Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies

Yong-Jia Wang, Qing-Feng Li

PDF(1943 KB)
PDF(1943 KB)
Front. Phys. ›› 2020, Vol. 15 ›› Issue (4) : 44302. DOI: 10.1007/s11467-020-0964-6
TOPICAL REVIEW
TOPICAL REVIEW

Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies

Author information +
History +

Abstract

The equation of state (EOS) of nuclear matter, i.e., the thermodynamic relationship between the binding energy per nucleon, temperature, density, as well as the isospin asymmetry, has been a hot topic in nuclear physics and astrophysics for a long time. The knowledge of the nuclear EOS is essential for studying the properties of nuclei, the structure of neutron stars, the dynamics of heavy ion collision (HIC), as well as neutron star mergers. HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory, but the formed dense nuclear matter exists only for a very short period, one cannot measure the nuclear EOS directly in experiments. Practically, transport models which often incorporate phenomenological potentials as an input are utilized to deduce the EOS from the comparison with the observables measured in laboratory. The ultrarelativistic quantum molecular dynamics (UrQMD) model has been widely employed for investigating HIC from the Fermi energy (40 MeV per nucleon) up to the CERN Large Hadron Collider energies (TeV). With further improvement in the nuclear mean-field potential term, the collision term, and the cluster recognition term of the UrQMD model, the newly measured collective flow and nuclear stopping data of light charged particles by the FOPI Collaboration can be reproduced. In this article we highlight our recent results on the studies of the nuclear EOS and the nuclear symmetry energy with the UrQMD model. New opportunities and challenges in the extraction of the nuclear EOS from transport models and HIC experiments are discussed.

Keywords

nuclear equation of state / symmetry energy / heavy ion collision / transport model

Cite this article

Download citation ▾
Yong-Jia Wang, Qing-Feng Li. Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies. Front. Phys., 2020, 15(4): 44302 https://doi.org/10.1007/s11467-020-0964-6

