44}^{96}{\rm Ru}+{}_{44}^{96}{\rm Ru} \) collisions at \(400a\) and \(1528a {\rm MeV} \). Phys. Rev. C 71, 034902 (2005)
M.D. Cozma, Neutron-proton elliptic flow difference as a probe for the high density dependence of the symmetry energy. Phys. Lett. B 700(2), 139–144 (2011)
R. Stock, Particle production in high energy nucleus-nucleus collisions. Phys. Rep. 135(5), 259–315 (1986)
A. Bonasera et al., Isospin effects on pion production by heavy ions. Phys. Lett. B 195(4), 521–523 (1987)
B.A. Li, Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions. Phys. Rev. Lett. 88, 192701 (2002)
Y.X. Zhang et al., Comparison of heavy-ion transport simulations: collision integral in a box. Phys. Rev. C 97, 034625 (2018)
A. Ono et al., Comparison of heavy-ion transport simulations: collision integral with pions and \({{\Delta }}\) resonances in a box. Phys. Rev. C 100, 044617 (2019)
M. Colonna et al., Comparison of heavy-ion transport simulations: mean-field dynamics in a box. Phys. Rev. C 104, 024603 (2021)
G. Ferini et al., Isospin effects on subthreshold kaon production at intermediate energies. Phys. Rev. Lett. 97, 202301 (2006)
J. Aichelin et al., Subthreshold kaon production as a probe of the nuclear equation of state. Phys. Rev. Lett. 55, 2661–2663 (1985)
C. Sturm et al., Evidence for a soft nuclear equation-of-state from kaon production in heavy-ion collisions. Phys. Rev. Lett. 86, 39–42 (2001)
Ch. Hartnack et al., Hadronic matter is soft. Phys. Rev. Lett. 96, 012302 (2006)
P. Crochet et al., Sideward flow of k+ mesons in ru+ru and ni+ni reactions near threshold. Phys. Lett. B 486(1), 6–12 (2000)
S. Albergo et al., \(\lambda \) spectra in \(116 a\) gev au-au collisions. Phys. Rev. Lett. 88, 062301 (2002)
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant Nos. 11927901 and 11890712, and by Tsinghua University Scientific Research Program.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Communicated by Carlos Munoz Camacho.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Guo, D., He, X., Li, P. et al. Studies of nuclear equation of state with the HIRFL-CSR external-target experiment. Eur. Phys. J. A 60, 36 (2024). https://doi.org/10.1140/epja/s10050-024-01245-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/s10050-024-01245-2