1. Probing the high-density symmetry energy from particle production in heavy-ion collisions
Zhao-Qing Feng (冯兆庆)
Institute of Modern Physics (IMP), CAS
Collaboration with: Wen-Jie Xie (谢文杰) (IMP, CAS)
Jie Chen (IMP, CAS), Gen-Ming Jin (IMP, CAS)

2. Outline
Introduction
Model description: Lanzhou Quantum Molecular Dynamics (LQMD) transport model
Isospin, density and momentum dependent mean-field potentials
Particle production (pseudoscalar mesons(, , K), hyperons etc)
In-medium modifications on particle production
In-medium and isospin effects on particle production in heavy-ion collisions
Summary
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3. I. Introduction Symmetry energy : (0.50< < 1.20)
Isospin observables from proton (electron)-nucleus and heavy-ion collisions:
Proton-nucleus elastic scattering in inverse kinematics
n/p ratio of fast, pre-equilibrium nucleons
Double n/p ratios of isotopic reaction systems
Isospin fractionation and isoscaling in nuclear multifragmentation
Isospin diffusion/transport
Neutron-proton differential flow
Neutron-proton correlation functions at low relative momenta
t/3He ratio
Based on several complementary approaches with
available data
Esym(0)=32.5  2.5 MeV, L=5525 MeV
Lie-Wen Chen, Nucl. Phys. Rev. 273 (2014) 284
《原子核物理评论》
Refs: B. A. Li et al., Phys. Rep. 464 (2008) 113; Shetty et al., PRC75 (07) ; Tsang et al., PRL 102, (2009); C. Xu et al.,Phys Rev C 82 (2010)
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4. Symmetry energy ( > 1.20)
J. M. Lattimer and M. Prakash, Science 304, 536 (2004)
Symmetry energy ( > 1.20)
Isospin observables from heavy-ion collisions :
π -/π + ratio, K0/K+ ratio, -/+ ratio
Neutron-proton differential flow
Double n/p, π -/π + , K0/K+ ratios of isotopic systems
Nucleon elliptical flow at high transverse momenta
n/p ratio of squeeze-out emission 
The information of high-density symmetry energy is poorly known, which is of importance in understanding the structure of neutron star, supernova explosion etc.
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5. HIAF(High-Intensity Heavy Ion Accelerator Facility)
Heavy-ion accelerator systems at Institute of Modern Physics
Taken from Hong-Wei Zhao at IWND2014, Aug in Lanzhou
HIAF(High-Intensity Heavy Ion Accelerator Facility)
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6. II. Model description
Lanzhou Quantum Molecular Dynamics (LQMD) model: Nuclear dynamics from 5 MeV/nucleon – 10 GeV/nucleon for HICs, antiproton (proton, , K, etc)
Dynamics of low-energy heavy-ion collisions (dynamical interaction potential, barrier distribution, neck dynamics, fusion/caption excitation functions etc)
Isospin physics at intermediate energies (constraining nuclear symmetry energy at sub- and supra- saturation densities in HICs and probing isospin splitting of nucleon effective mass from HICs)
In-medium properties of hadrons in dense nuclear matter from heavy-ion collisions (extracting optical potentials, i.e., (1232), N*(1440), N*(1535)), hyperons (,,,) and mesons (,K,,,,), hypernucleus dynamics)
Hadron (antiproton, proton, , K) induced reactions (hypernucleus production, e.g., ()X, X, X, X(S=1), in-medium modifications of hadrons, cold QGP)
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7. The mean-field potential of nucleons
J. Aichelin et al., Phys. Rev. Lett. 58, 1926 (1987)
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8. Density, isospin and momentum-dependent single-nucleon potential in LQMD
Zhao-Qing Feng, Phys. Rev. C 84 (2011)
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10. Particle production in LQMD:
and resonances ((1232), N*(1440), N*(1535), ) production:
Collisions between resonances, NN*N, NN*NN*
Strangeness channels:
Reaction channels with antiproton:
Statistical model with SU(3) symmetry
(E.S. Golubeva et al., Nucl. Phys. A 537, 393 (1992))
Similar to the GiBUU model, the PYTHIA and FRITIOF code are used for baryon(meson)-baryon and antibaryon-baryon collisions at high invariant energies