References

[1]
B. A. Li, L. W. Chen, and C. M. Ko, Recent progress and new challenges in isospin physics with heavy-ion reactions, Phys. Rep. 464(4–6), 113 (2008)
CrossRef ADS Google scholar
[2]
M. B. Tsang, J. R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C. J. Horowitz, J. Lee, W. G. Lynch, Z. Kohley, R. Lemmon, P. Möller, T. Murakami, S. Riordan, X. Roca-Maza, F. Sammarruca, A. W. Steiner, I. Vidaña, and S. J. Yennello, Constraints on the symmetry energy and neutron skins from experiments and theory, Phys. Rev. C 86(1), 015803 (2012)
CrossRef ADS Google scholar
[3]
M. Baldo and G. F. Burgio, The nuclear symmetry energy, Prog. Part. Nucl. Phys. 91, 203 (2016)
CrossRef ADS Google scholar
[4]
M. Oertel, M. Hempel, T. Klähn, and S. Typel, Equations of state for supernovae and compact stars, Rev. Mod. Phys. 89, 015007 (2017)
CrossRef ADS Google scholar
[5]
B. A. Li, B. J. Cai, L. W. Chen, and J. Xu, Nucleon effective masses in neutron-rich matter, Prog. Part. Nucl. Phys. 99, 29 (2018)
CrossRef ADS Google scholar
[6]
X. Roca-Maza and N. Paar, Nuclear equation of state from ground and collective excited state properties of nuclei, Prog. Part. Nucl. Phys. 101, 96 (2018)
CrossRef ADS Google scholar
[7]
S. Burrello, M. Colonna, and H. Zheng, The symmetry energy of the nuclear EoS: A study of collective motion and low-energy reaction dynamics in semiclassical approaches, Front. Phys. 7, 53 (2019)
CrossRef ADS Google scholar
[8]
G. Giuliani, H. Zheng, and A. Bonasera, The many facets of the (non-relativistic) nuclear equation of state, Prog. Part. Nucl. Phys. 76, 116 (2014)
CrossRef ADS Google scholar
[9]
C. W. Ma and Y. G. Ma, Shannon information entropy in heavy-ion collisions, Prog. Part. Nucl. Phys. 99, 120 (2018)
CrossRef ADS Google scholar
[10]
A. Ono, Dynamics of clusters and fragments in heavy-ion collisions, Prog. Part. Nucl. Phys. 105, 139 (2019)
CrossRef ADS Google scholar
[11]
J. Xu, Transport approaches for the description of intermediate-energy heavy-ion collisions, Prog. Part. Nucl. Phys. 106, 312 (2019)
CrossRef ADS Google scholar
[12]
H. Gao, S. K. Ai, Z. J. Cao, B. Zhang, Z. Y. Zhu, A. Li, N. B. Zhang, and A. Bauswein, Relation between gravitational mass and baryonic mass for non-rotating and rapidly rotating neutron stars, Front. Phys. 15(2), 24603 (2020)
CrossRef ADS Google scholar
[13]
L. W. Chen, C. M. Ko, B. A. Li, C. Xu, and J. Xu, Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter, Eur. Phys. J. A 50(2), 29 (2014)
CrossRef ADS Google scholar
[14]
J. Xu, L. W. Chen, B. A. Li, and H. R. Ma, Nuclear constraints on properties of neutron star crusts, Astrophys. J. 697(2), 1549 (2009)
CrossRef ADS Google scholar
[15]
B. J. Cai and L. W. Chen, Nuclear matter fourth-order symmetry energy in the relativistic mean field models, Phys. Rev. C 85(2), 024302 (2012)
CrossRef ADS Google scholar
[16]
A. W. Steiner, High-density symmetry energy and direct Urca process, Phys. Rev. C 74(4), 045808 (2006)
CrossRef ADS Google scholar
[17]
J. Pu, Z. Zhang and L. W. Chen, Nuclear matter fourthorder symmetry energy in nonrelativistic mean-field models, Phys. Rev. C 96, 054311 (2017)
CrossRef ADS Google scholar
[18]
Z. W. Liu, Z. Qian, R. Y. Xing, J. R. Niu and B. Y. Sun, Nuclear fourth-order symmetry energy and its effects on neutron star properties in the relativistic Hartree–Fock theory, Phys. Rev. C 97, 2, 025801 (2018)
CrossRef ADS Google scholar
[19]
S. A. Bass, et al. (UrQMD-Collaboration), Microscopic models for ultrarelativistic heavy ion collisions, Prog. Part. Nucl. Phys. 41, 255 (1998)
CrossRef ADS Google scholar
[20]
M. Bleicher, E. Zabrodin, C. Spieles, S. A. Bass, C. Ernst, S. Soff, L. Bravina, M. Belkacem, H. Weber, H. Stöcker, and W. Greiner, Relativistic hadron–hadron collisions in the ultra-relativistic quantum molecular dynamics model,J. Phys. G 25(9), 1859 (1999)
CrossRef ADS Google scholar
[21]
Q. Li, C. Shen, C. Guo, Y. Wang, Z. Li, J. Lukasik, and W. Trautmann, Nonequilibrium dynamics in heavy-ion collisions at low energies available at the GSI Schwerionen Synchrotron, Phys. Rev. C 83(4), 044617 (2011)
CrossRef ADS Google scholar
[22]
Q. Li, G. Graf, and M. Bleicher, Ultrarelativistic quantum molecular dynamics calculations of two-pion Hanbury–Brown–Twiss correlations in central Pb–Pb collisions at sNN=2.76⁢ ⁡TeV, Phys. Rev. C 85(3), 034908 (2012)
CrossRef ADS Google scholar
[23]
J. Aichelin, “Quantum” molecular dynamics — a dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions, Phys. Rep. 202(5–6), 233 (1991)
CrossRef ADS Google scholar
[24]
C. Hartnack, R. K. Puri, J. Aichelin, J. Konopka, S. A. Bass, H. Stöcker, and W. Greiner, Modelling the manybody dynamics of heavy ion collisions: Present status and future perspective, Eur. Phys. J. A 1(2), 151 (1998)
CrossRef ADS Google scholar
[25]
Q. F. Li, Z. X. Li, S. Soff, M. Bleicher, and H. Stöcker, Probing the equation of state with pions, J. Phys. G 32(2), 151 (2006)
CrossRef ADS Google scholar
[26]
