Probing twoparticle sources in HIC

1
Probing two-particle sources in HIC
Giuseppe Verde, NSCL/Michigan State University
HIC03, Montreal, 25-28 June, 2003

• Outline
• p-p correlation functions physics information
  content
• Imaging
• Complex particle correlations (d-a), effects of
  collective flow
• Conclusions

2
HIC at intermediate energies
Probe nuclear equation of state (EoS)

• Volume, density, shape, lifetime of fragmenting
  system
• Probe reaction models (transport, dynamics/EoS)

• Find pace-time probes of the reaction Taking
  photographs

3
Intensity interferometry from large scales ...
Star
to subatomic physic scales (p-p, K-K, g-g,
p-p, n-n, IMF-IMF, )
G. Goldhaber et al., PR 120 (1960) 300
Detectors
Nuclear reaction
RVt
d gtgt R
Fast evolving systems 10-23-10-15 sec geometry
changing in time
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Measuring correlation functions
LASSA (IU, MSU, WU)
p-p
d-a
6Li2.19
6Li4.31
124Sn
E/A50 MeV/u
R(q) probes space-time properties of source
112Sn
5
Koonin-Pratt Eqn and Source function
S.E. Koonin, PLB70 (1977) 43 S.Pratt et al.,
PRC42 (1990) 2646
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Very-Long-Lived emitting sources
such as secondary decays, evaporation,
proton
proton
Source elongated up to
Directional correlation functions insensitive
7
Angle-averaged correlation functions

• Spherical symmetric Gaussian profiles extensively
  used

Gaussian spherical sources
8
Fast and slow emitting sources in HIC

• Low q region not accessible experimentally
  probing only fast source

Fast
Slow
Contribution from
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Size of two-proton sources
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Fast and slow d-a sources

• Size of fast source from width of peak 2

d-a source
d-a correlation
1
6Li (2.19)
1R(q)
S(r) (fm-3)
2
6Li (4.31)
r (fm)
q (MeV/c)
Peak 1 dominated by detector resolution
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p-p correlations physics information content
YtotalPre-eq. Sec. Decays Yfast
Yslow
G. Verde at al., PRC65, 054609 (2002)
Peak width (shape) Size (shape) of two-proton
fast source S(r)
G. Verde et al., PRC65, 054609 (2002)
1R(q)
Peak Height Relative contribution from fast
pre-eq. source Yfast/Ytotal
q (MeV/c)
Shape analysis required!
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Imaging two-proton sources
D.A. Brown, P. Danielewicz PRC57 (1998) 2474,
PRC64 (2001) 014902 G. Verde et al., PRC65 (2002)
054609
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14N197Au E/A75 MeV qave25o

• Imaging profile of the short-lived dynamical
  source
• size from r1/2
• relative contribution from long-t emissions

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Properties of two-proton sources

• r1/2 weakly sensitive to Psum size of fast
  dynamical sources
• Long-lifetime contributions 1-f strongly depend
  on Psum

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Imaging p-p correlations

• Profile of dynamical two-proton emitting source

• Size of emitting sources from peak width
  (shape), not from peak height!
• Measure densities

• Relative contributions from FAST and SLOW
  emitting sources
• Constraints on secondary decays

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Test of transport theories
G. Verde et al., Phys. Rev. C 67, 034606 (2003)
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Source shape probing transport models
G. Verde et al., Phys. Rev. C 67, 034606 (2003)
ArSc, E/A120 MeV
Shape of BUU source probes probes details about
sNN
Imaging
S(r) (fm-3)
Reduced sNN favored
r (fm)
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IBUU Isospin effects in p-p correlations
52Ca48Ca, 80 MeV/u

• Peak height sensitive to Vasy(r/r0) Shorter
  emission times for asy-stiff?
• Peak height not reliable (long-lifetime decays)

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IBUU Source shape and Asy-EOS
Lie-Wen Chen et al., nucl-th/0211002, Nov 2002
Sources
52Ca48Ca, 80 MeV/u
Pgt500 MeV/c

• Shape of peak sensitive to Asy-EOS
• Asy-soft more extended source, longer proton
  emission times
• Measure at qlt15 MeV/c required!!

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Isospin effects in Two-proton sources
Central collisions
Preliminary
Preliminary
LASSA

• Need more statistics and higher resolution
  (future experiments) explore the shape up to qlt8
  MeV/c
• Protons from secondary decays more in 112Sn112Sn

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Two-proton correlations in 112Sn112Sn and
124Sn124Sn
124Sn124Sn
124Sn124Sn
112Sn112Sn
1R(q)
1R(q)
112Sn112Sn
Fast protons
Slow protons
E1,E2gt60 MeV
E1,E2lt50 MeV
q (MeV/c)
q (MeV/c)
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Complex particle correlations

• Densities, fast/slow contributions, source
  profiles and test of reaction models

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d-a in 112Sn124Sn reactions
Sources
Central 112Sn124Sn, E/A50 MeV
d-a Size3.5-0.5
Size
1R(q)
S(r) (fm-3)
p-p Size5.5-0.5
LASSA
r (fm)
q (MeV/c)

• Good news d-a can probe long-lived emitting
  source
• Warning! Height of peak 2 overpredicted

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Collective motion requires special considerations

• Reduction of source size
• Shape of correlation functions between complex
  particles (d-a) strongly distorted.

25
Source size reduction
Size reduction enhanced with heavier particles
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Collective motion distortions
G. Verde et al., in prep.
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Effective temperature correction
G. Verde et al., in prep.
Nuclear part of correlation function needs
correction
No Flow
1R(q)
Flow
1R(q)
KP eq.
q (MeV/c)
Data reproduced for Teff5 MeV
q (MeV/c)
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Size correction p-p vs d-a
Central 112Sn124Sn, E/A50 MeV
Before correction
Source sizes p-p 5.5?0.2 fm d-a 3.5 ?0.5 fm
S(r) (fm-3)
p-p
d-a
After correction
Source sizes p-p 7.5?0.5 fm d-a 6 ?1 fm
S(r) (fm-3)
p-p
d-a

• Differences p-p vs d-a reduced
• p-p and d-a probe different sources

r (fm)
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Conclusions

• Important physics information from imaging of p-p
• size (from width/shape of correlation peak),
• contributions from dynamical/equilibrium
  emissions,
• profiles of dynamical sources (probes of
  microscopic models, BUU, IBUU, )
• Extension to more complex particle correlations
  (d-a)
• Effects of collective flow need special
  consideration (sizes, shape of nuclear resonance
  peaks)
• Two-particle correlations can provide snapshots
  of emitting sources
• and we actually need them!

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Acknowledgements

• D.A. Brown, LLNL
• P. Danielewicz, C.K. Gelbke, T.X. Liu, X.D. Liu,
  W.G. Lynch, W.P. Tan, M.B. Tsang, A.Wagner, H.S.
  Xu, NSCL/MSU
• B. Davin, Y. Larochelle, R.T. de Souza, IU
• R.J. Charity, L.G. Sobotka, WU