1. Light cluster coalescence production in heavy ion collisions
Lie-Wen Chen (陈列文)
(INPAC/Department of Physics, Shanghai Jiao Tong University.
Collaborators：
Che Ming Ko (TAMU)
Bao-An Li (TAMU-Commerce)
Kai-Jia Sun and Rui Wang (SJTU)
The 9th Workshop on QCD phase transitions and relativistic heavy ion collisions, Hangzhou, China, July 18-20, 2011

2. Outline Coalescence model
Light nucleus production in heavy-ion collisions at intermediate energies (IBUU+Coalescence):
Probing Symmetry Energy
Light nucleus production in heavy-ion collisions at RHIC/LHC (Blast-wave + Coalescence):
Extracting Freeze-Out Information
H-dibaryon production in heavy-ion collisions at RHIC(Blast-wave + Coalescence):
Testing QCD
Summary and outlook 1

3. 1. Coalescence model 2

4. Why coalescence?
Understanding particle production in heavy ion collisions at
different energy regions is among the fundamental questions
in nuclear physics.
Particle production in heavy ion collisions provides important
probe for the nuclear reaction dynamics
Coalescence model provides a useful tool to describe light
nucleus production in HIC’s
Coalescence model also provides a useful tool to describe
hadron production from partonic matter (hadronization) ……
Butler, Pearson, Sato, Yazaki, Gyulassy, Frankel, Remler, Dove, Scheibl, Heinz, Schnedermann, Mattiello, Nagle, Polleri, …
Biro, Zimanyi, Levai, Csizmadia, Hwa, Yang, Ko, Lin , Greco, Chen, Fries, Muller, Nonaka, Bass, Voloshin, Molnar, Xie, Shao, … 3

5. Dover/Heinz/Schnedermann/Zimanyi, PRC44, 1636 (1991)
Coalescence model
Covariant coalescence model
Dover/Heinz/Schnedermann/Zimanyi, PRC44, 1636 (1991)
Invariant phase-space factor
Wigner function
Phase-space distribution function
Statistical factor
Depends on constituents’ space-time structure at freeze-out (Reaction Dynamics)
Neglecting the binding energy effect (T or E >>Ebinding),
Coalescence probability: Semi-classical Wigner function. (Wave Function, Correlation)
Rare process has been assumed (the coalescence process can be treated perturbatively).
Higher energy collisions and higher energy cluster/particle production! 4

6. 2. Light nucleus production in heavy-ion collisions at intermediate energies (IBUU+Coalescence): Probing Symmetry Energy 5

7. Why light nucleus production?
The correlation between neutron and proton with small relative momentum
and deuteron formation both appear due to the final state interaction
(S. Mrowczynsky, PLB248 (1990), P. Danielewicz et al., PLB274 (1992))
The n-p pair in a scattering state with small relative momentum and
deuteron (n-p pair in a bound state) should provide the same space-time
information about the size of an emission source
Using stiff symmetry energy will produce more deuterons than using
soft symmetry energy?
Similarly to the n-p correlation function (HBT), is deutron yield in HIC’s induced by neutron-rich nuclei a sensitive probe of the nuclear symmetry energy???
Deutron: Chen/Ko/Li, PRC68, (2003); NPA729, 809 (2003)
n-p HBT: Chen/Greco/Ko/Li, PRL90, (2003); PRC68, (2003) 6

8. The nuclear matter symmetry energy
EOS of Isospin Asymmetric Nuclear Matter
(Parabolic law)
Symmetric Nuclear Matter
(relatively well-determined)
Symmetry energy term
(poorly known)
Isospin asymmetry
Li/Chen/Ko
Phys. Rep. 464, 113 (2008)
The Nuclear Symmetry Energy 7

9. Light nucleus production8

10. Light nucleus production
Wigner phase-space density for Deuteron
Wigner transformation
Hulthen wave function 9

11. Light nucleus production
Wigner phase-space density for t/3He
Assume nucleon wave function in t/3He can be described by the harmonic oscillator wave function, i.e.,
t/3He Wigner phase-space density and root-mean-square radius: 10

12. Freeze-out from Transport Theory
Transport Models
Ni + Au, E/A = 45 MeV/A
Transport Models for HIC’s at intermediate energies:
N-body approaches
CMD, QMD,IQMD,IDQMD,
ImQMD,ImIQMD,AMD,FMD
One-body approaches
BUU/VUU, BNV, LV, IBL
Relativistic covariant approaches
RVUU/RBUU,RQMD…
Central collisions
Broad applications of transport models
in astrophysics, plasma physics, electron transport in semiconductor and nanostructures, particle and nuclear physics, …… 11

