Unified description of nuclear stopping in central heavy-ion collisions from 10A MeV to 1.2A GeV

Yu-Gang MaShanghai INstitute of Applied Physics,

Chinese Academy of Sciences （ SINAP ， CAS ）Collaborated with

Guo-Qiang Zhang, Xi-Guang Cao, De-Qing Fang, Cheng-Long Zhou et al.

Comparison of the IQMD-simulations of heavy ion collisions with experimental data of INDRA&FOPI

Third International Conference on Nuclear Fragmentation From Basic Research to Applications October 2 - 9, 2011, Kemer (Antalya), Turkey

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Motivations:Constrain the properties of nuclear matter● NN cross-section from nuclear stopping● Nuclear EOS from nuclear stoppingStudy of transport phenomena in central HIC● Multifragmentation or the other?● Equilibrium stage being reached?

Outline:Background of nuclear stopping studiesNuclear EOS, EquilibriumINDRA Collaboration: Near Fermi energyFOPI Collaboration: 102 A MeV ~ A GeVCompare with IQMD● Describe nuclear stopping in different phase space● Stopping at event level and fragment level

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Motivations and outline

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Nuclear EOS From GMR

D. H. Youngblood, H. L. Clark, and Y.-W. Lui, Phys. Rev. Lett. 82, 691 (1999)

Giant Monopole Resonance

K0=231±5 MeV

0

22

0 0 2Incompressibility: K =9 ( ) d Ed

ρ ~ρ0

soft EOS!

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Nuclear EOS Kaon production

J. Aichelin and C. M. Ko, PRL55, 2661 (1985)

C. Fuchs et al, PRL86, 197(2001)

C. Hartnack, H. Oeschler, and J. Aichelin, PRL96, 012302 (2006)

A soft EOS is favoured!

1ρ0< ρ < 3ρ0

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Nuclear EOS from flows

Both in-plane flow and out-of-plane flow favor softer EOS (K~300MeV).

Danielewicz, P.; Lacey, R. & Lynch, W. G. Science, 2002, 298, 1592-1596

1.5ρ0< ρ < 7ρ0

stopping and flow

Left: pxdir @ b=5 fm (b/bmax=0.38)Right: yt and yl @b<2 fm ( b/bmax <0.15)

Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, 232301Andronic, A et al. Eur. Phys. J., 2006, A30, 31-46

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FOPI experiment

Scaled directed flow

The ratio of the transverse over longitudinal variances; vartl1, full stopping, equilibration

The EoS is a relation between pressure and density, it is understandable that the stopping & flow are related to the EoS: flow is generated by pressure gradients established in compressed matter, while the achieved density is connected to the degree of stopping.

Reisdorf, W. et al. Phys. Rev. Lett., 2004, 92, 232301Andronic, A et al. Eur. Phys. J., 2006, A30, 31-46

1. Peak at 400MeV/u for vartl & flow2. pxdir vs stopping: strong linear correl.3. Size dependent

stopping and flow

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FOPI experiment

A strong correlation exists between the stopping, measured in central collisions and the directedflow measured at impact parameters where it is maximal

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EOS from stopping in central HIC?

Isospin Equilibrium?

Dynamical Equilibrium?pz

pt

pz

ptNuclear Stopping

Isospin tracing Isospin diffusion/transparency

Multifragmentation?

EOS from nuclear stopping?

Bauer, W. Phys. Rev. Lett., 1988, 61, 2534-2537

Nuclear stopping in Momentum moment

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pz

pt

energy dependent centrality dependent size dependent

Qzz0, full stopping, equilibration

Alternative definition on nuclear stopping:

More works

T. Gaitanos et al., Phys. Lett. B595, 209 (2004). stopping, isospin equilibrationT. Gaitanos et al., Phys. Lett. B 609,241 (2005) . stopping, flow, viscosity, NN K. Zbiri et al., Phys. Rev. C75, 034612 (2007). BQMD FOPIFu, F. et al. Phys. Lett., B666, 359-363 (2008). stopping, compression, radial flow P. Danielewicz et al., AIP Conf. Proc. 1128, 104 (2009). BUU viscosity, NN X. G. Cao et al., Phys. Rev. C 81, 061603(R) (2010). Deformed nuclei, stopping, flow B.B. Back, et al., E917 Collaboration, Phys. Rev. Lett. 86, 1970(2001) AGS net-protonH. Appelshäuser, et al., NA49 Collaboration, Phys. Rev. Lett. 82,2471 (1999) SPS net-proton........