F. S. Zhang, C. Li, L. Zhu and P. Wen, Production cross sections for exotic nuclei with multinucleon transfer reactions, Front. Phys. 13(6), 132113 (2018)
CrossRef ADS Google scholar
[27]
Y. Zhang and Z. Li, Elliptic flow and system size dependence of transition energies at intermediate energies, Phys. Rev. C 74(1), 014602 (2006)
CrossRef ADS Google scholar
[28]
Y. Zhang, Z. Li, and P. Danielewicz, In-medium NN cross sections determined from the nuclear stopping and collective flow in heavy-ion collisions at intermediate energies, Phys. Rev. C 75(3), 034615 (2007)
CrossRef ADS Google scholar
[29]
Y. Wang, C. Guo, Q. Li, H. Zhang, Z. Li, and W. Trautmann, Collective flow of light particles in Au+Au collisions at intermediate energies, Phys. Rev. C 89(3), 034606 (2014)
CrossRef ADS Google scholar
[30]
Y. Wang, C. Guo, Q. Li, H. Zhang, Y. Leifels, and W. Trautmann, Constraining the high-density nuclear symmetry energy with the transverse-momentum-dependent elliptic flow, Phys. Rev. C 89, 044603 (2014)
CrossRef ADS Google scholar
[31]
Y. Du, Y. Wang, Q. Li, and L. Liu, The effect of Lorentzlike force on collective flows of K+ in Au+Au collisions at 1.5 GeV/nucleon, Sci. China Phys. Mech. Astron. 61, 062011 (2018)
CrossRef ADS Google scholar
[32]
Y. Liu, Y. Wang, Q. Li, and L. Liu, Collective flows of pions in Au+Au collisions at energies 1.0 and 1.5 GeV/nucleon, Phys. Rev. C 97, 034602 (2018)
CrossRef ADS Google scholar
[33]
G. Q. Li and R. Machleidt, Microscopic calculation of in-medium nucleon–nucleon cross sections, Phys. Rev. C 48(4), 1702 (1993)
CrossRef ADS Google scholar
[34]
G. Q. Li and R. Machleidt, Microscopic calculation of in-medium proton–proton cross sections, Phys. Rev. C 49(1), 566 (1994)
CrossRef ADS Google scholar
[35]
F. Sammarruca and P. Krastev, Effective nucleon– nucleon cross sections in symmetric and asymmetric nuclear matter, Phys. Rev. C 73(1), 014001 (2006)
CrossRef ADS Google scholar
[36]
H. J. Schulze, A. Schnell, G. Ropke, and U. Lombardo, Nucleon–nucleon cross sections in nuclear matter, Phys. Rev. C 55(6), 3006 (1997)
CrossRef ADS Google scholar
[37]
C. Fuchs, A. Faessler, and M. El-Shabshiry, Off-shell behavior of the in-medium nucleon–nucleon cross section, Phys. Rev. C 64(2), 024003 (2001)
CrossRef ADS Google scholar
[38]
H. F. Zhang, Z. H. Li, U. Lombardo, P. Y. Luo, F. Sammarruca, and W. Zuo, Nucleon–nucleon cross sections in dense nuclear matter, Phys. Rev. C 76(5), 054001 (2007)
CrossRef ADS Google scholar
[39]
H. F. Zhang, U. Lombardo, and W. Zuo, Transport parameters in neutron stars from in-medium NN cross sections, Phys. Rev. C 82(1), 015805 (2010)
CrossRef ADS Google scholar
[40]
W. G. Love and M. A. Franey, Effective nucleon–nucleon interaction for scattering at intermediate energies, Phys. Rev. C 24, 1073 (1981)
CrossRef ADS Google scholar
[41]
T. Alm, G. Röpke, W. Bauer, F. Daffin, and M. Schmidt, The in-medium nucleon–nucleon cross section and BUU simulations of heavy-ion reactions, Nucl. Phys. A 587(4), 815 (1995)
CrossRef ADS Google scholar
[42]
G. J. Mao, Z. X. Li, Y. Z. Zhuo, and Z. Q. Yu, Medium effects on the NN inelastic cross section in relativistic heavy-ion collisions, Phys. Lett. B 327(3–4), 183 (1994)
CrossRef ADS Google scholar
[43]
G. J. Mao, Z. X. Li, Y. Z. Zhuo, Y. Han, and Z. Yu, Study of in-medium NN inelastic cross section from relativistic Boltzmann-Uehling-Uhlenbeck approach, Phys. Rev. C 49(6), 3137 (1994)
CrossRef ADS Google scholar
[44]
Q. F. Li, Z. X. Li, and G. J. Mao, Isospin dependence of nucleon–nucleon elastic cross section, Phys. Rev. C 62(1), 014606 (2000)
CrossRef ADS Google scholar
[45]
Q. F. Li, Z. X. Li, and E. G. Zhao, Density and temperature dependence of nucleon–nucleon elastic cross section, Phys. Rev. C 69(1), 017601 (2004)
CrossRef ADS Google scholar
[46]
Q. F. Li and Z. X. Li, The isospin dependent nucleon– nucleon inelastic cross section in the nuclear medium, Phys. Lett. B 773, 557 (2017)
CrossRef ADS Google scholar
[47]
G. D. Westfall, W. Bauer, D. Craig, M. Cronqvist, E. Gaultieri, S. Hannuschke, D. Klakow, T. Li, T. Reposeur, A. M. Vander Molen, W. K. Wilson, J. S. Winfield, J. Yee, S. J. Yennello, R. Lacey, A. Elmaani, J. Lauret, A. Nadasen, and E. Norbeck, Mass dependence of the disappearance of flow in nuclear collisions, Phys. Rev. Lett. 71(13), 1986 (1993)
CrossRef ADS Google scholar
[48]
D. D. S. Coupland, W. G. Lynch, M. B. Tsang, P. Danielewicz, and Y. X. Zhang, Influence of transport variables on isospin transport ratios, Phys. Rev. C 84(5), 054603 (2011)
CrossRef ADS Google scholar
[49]
B. A. Li, P. Danielewicz, and W. G. Lynch, Probing the isospin dependence of the in-medium nucleon–nucleon cross sections with radioactive beams, Phys. Rev. C 71(5), 054603 (2005)
CrossRef ADS Google scholar
[50]
B. A. Li and L. W. Chen, Nucleon–nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies, Phys. Rev. C 72(6), 064611 (2005)
CrossRef ADS Google scholar
[51]
Z. Q. Feng, Nuclear in-medium effects and collective flows in heavy-ion collisions at intermediate energies, Phys. Rev. C 85(1), 014604 (2012)