13. Transport model for HIC’s
Isospin-dependent BUU (IBUU) model
Solve the Boltzmann equation using test particle method
Isospin-dependent initialization
Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections
a. Experimental free space N-N cross section σexp
b. In-medium N-N cross section from the Dirac-Brueckner
approach based on Bonn A potential σin-medium
c. Mean-field consistent cross section due to m*
Isospin-dependent Pauli Blocking
EOS 12

14. Transport model: IBUU04
Isospin- and momentum-dependent potential (MDI)
Das/Das Gupta/Gale/Li,
PRC67, (2003)
Chen/Ko/Li,
PRL94, (2005)
Li/Chen,
PRC72, (2005) 13

15. Light nucleus production
Isospin symmetric collisions at E/A≈100 MeV
Try Coalescence model
at intermediate energies!
Deuteron energy spectra
reproduced
Low energy tritons slightly
underestimated
Inverse slope parameter of
3He underestimated; probably
due to neglect of
larger binding effect
stronger Coulomb effect
wave function
Chen/Ko/Li, NPA729, 809 (2003)
Data are taken from INDRA Collaboration (P. Pawlowski, EPJA9) 14

16. Esym effects on light nucleus production
Chen/Ko/Li, PRC68, (2003)
Symmetry energy effects are about 51%, 73%, and 100% on deuteron,
triton and 3He yields with stiffer one producing more
Effects of isoscalar potential and NN cross sections small 15

17. Esym effects on t/3He ratio
Chen/Ko/Li, NPA729, 809 (2003)
Stiffer symmetry energy gives smaller t/3He ratio
With increasing kinetic energy, t/3He ratio increases for soft symmetry
energy but slightly decreases for stiff symmetry energy 16

18. Esym effects on t/3He ratio
Effects of momentum-dependence of nuclear potential
Chen/Ko/Li,
PRC69, (2004)
Stiffer symmetry energy gives smaller t/3He ratio 17

19. 3. Light nucleus production in heavy-ion collisions at RHIC (Blast-wave + Coalescence) Extracting Freeze-Out Information 18

20. Freeze-out: Blast-Wave Model
Anisotropic Blast-Wave Model
F. Retiere and M.A. Lisa, PRC70, (2004)
Boosted by the transverse rapidity
Blast-Wave Model:
Westfall, Bondorf, Garpman, and Zimanyi
Siemens, Rasmussen, Schnedermann, Huovinen,…… 19

21. Blast-wave for Protons from AuAu at RHIC
T=110 MeV
Rho0=0.9 20

22. V2 of light nuclei from AuAu at RHIC
Coalescence model predict very different v2 from blast wave model
Positive proton v2 can lead to negative v2 for d, t, 4He
Constituent nucleon number scaling is approximately satisfied 21

23. Protons from central AuAu at RHIC/LHC22

24. Light nuclei from central AuAu at RHIC
Preliminary results
3He: p+p+n,p+d
4He: p+p+n+n,
p+n+d
p+t,n+3He,d+d
Light nuclei yield is very sensitive to the freeze-out temperature
A freeze-out temperature of about 125 MeV can reasonably describe the data 23

25. Light nuclei from central PbPb at LHC
Preliminary results
Ebinding:
4He~28.3 MeV Li~32 MeV
Rms radius:
4He~1.68 fm Li~2.54 fm
9-D integral
15-D integral !
21-D integral !!
33-D integral !!!
anti-6Li/anti-4He is about 1/2E6 24

26. 4. H-dibaryon production in heavy-ion collisions at RHIC (Blast-wave + Coalescence) Testing QCD25

27. 26

28. 27

29. ~ 1/sqrt(2mLambdaEbinding)
Di-Lambda production from AuAu at RHIC
Preliminary results
Rms radius:
~ 1/sqrt(2mLambdaEbinding)
STAR
di-Lambda yield is larger than that of 3He but less than that of d 28

30. 5. Summary and outlook 29

31. Summary and Outlook
Coalescence model is a useful tool to describe the light nucleus
production at both medium and ultra-relativistic HIC’s, which
can be used to probe the nuclear symmetry energy and nucleon
freeze-out information
H-dibaryon yield at RHIC is between that of d and 3He
It is easy to extend “Blast-wave + Coalescence” to study the
(exotic) hadron production from QGP 30

32. 谢 谢！ Thanks!