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11. Mean-field potentials for resonances, hyperons and mesons
1. Mean-field potentials for resonances ((1232), N*(1440), ) are
considered based on nucleon potentials, but distinguishing isospin
E.g., U++= C Up(, p), U+= C (2Up(, p)/3 + Un(, p)/3)
U0 = C (Up(, p)/3 + 2Un(, p)/3), U-= C Un(, p)
The parameter C is used to get the phenomenological ansatz -30
MeV at = 0
2. Mean-field potentials for hyperons and antiprotons in nuclear medium
A factor ξ is introduced in evaluating self-energies of the antinucleon, e.g., ξ=0.25 for VNN= -160 MeV at  = 0
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13. Z. Q. Feng et al., Phys. Rev. C 92 (2015) 044604
3. Mean-field potentials for pion dynamics
z=1, 0, -1 for -, 0 and +
Evaluation of isoscalar
1) phenomenological ansatz
(C. Gale and J. Kapusta, Phys. Rev. C 35, 2107 (1987);
C. Fuchs et al., Phys. Rev. C 55, 411 (1997);
Z. Q. Feng, G. M. Jin, Phys. Rev. C 82, (2010))
2) -hole model (L. Xiong, C. M. Ko, V. Koch, Phys. Rev. C 47, 788 (1993);
C. Fuchs et al., Phys. Rev. C 55, 411 (1997))
Z. Q. Feng et al., Phys. Rev. C 92 (2015)
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14. Momentum and density dependence of the pion energy and the optical potential in dense nuclear matter
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15. The total number of pions is reduced with inclusion of the pion-nucleon potential. However, the π−/π+ ratio is enhanced!
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16. IV. Probing the high-density symmetry energy from particle production
1. Mid-rapidity nucleon emission in the 124Sn+124Sn reaction at incident energy of 400 MeV/nucleon (Z. Q. Feng, Phys. Lett. B 707 (2012) 83-87)
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17. Sensitive to symmetry energy!
DR(n/p)=
(n/p(124Sn+124Sn))/
(n/p (112Sn+112Sn))
Sensitive to symmetry energy!
Independent on mass splitting!
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18. 2. Nucleon collective flows
MeV/nucleon (Zhao-Qing Feng, Nuclear Physics A 878 (2012) 3-13)
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19. 197Au+197Au@400 MeV/nucleon, b=6 fm (Zhao-Qing Feng, Nuclear Physics A 878 (2012) 3-13)
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20. 3. Pion production near threshold energies in heavy-ion collisions
LQMD: Phys. Lett. B 683 (2010) 140
RBUU: PRL97 (2006)
IBUU04: PRL102(2009)062502
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21. Threshold effects of  production!
Taesoo Song, Che Ming Ko,
Phys. Rev. C 91, (2015)
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22. Pion-nucleon potential:
Jun Hong and P. Danielewicz, Phys. Rev. C 90, (2014) pBUU
Elab = 300 MeV/nucleon
LQMD
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23. Directed flows of charged pions in the 197Au+197Au reaction at an incident energy of 400 A MeV for semi-central (b = 6 fm) collisions
Zhao-Qing Feng, Phys. Rev. C 85, (2012)
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24. Impact factors on the pion dynamics in heavy-ion collisions near threshold energies:
1. Threshold energy corrections (-nucleon potential)
2. pion-nucleon potential
3. Reabsorption of  by surrounding nucleons
4. Reabsorption of pions by surrounding nucleons
5. In-medium decay width of 
6. Elastic scattering between  and nucleons   N  N
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25. 4. Isospin effects of strangeness produced in HICs
Z. Q. Feng, Nucl. Phys. A 919 (2013) 32-45
197Au+197Au
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26. VI. Summary
Nucleons squeezed out in the ‘fire ball’ are sensitive to the stiffness of symmetry energy, in particular PT distribution of n/p and double ratio, flow difference could be a nice experimental observables.
The -/+ and K0/K+ near threshold energies depend on symmetry energy. But the observables are related to the in-medium properties of ,  and K, e.g., mean-field potentials, production and reabsorption cross sections etc.
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