CrossRef ADS Google scholar
[52]
W. M. Guo, G. C. Yong, Y. Wang, Q. Li, H. Zhang, and W. Zuo, Model dependence of isospin sensitive observables at high densities, Phys. Lett. B 726(1–3), 211 (2013)
CrossRef ADS Google scholar
[53]
S. A. Bass, C. Hartnack, H. Stöcker, and W. Greiner, Azimuthal correlations of pions in relativistic heavy-ion collisions at 1 GeV/nucleon, Phys. Rev. C 51(6), 3343 (1995)
CrossRef ADS Google scholar
[54]
Y. Wang, C. Guo, Q. Li, and H. Zhang, The effect of symmetry potential on the balance energy of light particles emitted from mass symmetric heavy-ion collisions with isotopes, isobars and isotones, Sci. China Phys. Mech. Astron. 55(12), 2407 (2012)
CrossRef ADS Google scholar
[55]
C. Guo, Y. Wang, Q. Li, W. Trautmann, L. Liu, and L. Wu, Influence of the symmetry energy on the balance energy of the directed flow, Sci. China Phys. Mech. Astron. 55(2), 252 (2012)
CrossRef ADS Google scholar
[56]
P. C. Li, Y. J. Wang, Q. F. Li, and H. F. 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)
CrossRef ADS Google scholar
[57]
P. C. Li, Y. J. Wang, Q. F. Li, and H. F. Zhang, Collective flow and nuclear stopping in heavy ion collisions in Fermi energy domain, Nucl. Sci. Tech. 29(12), 177 (2018)
CrossRef ADS Google scholar
[58]
P. Russotto, P. Z. Wu, M. Zoric, M. Chartier, Y. Leifels, R. C. Lemmon, Q. Li, J. Łukasik, A. Pagano, P. Pawłowski, and W. Trautmann, Symmetry energy from elliptic flow in 197Au+197Au, Phys. Lett. B 697(5), 471 (2011)
CrossRef ADS Google scholar
[59]
Y. Zhang, Z. Li, C. Zhou, and M. B. Tsang, Effect of isospin-dependent cluster recognition on the observables in heavy ion collisions, Phys. Rev. C 85(5), 051602 (2012)
CrossRef ADS Google scholar
[60]
K. Zbiri, A. L. Fèvre, J. Aichelin, J. Łukasik, W. Reisdorf, et al., Transition from participant to spectator fragmentation in Au+Au reactions between 60Aand 150AMeV, Phys. Rev. C 75(3), 034612 (2007)
CrossRef ADS Google scholar
[61]
Q. Li, Y. Wang, X. Wang, and C. Shen, Rapidity distribution of protons from the potential version of UrQMD model and the traditional coalescence afterburner, Sci. China Phys. Mech. Astron. 59, 622001 (2016)
CrossRef ADS Google scholar
[62]
W. Reisdorf and H. G. Ritter, Collective flow in heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 47(1), 663 (1997)
CrossRef ADS Google scholar
[63]
W. Reisdorf, et al. (FOPI Collaboration), Systematics of azimuthal asymmetries in heavy ion collisions in the regime, Nucl. Phys. A 876, 1 (2012)
[64]
U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 63(1), 123 (2013)
CrossRef ADS Google scholar
[65]
P. Danielewicz, R. Lacey, and W. G. Lynch, Determination of the equation of state of dense matter, Science 298(5598), 1592 (2002)
CrossRef ADS Google scholar
[66]
J. Y. Ollitrault, Flow systematics from SIS to SPS energies, Nucl. Phys. A 638(1–2), 195c (1998)
CrossRef ADS Google scholar
[67]
A. Andronic, J. Lukasik, W. Reisdorf, and W. Trautmann, Systematics of stopping and flow in Au+Au collisions, Eur. Phys. J. A 30(1), 31 (2006)
CrossRef ADS Google scholar
[68]
A. Andronic, et al. (FOPI Collaboration), Excitation function of elliptic flow in Au+Au collisions and the nuclear matter equation of state, Phys. Lett. B 612(3–4), 173 (2005)
[69]
A. Le Fèvre, Y. Leifels, C. Hartnack, and J. Aichelin, Origin of elliptic flow and its dependence on the equation of state in heavy ion reactions at intermediate energies, Phys. Rev. C 98(3), 034901 (2018)
CrossRef ADS Google scholar
[70]
Y. M. Zheng, C. M. Ko, B. A. Li, and B. Zhang, Elliptic flow in heavy-ion collisions near the balance energy, Phys. Rev. Lett. 83(13), 2534 (1999)
CrossRef ADS Google scholar
[71]
D. Persram and C. Gale, Elliptic flow in intermediate energy heavy ion collisions and in-medium effects, Phys. Rev. C 65(6), 064611 (2002)
CrossRef ADS Google scholar
[72]
T. Gaitanos, C. Fuchs, and H. H. Wolter, Nuclear stopping and flow in heavy-ion collisions and the in-medium NN cross section, Phys. Lett. B 609(3–4), 241 (2005)
CrossRef ADS Google scholar
[73]
B. A. Li and L. W. Chen, Nucleon–nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies, Phys. Rev. C 72(6), 064611 (2005)
CrossRef ADS Google scholar
[74]
M. Kaur and S. Gautam, Influence of the constant and density-dependent scaling of the scattering cross-section on reaction dynamics, J. Phys. G 43, 2, 025103 (2016)
CrossRef ADS Google scholar
[75]
B. Barker and P. Danielewicz, Shear viscosity from nuclear stopping, Phys. Rev. C 99, 034607 (2019)
CrossRef ADS Google scholar
[76]
Z. Basrak, P. Eudes, and V. de la Mota, Aspects of the momentum dependence of the equation of state and of the residual NN cross section, and their effects on nuclear stopping, Phys. Rev. C 93, 054609 (2016)
CrossRef ADS Google scholar
[77]
G. Lehaut, et al. (INDRA and ALADIN Collaborations), Study of nuclear stopping in central collisions at intermediate energies, Phys. Rev. Lett. 104(23), 232701 (2010)