?

AGS

SPS

1. No full Equilibration!2. Low energy?3. Why?4. EOS from stopping?

Reisdorf, W. et al., Nucl. Phys., 2010, A848, 366-427 NUFRA2011 Turkey

Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701

INDRA experiment: stopping near Fermi energy

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Liu, J.-Y. et al., Phys. Rev. Lett., 2001, 86, 975

Momentum ratio in central HICIn nucleon phase space!

Liu IQMD isospin stopping

Symmetry energy && NN cross section112Sn+112Sn@100MeV/u

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Potentials in IQMD

Bethe Weizsaecker –mass formula:Volume term

(with eos)

+Surface term +Coulomb term +symmetry term(+pairing term not included)

2 and 3 body interactions (no equilibrium required)

Hartnack, C. et al. Eur. Phys. J., 1998, A1, 151-169; Nucl. Phys., 1989, A495, 303c-320c

EOS and NN cross section in IQMD

Hartnack, C. et al. Eur. Phys. J., 1998, A1, 151-169; Nucl. Phys., 1989, A495, 303c-320c

nn is the same as pp.

IQMD results: phase space

Nucleon phase space VS. Cluster phase space

Higher stopping in nucleon phase space (red line) comes from the istropic Fermi motion inside cluster !!!!

nucleon phase spacecluster phase space

NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

IQMD results: centrality

Mean~0.56 , width~0.42Mean~0.56 ,width~0.47

INDRA & ALADIN VS. IQMD

1. Cluster phase space in IQMD and experimental data can fit each other very well2. Impact parameter mixing is serious

129Xe+119Sn@50 MeV/u

NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701

IQMD results: time evolution

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Sn b

G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

Soft EOS is favored!

IQMD results: excitation function

1. Minimal at Fermi energy2. Maximal at 300MeV/u-400MeV/u3. EOS dependent! Soft EOS is favored4. System size dependent!5. Fluctuation

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Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

129Xe+120Sn

IQMD results: excitation function

1. Again soft EOS is favored!2. System size dependent! 3. Smaller system, less stopping, higher fluctuation!

NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

Data: Lehaut et. al, Phys. Rev. Lett., 2010, 104, 232701

Stopping at cluster level

1. The heavier fragment, the smaller stopping more transparency 2. Fermi energy, strongest entrance effect!3. Power law of Z-distribution @ Fermi energy4. Beam energy dependent!

NUFRA2011 Turkey G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612 (2011)

Stopping at cluster level

Reisdorf, W. et al., Nucl. Phys., 2010, A848, 366-427 1. The heavier fragment, the smaller stopping2. EOS dependent3. Beam energy dependent4. Fluctuations are still too large to constrain the definite EOS NUFRA2011 Turkey

?

G.Q. Zhang Y.G. Ma et al., Phys. Rev. C 84, 034612(11)

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Multifragmentation or fission or …

fusion and evaporation fusion-fission/multifragmentation vaporization

E

RE

Fermi Energy

σ(RE) RE /σ(RE)

Mean fieldOne-body motion

NN collisionTwo-body collision

Maximal Fluctuation at Fermi energy

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1. Maximal Fluctuation!

2. Nuclear stopping as L-G transition signal?

3. Experimental result?

Conclusions and outlooks

1. The wide-range excitation function of nuclear stopping from 10 MeV/u to 1.2 GeV/u can be described within IQMD.

2. Minimum at Fermi energy, and Maximum at 300-400MeV/u was observed, consistent with the data.

3. Apart from 300MeV/u-400MeV/u, no equilibration state is expected during intermediate energy HIC.

4. In very central HIC, near Fermi energy, there exists the strongest entrance channel effect.

5. Nuclear stopping shows EOS dependence (soft EOS is favored).

6.NN cross section is also likely to be determined.

7.Chemical equilibration? Isospin?

NUFRA2011 Turkey Thanks for your attention!