1. Nuclear Stopping and Nuclear Equation of State
Qingfeng Li
(Huzhou Teachers College)
湖州师范学院

2. Chifeng-Nuclear Structure & Quantum Mechanics
Outline
Motivation
Brief Introduction of the transport model and updates
Some results and discussions
Conclusion and outlook
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Chifeng-Nuclear Structure & Quantum Mechanics

3. Chifeng-Nuclear Structure & Quantum Mechanics
Motiviation
The uncertainties of the nuclear equation of state.
The global dynamic process of the nuclear reaction.
The close relationship with other observables such as the flow and the HBT correlation
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Chifeng-Nuclear Structure & Quantum Mechanics

4. Chifeng-Nuclear Structure & Quantum Mechanics
Motivation
Phys.Rev.Lett.97:052701,2006
By westen Michigen Uni.
What we are more sure
Science 298 (2002)
BHF
Skyrme
RMF
What we are not sure
The bottom plot was stolen from Zoran Basrak, :)
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Chifeng-Nuclear Structure & Quantum Mechanics

5. Puzzles have been shown
Z.Q. Feng, G.M. Jin, PL B683 (2010) 140
Phys. Rev. Lett. 102, , 2009
Supersoft or Stiff?
Dynamics of the whole process should be checked CAREFULLY
Anybody has his own judgment, but nobody makes it for 100% sure.
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Chifeng-Nuclear Structure & Quantum Mechanics

6. Chifeng-Nuclear Structure & Quantum Mechanics
More
From W. Reisdorf, et al. (FOPI Collaboration), ArXiv:
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7. Chifeng-Nuclear Structure & Quantum Mechanics
And …
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Chifeng-Nuclear Structure & Quantum Mechanics

8. Chifeng-Nuclear Structure & Quantum Mechanics
First glance of UrQMD
UrQMD : Ultra-relativistic Quantum Molecular Dynamics,
written mainly by the theoretical group in Frankfurt 10 years ago.
It is a non-equilibrium transport model
It includes 55 baryon species (with mass up to 2.25GeV) and 32 meson species (with mass up to 1.91GeV) . Hadrons are represented by Gaussian wave packets in phase space
Particles interact via:
- Mean Field modification Collisions (with measured and calculated cross sections) Particles produce via:
- Formation and decay of resonance
- Excitation and fragmentation of string
It provides full phase-space dynamics of heavy-ion collisions
It can be used to study HICs at energies from SIS to RHIC
The current version is v2.3. (
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9. And our progresses in the transport model UrQMD
Better description of the mean-field term (sym.pot., mom.dep., Mes.Coul., Relat.Eff., More Skyrme…)
Medium modified cross sections (Den.Dep., Mom.Dep.,Iso.Dep.,SplittingEff., …)
Mean-field potentials for “pre-formed” hadrons (from String fragmentation) …
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10. Our Recent Publications related to above progresses
Physical Review C 81 (2010)
Modern Physics Letters A 25 (2010) 669
Progress in Particle and Nuclear Physics 62 (2009) 425
Phys. Lett. B 674 (2009) 111
Mod. Phys. Lett. A 24 (2009) 41-51
J. Phys. G: Nucl. Part. Phys. 36 (2009)
Science in China Series G: Physics, Mechanics, Astronomy, 52 (2009) 1530
Phys. Lett. B 663 (2008)
Phys. Lett. B 659 (2008)
J. Phys. G: Nucl. Part. Phys. 34 (2007)
J. Phys. G: Nucl. Part. Phys. 34 (2007)
…Totally, about 20 publications
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11. Some interesting results
From PRC69, (2004)
From JPG32, 151 (2006)
Eb (A GeV)
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12. Constraints from Collective Flow: Neutron and Proton Elliptic Flow
197Au+197Au at 400 AMeV with LAND+FOPI (Phase 1)
neutron and proton flow measured in same detector (LAND)
UrQMD calculations of Q. Li et al.
symmetry energy parametrisation F(u) = u
 = 0.86  21 ( = 1.5 – stiff;  = 0.5 – soft)
Newest result: 1 0.3
From W. Trautmann
Partly from Prog. Part. Nucl. Phys. 62 (2009)425
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Chifeng-Nuclear Structure & Quantum Mechanics

13. Chifeng-Nuclear Structure & Quantum Mechanics
Cont’d
v2=<(px2-py2)/pt2>
v1=<px/pt>
From PRC74, (2006)
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14. To solve the HBT t-puzzle
From PLB659, 525(2008)
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15. Improvement to the mT-scaling
Left Plots:
Without “pre-formed” hadron potential:
RL: of kaons and Lambdas: Large
RO: of all particles : Large
RS: of Lambdas : Large
Right Plots:
With “pre-formed” Hadron potential:
RL: of Kaons and Lambda: follow
RO: of all particles : follow
RS: of pions and Kaons : follow
the mT-scaling
T.Csorgo etc, PRC 54, 1390(1996)
From PLB663, 395(2008)
Without the consideration of the FSI in hydro-dynamics
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16. Chifeng-Nuclear Structure & Quantum Mechanics
Nuclear Stopping
[e.g. CPL19, (2002) 321]
Conventionally, 1 2
Popularly,
(By FOPI/GSI, termed as vartl or varxz)
e.g., Phys. Rev. Lett. 92, (2004) 3
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17. Stiffness of EoS on vartl
The free nucleon-nucleon elastic cross sections are used.
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Chifeng-Nuclear Structure & Quantum Mechanics

18. Medium dependence of CS on vartl
=0.5
Based on RBUU approach
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Chifeng-Nuclear Structure & Quantum Mechanics

19. Chifeng-Nuclear Structure & Quantum Mechanics
Problems
The medium modifications of CS at low beam energies (50-250A MeV) (Stronger? Or?)
The pauli blocking effect on stopping
The (vanishing) flow at low beam energies (40-120A MeV)
The nuclear stopping at high beam energies (AGS/SPS/RHIC…)
The stability of nucleus (pauli blocking/pot., Gaussian wave package,…nuclear structure) on stopping at low energies ? ?
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20. Conclusion and Outlook
UrQMD has been successfully extended to the physics at SIS energies.
Global dynamics should be paid more attention. For example, the nuclear stopping should be checked for HICs at all beam energies.
At low and high beam energies, the nuclear stopping should be checked more carefully, from which one can dig deeper information of the basic transport process, beside exciting topics in our community.
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21. Thanks for patience liqf@hutc.zj.cn
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