CrossRef ADS Google scholar
[78]
W. Reisdorf, et al. (FOPI Collaboration), Nuclear stopping from 0.09Ato 1.93AGeV and its correlation to flow, Phys. Rev. Lett. 92(23), 232301 (2004)
[79]
W. Reisdorf, et al. (FOPI Collaboration), Systematics of central heavy ion collisions in the regime,Nucl. Phys. A 848(3–4), 366 (2010)
[80]
P. Li, Y. Wang, Q. Li, J. Wang, and H. Zhang, Effects of impact parameter filters on observables in heavy-ion collisions at INDRA energies, J. Phys. G 47(3), 035108 (2020)
CrossRef ADS Google scholar
[81]
Y. Wang, C. Guo, Q. Li, Z. Li, J. Su, and H. Zhang, Influence of differential elastic nucleon–nucleon cross section on stopping and collective flow in heavy-ion collisions at intermediate energies, Phys. Rev. C 94, 024608 (2016)
CrossRef ADS Google scholar
[82]
J. R. Stone, N. J. Stone, and S. A. Moszkowski, Incompressibility in finite nuclei and nuclear matter, Phys. Rev. C 89, 044316 (2014)
CrossRef ADS Google scholar
[83]
E. Khan and J. Margueron, Determination of the density dependence of the nuclear incompressibility, Phys. Rev. C 88, 034319 (2013)
CrossRef ADS Google scholar
[84]
E. Khan, J. Margueron, and I. Vidaña, Constraining the nuclear equation of state at subsaturation densities, Phys. Rev. Lett. 109(9), 092501 (2012)
CrossRef ADS Google scholar
[85]
J. J. Molitoris, D. Hahn, and H. Stöcker, Circumstantial evidence for a stiff nuclear equation of state, Nucl. Phys. A 447, 13 (1986)
CrossRef ADS Google scholar
[86]
J. J. Molitoris and H. Stöcker, Further evidence for a stiff nuclear equation of state from a transverse-momentum analysis of Ar(1800 MeV/nucleon) + KCl, Phys. Rev. C 32(1), 346 (1985)
CrossRef ADS Google scholar
[87]
H. Kruse, B. V. Jacak, and H. Stöcker, Microscopic theory of pion production and Sidewards flow in heavy-ion collisions, Phys. Rev. Lett. 54(4), 289 (1985)
CrossRef ADS Google scholar
[88]
J. Aichelin and C. M. Ko, Subthreshold Kaon production as a probe of the nuclear equation of state, Phys. Rev. Lett. 55(24), 2661 (1985)
CrossRef ADS Google scholar
[89]
H. Stöcker and W. Greiner, High energy heavy ion collisions — probing the equation of state of highly excited hardronic matter, Phys. Rep. 137(5–6), 277 (1986)
CrossRef ADS Google scholar
[90]
W. Cassing, V. Metag, U. Mosel, and K. Niita, Production of energetic particles in heavy-ion collisions, Phys. Rep. 188(6), 363 (1990)
CrossRef ADS Google scholar
[91]
C. Sturm, I. Böttcher, M. Dbowski, A. Förster, E. Grosse, P. Koczoń, B. Kohlmeyer, F. Laue, M. Mang, L. Naumann, H. Oeschler, F. Pühlhofer, E. Schwab, P. Senger, Y. Shin, J. Speer, H. Ströbele, G. Surówka, F. Uhlig, A. Wagner, and W. Waluś, Evidence for a soft nuclear equation-of-state from Kaon production in heavy-ion collisions, Phys. Rev. Lett. 86(1), 39 (2001)
CrossRef ADS Google scholar
[92]
C. Fuchs, A. Faessler, E. Zabrodin, and Y. M. Zheng, Probing the nuclear equation of state by K+ production in heavy-ion collisions, Phys. Rev. Lett. 86(10), 1974 (2001)
CrossRef ADS Google scholar
[93]
C. Hartnack, H. Oeschler, and J. Aichelin, Hadronic matter is soft, Phys. Rev. Lett. 96(1), 012302 (2006)
CrossRef ADS Google scholar
[94]
Z. Q. Feng, Constraining the high-density behavior of the nuclear equation of state from strangeness production in heavy-ion collisions, Phys. Rev. C 83(6), 067604 (2011)
CrossRef ADS Google scholar
[95]
A. Le Fèvre, Y. Leifels, W. Reisdorf, J. Aichelin, and C. Hartnack, Constraining the nuclear matter equation of state around twice saturation density, Nucl. Phys. A 945, 112 (2016)
CrossRef ADS Google scholar
[96]
J. Xu, L.-W. Chen, M. Y. B. Tsang, et al., Understanding transport simulations of heavy-ion collisions at 100Aand 400AMeV: Comparison of heavy-ion transport codes under controlled conditions, Phys. Rev. C 93, 044609 (2016)
CrossRef ADS Google scholar
[97]
M. Dutra, O. Lourenco, J. S. Sa Martins, A. Delfino, J. R. Stone, and P. D. Stevenson, Skyrme interaction and nuclear matter constraints, Phys. Rev. C 85(3), 035201 (2012)
CrossRef ADS Google scholar
[98]
Y. Wang, C. Guo, Q. Li, A. Le Fèvre, Y. Leifels, and W. Trautmann, Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4A–1.0AGeV, Phys. Lett. B 778, 207 (2018)
CrossRef ADS Google scholar
[99]
P. Russotto, et al., Results of the ASY-EOS experiment at GSI: The symmetry energy at suprasaturation density, Phys. Rev. C 94, 034608 (2016)
[100]
L. W. Chen, Higher order bulk characteristic parameters of asymmetric nuclear matter, Sci. China Phys. Mech. Astron. 54(S1), 124 (2011)
CrossRef ADS Google scholar
[101]
L. W. Chen, B. J. Cai, C. M. Ko, B. A. Li, C. Shen, and J. Xu, Higher-order effects on the incompressibility of isospin asymmetric nuclear matter, Phys. Rev. C 80(1), 014322 (2009)
CrossRef ADS Google scholar
[102]
B. A. Li, Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions, Phys. Rev. Lett. 88(19), 192701 (2002)
CrossRef ADS Google scholar
[103]
Z. Xiao, B. A. Li, L. W. Chen, G. C. Yong, and M. Zhang, Circumstantial evidence for a soft nuclear symmetry energy at suprasaturation densities, Phys. Rev. Lett. 102(6), 062502 (2009)
CrossRef ADS Google scholar
[104]
Z. Q. Feng and G. M. Jin, Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions, Phys. Lett. B 683(2–3), 140 (2010)
CrossRef ADS Google scholar
[105]
N. B. Zhang and B. A. Li, Extracting nuclear symmetry energies at high densities from observations of neutron stars and gravitational waves, Eur. Phys. J. A 55(3), 39 (2019)
CrossRef ADS Google scholar
[106]
W. J. Xie and B. A. Li, Bayesian inference of high-density nuclear symmetry energy from radii of canonical neutron stars, Astrophys. J. 883(2), 174 (2019)
CrossRef ADS Google scholar
[107]
Y. Zhou, L. Chen, and Z. Zhang, Equation of state of dense matter in the multimessenger era, Phys. Rev. D 99(12), 121301 (2019)
CrossRef ADS Google scholar
[108]
Y. Wang, C. Guo, Q. Li, and H. Zhang, 3H/3He ratio as a probe of the nuclear symmetry energy at sub-saturation densities, Eur. Phys. J. A 51, 37 (2015)
CrossRef ADS Google scholar
[109]
M. Di Toro, V. Baran, M. Colonna, and V. Greco, Probing the nuclear symmetry energy with heavy-ion collisions, J. Phys. G 37(8), 083101 (2010)
CrossRef ADS Google scholar
[110]
M. B. Tsang, Y. Zhang, P. Danielewicz, M. Famiano, Z. Li, W. G. Lynch, and A. W. Steiner, Constraints on the density dependence of the symmetry energy, Phys. Rev. Lett. 102, 122701 (2009)
CrossRef ADS Google scholar
[111]
M. B. Tsang, et al., Constraints on the density dependence of the symmetry energy, Int. J. Mod. Phys. E 19, 1631 (2010)
[112]
X. Lopez, et al. (FOPI Collaboration), Isospin dependence of relative yields of K+ and K0 mesons at 1.528AGeV, Phys. Rev. C 75, 011901(R) (2007)
[113]
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 (2011)
CrossRef ADS Google scholar
[114]
M. D. Cozma, Y. Leifels, W. Trautmann, Q. Li, and P. Russotto, Toward a model-independent constraint of the high-density dependence of the symmetry energy, Phys. Rev. C 88(4), 044912 (2013)
CrossRef ADS Google scholar
[115]
S. Kumar, Y. G. Ma, G. Q. Zhang, and C. L. Zhou, Sensitivity of neutron to proton ratio toward the high density behavior of the symmetry energy in heavy-ion collisions, Phys. Rev. C 85(2), 024620 (2012)
CrossRef ADS Google scholar
[116]
L. Lü, H. Yi, Z. Xiao, M. Shao, S. Zhang, G. Xiao, and N. Xu, Conceptual design of the HIRFL-CSR externaltarget experiment, Sci. China Phys. Mech. Astron. 60, 1, 012021 (2017)
CrossRef ADS Google scholar
[117]
P. Russotto, M. D. Cozma, A. Fèvre, Y. Leifels, R. Lemmon, Q. Li, J. Lukasik, and W. Trautmann, Flow probe of symmetry energy in relativistic heavy-ion reactions, Eur. Phys. J. A 50(2), 38 (2014)
CrossRef ADS Google scholar
[118]
W. J. Xie, J. Su, L. Zhu, and F. S. Zhang, Symmetry energy and pion production in the Boltzmann-Langevin approach, Phys. Lett. B 718(4–5), 1510 (2013)
CrossRef ADS Google scholar
[119]
Q. Li, Z. Li, S. Soff, R. K. Gupta, M. Bleicher, and H. Stöcker, Probing the density dependence of the symmetry potential in intermediate-energy heavy ion collisions, J. Phys. G 31(11), 1359 (2005)
CrossRef ADS Google scholar
[120]
Q. Li, Z. Li, E. Zhao, and R. K. Gupta, Σ−/Σ+ ratio as a candidate for probing the density dependence of the symmetry potential at high nuclear densities, Phys. Rev. C 71(5), 054907 (2005)
CrossRef ADS Google scholar
[121]
S. Gautam, A. D. Sood, R. K. Puri, and J. Aichelin, Isospin effects in the disappearance of flow as a function of colliding geometry, Phys. Rev. C 83(1), 014603 (2011)
CrossRef ADS Google scholar
[122]
M. B. Tsang, et al. (SRIT Collaboration), Pion production in rare-isotope collisions, Phys. Rev. C 95, 044614 (2017)
CrossRef ADS Google scholar
[123]
B. A. Li, L. W. Chen, F. J. Fattoyev, W. G. Newton, and C. Xu, Probing nuclear symmetry energy and its imprints on properties of nuclei, nuclear reactions, neutron stars and gravitational waves, J. Phys. Conf. Ser. 413, 012021 (2013)
CrossRef ADS Google scholar
[124]
L. W. Chen, Recent progress on the determination of the symmetry energy, arXiv: 1212.0284 [nucl-th] (2012)
[125]
H. Wolter, Proceedings of Science (Bormio2012), 059 (2012)
[126]
B. A. Li and X. Han, Constraining the neutron-proton effective mass splitting using empirical constraints on the density dependence of nuclear symmetry energy around normal density, Phys. Lett. B 727(1–3), 276 (2013)
CrossRef ADS Google scholar
[127]
P. Danielewicz and J. Lee, Symmetry energy II: Isobaric analog states, Nucl. Phys. A 922, 1 (2014)
CrossRef ADS Google scholar
[128]
X. Roca-Maza, M. Brenna, B. K. Agrawal, P. F. Bortignon, G. Colò, L. G. Cao, N. Paar, and D. Vretenar, Giant quadrupole resonances in 208Pb, the nuclear symmetry energy, and the neutron skin thickness, Phys. Rev. C 87(3), 034301 (2013)
CrossRef ADS Google scholar
[129]
B. A. Brown, Constraints on the skyrme equations of state from properties of doubly magic nuclei, Phys. Rev. Lett. 111(23), 232502 (2013)
CrossRef ADS Google scholar
[130]
Z. Zhang and L. W. Chen, Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness, Phys. Lett. B 726(1–3), 234 (2013)
CrossRef ADS Google scholar
[131]
N. Wang, M. Liu, L. Ou, and Y. Zhang, Properties of nuclear matter from macroscopic–microscopic mass formulas, Phys. Lett. B 751, 553 (2015)
CrossRef ADS Google scholar
[132]
X. Fan, J. Dong, and W. Zuo, Density-dependent symmetry energy at subsaturation densities from nuclear mass differences, Phys. Rev. C 89(1), 017305 (2014)
CrossRef ADS Google scholar
[133]
L. W. Chen, C. M. Ko, and B. A. Li, Light clusters production as a probe to nuclear symmetry energy, Phys. Rev. C 68(1), 017601 (2003)
CrossRef ADS Google scholar
[134]
L. W. Chen, C. M. Ko, and B. A. Li, Light cluster production in intermediate energy heavy-ion collisions induced by neutron-rich nuclei, Nucl. Phys. A 729(2–4), 809 (2003)
CrossRef ADS Google scholar
[135]
L. W. Chen, C. M. Ko, and B. A. Li, 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(5), 054606 (2004)
CrossRef ADS Google scholar
[136]
Q. Li, Z. Li, S. Soff, M. Bleicher, and H. Stöcker, Probing the density dependence of the symmetry potential at low and high densities, Phys. Rev. C. 72(3), 034613 (2005)
CrossRef ADS Google scholar
[137]
Y. Zhang and Z. Li, Probing the density dependence of the symmetry potential with peripheral heavy-ion collisions, Phys. Rev. C 71(2), 024604 (2005)
CrossRef ADS Google scholar
[138]
G. C. Yong, B. A. Li, L. W. Chen, and X. C. Zhang, Triton-3He relative and differential flows as probes of the nuclear symmetry energy at supra-saturation densities, Phys. Rev. C 80(4), 044608 (2009)
CrossRef ADS Google scholar
[139]
B. A. Li, Neutron–proton differential flow as a probe of isospin-dependence of the nuclear equation of state, Phys. Rev. Lett. 85(20), 4221 (2000)
CrossRef ADS Google scholar
[140]
V. Greco, V. Baran, M. Colonna, M. Di Toro, T. Gaitanos, and H. H. Wolter, Relativistic effects in the search for high density symmetry energy, Phys. Lett. B 562(3–4), 215 (2003)
CrossRef ADS Google scholar
[141]
W. Trautmann, M. Chartier, Y. Leifels, R. C. Lemmon, Q. Li, J. Łukasik, A. Pagano, P. Pawłowski, P. Russotto, and P. Wu, Differential neutron–proton squeeze– out, Prog. Part. Nucl. Phys. 62(2), 425 (2009)
CrossRef ADS Google scholar
[142]
W. Trautmann, et al., The symmetry energy in nuclear reactions, Int. J. Mod. Phys. E 19, 1653 (2010)
[143]
M. D. Cozma, Feasibility of constraining the curvature parameter of the symmetry energy using elliptic flow data, Eur. Phys. J. A 54, 40 (2018)
CrossRef ADS Google scholar
[144]
Y. Wang, Q. Li, A. Le Fèvre, and Y. Leifels, 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)
CrossRef ADS Google scholar
[145]
Y. X. Zhang, et al., Comparison of heavy-ion transport simulations: Collision integral in a box, Phys. Rev. C 97, 034625 (2018)
CrossRef ADS Google scholar
[146]
A. Ono, et al., Comparison of heavy-ion transport simulations: Collision integral with pions and Δ resonances in a box, Phys. Rev. C 100, 044617 (2019)
CrossRef ADS Google scholar
[147]
Y. F. Guo and G. C. Yong, High ptsqueezed-out n/p ratio as a probe of Ksym of the symmetry energy, Phys. Rev. C 100, 014617 (2019)
CrossRef ADS Google scholar
[148]
Y. F. Guo and G. C. Yong, Effects of curvature of the symmetry energy in Sn+Sn reactions at 270 MeV/nucleon, arXiv: 1909.13566 [nucl-th] (2019)
[149]
B. A. Li, Symmetry potential of the Δ(1232) resonance and its effects on the π−/π+ ratio in heavy-ion collisions near the pion-production threshold, Phys. Rev. C 92, 034603 (2015)
CrossRef ADS Google scholar
[150]
M. D. Cozma, Constraining the density dependence of the symmetry energy using the multiplicity and average pTratios of charged pions, Phys. Rev. C 95, 014601 (2017)
CrossRef ADS Google scholar
[151]
Z. Zhang and C. M. Ko, Medium effects on pion production in heavy ion collisions, Phys. Rev. C 95, 064604 (2017)
CrossRef ADS Google scholar
[152]
W. M. Guo, G. C. Yong, H. Liu, and W. Zuo, Effects of pion potential and nuclear symmetry energy on the π−/π+ ratio in heavy-ion collisions at beam energies around the pion production threshold, Phys. Rev. C 91, 054616 (2015)
CrossRef ADS Google scholar
[153]
W. M. Guo, G. C. Yong, and W. Zuo, Effect of Δ potential on the π−/π+ ratio in heavy-ion collisions at intermediate energies, Phys. Rev. C 92, 054619 (2015)
CrossRef ADS Google scholar
[154]
G. C. Yong, Modeling pion production in heavy-ion collisions at intermediate energies, Phys. Rev. C 96, 044605 (2017)
CrossRef ADS Google scholar
[155]
T. Song and C. M. Ko, Modifications of the pionproduction threshold in the nuclear medium in heavy ion collisions and the nuclear symmetry energy, Phys. Rev. C 91, 014901 (2015)
CrossRef ADS Google scholar
[156]
Q. Li and Z. Li, The isospin dependent nucleon–nucleon inelastic cross section in the nuclear medium, Phys. Lett. B 773, 557 (2017)
CrossRef ADS Google scholar
[157]
Q. Li and Z. Li, The density- and isospin-dependent Δ- formation cross section and its decay width, Sci. China Phys. Mech. Astron. 62, 972011 (2019)
CrossRef ADS Google scholar
[158]
Y. Cui, Y. Zhang, and Z. Li, In-medium NN→NΔ cross section and its dependence on effective Lagrange parameters in isospin-asymmetric nuclear matter, Chin. Phys. C 43, 024105 (2019)
CrossRef ADS Google scholar
[159]
Y. Cui, Y. Zhang, and Z. Li, The Δ mass dependence of the Mmatrix and its influence on the NΔ→NN cross-sections, Chin. Phys. C 44, 024106 (2020)
CrossRef ADS Google scholar
[160]
Y. Cui, Y. Zhang, and Z. Li, Effect of energy conservation on the in-medium NN ! NΔ cross section in isospinasymmetric nuclear matter, Phys. Rev. C 98, 054605 (2018)
CrossRef ADS Google scholar
[161]
W. M. Guo, G. C. Yong, and W. Zuo, Effects of nuclear symmetry energy and in-medium NN cross section in heavy-ion collisions at beam energies below the pion production threshold, Phys. Rev. C 90, 044605 (2014)
CrossRef ADS Google scholar
[162]
Y. Gao, G. C. Yong, L. Zhang, and W. Zuo, Influence of the nuclear symmetry energy on the collective flows of charged pions, Phys. Rev. C 97, 014609 (2018)
CrossRef ADS Google scholar
[163]
S. J. Cheng, G. C. Yong, and D. H. Wen, Effects of the symmetry energy in the 132Sn+124 Sn reaction at 300 MeV/nucleon, Phys. Rev. C 94, 064621 (2016)
CrossRef ADS Google scholar
[164]
B. A. Li and L. W. Chen, Neutron–proton effective mass splitting in neutron-rich matter and its impacts on nuclear reactions, Mod. Phys. Lett. A 30, 1530010 (2015)
CrossRef ADS Google scholar
[165]
W. J. Xie, J. Su, L. Zhu, and F. S. Zhang, Neutron–proton effective mass splitting in a Boltzmann–Langevin approach, Phys. Rev. C 88, 061601(R) (2013)
CrossRef ADS Google scholar
[166]
W. J. Xie, Z. Q. Feng, J. Su, and F. S. Zhang, Probing the momentum-dependent symmetry potential via nuclear collective flows, Phys. Rev. C 91, 054609 (2015)
CrossRef ADS Google scholar
[167]
Z. Q. Feng, Momentum dependence of the symmetry potential and its influence on nuclear reactions, Phys. Rev. C 84(2), 024610 (2011)
CrossRef ADS Google scholar
[168]
Z. Q. Feng, Nuclear dynamics and particle production near threshold energies in heavy-ion collisions, Nucl. Sci. Tech. 29, 40 (2018)
CrossRef ADS Google scholar
[169]
Z. Q. Feng, Effective mass splitting of neutron and proton and isospin emission in heavy-ion collisions, Nucl. Phys. A 878, 3 (2012)
CrossRef ADS Google scholar
[170]
V. Giordano, M. Colonna, M. Di Toro, V. Greco, and J. Rizzo, Isospin emission and flow at high baryon density: A test of the symmetry potential, Phys. Rev. C 81(4), 044611 (2010)
CrossRef ADS Google scholar
[171]
L. Y. Tong, P. C. Li, F. P. Li, Y. J. Wang, Q. F. Li, and F. X. Liu, Effects of the nucleon effective mass splitting and density-dependent symmetry energy on the elliptic flow in heavy ion collisions at Elab=0.09–1.5 GeV/nucleon, Chin. Phys. C (2020) (accepted)
[172]
O. Hen, B. A. Li, W. J. Guo, L. B. Weinstein, and E. Piasetzky, Symmetry energy of nucleonic matter with tensor correlations, Phys. Rev. C 91, 025803 (2015)
CrossRef ADS Google scholar
[173]
B. A. Li, W. J. Guo, and Z. Shi, Effects of the kinetic symmetry energy reduced by short-range correlations in heavy-ion collisions at intermediate energies, Phys. Rev. C 91, 044601 (2015)
CrossRef ADS Google scholar
[174]
H. L. Liu, G. C. Yong and D. H. Wen, Probing the momentum dependence of the symmetry potential by the free n/p ratio of pre-equilibrium emission, Phys. Rev. C 91, 024604 (2015)
CrossRef ADS Google scholar
[175]
G. C. Yong, Constraining nucleon high momentum in nuclei, Phys. Lett. B 765, 104 (2017)
CrossRef ADS Google scholar
[176]
G. C. Yong and B. A. Li, Interplay of short-range correlations and nuclear symmetry energy in hard-photon production from heavy-ion reactions at Fermi energies, Phys. Rev. C 96, 064614 (2017)
CrossRef ADS Google scholar
[177]
Z. X. Yang, X. H. Fan, G. C. Yong, and W. Zuo, Effects of the initialization of nucleon momentum in heavy-ion collisions at medium energies, Phys. Rev. C 98, 014623 (2018)
CrossRef ADS Google scholar
[178]
G. C. Yong, Probing proton transition momentum in neutron-rich matter, Phys. Lett. B 776, 447 (2018)
CrossRef ADS Google scholar
[179]
Z. X. Yang, X. L. Shang, G. C. Yong, W. Zuo, and Y. Gao, Nucleon momentum distributions in asymmetric nuclear matter, Phys. Rev. C 100, 054325 (2019)
CrossRef ADS Google scholar
[180]
B. A. Li, P. G. Krastev, D. H. Wen, and N. B. Zhang, Towards understanding astrophysical effects of nuclear symmetry energy, Eur. Phys. J. A 55, 117 (2019)
CrossRef ADS Google scholar
[181]
M. B. Tsang, W. G. Lynch, P. Danielewicz, and C. Y. Tsang, Symmetry energy constraints from GW170817 and laboratory experiments, Phys. Lett. B 795, 533 (2019)
CrossRef ADS Google scholar
[182]
L. Baiotti, Gravitational waves from neutron star mergers and their relation to the nuclear equation of state, Prog. Part. Nucl. Phys. 109, 103714 (2019)
CrossRef ADS Google scholar

RIGHTS & PERMISSIONS

2020 Higher Education Press
AI Summary AI Mindmap
PDF(1943 KB)

Accesses

Citations

Detail

Sections
Recommended

/