probing two-particle sources in hic giuseppe verde, nscl/michigan state university hic03, montreal,...
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Probing two-particle sources in HICGiuseppe Verde, NSCL/Michigan State University
HIC03, Montreal, 25-28 June, 2003
1p 2p
1+R(E
* )
E*(MeV)
p-p
d-
-6Li
Outline
• p-p correlation functions: physics information content
• Imaging
• Complex particle correlations (d-), effects of collective flow
• Conclusions
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HIC at intermediate energies
ProjectileTarget Pre-equilibrium
Compression Expansion Fragmentation
Secondary decays
Short time scales Long time scales
Probe nuclear equation of state (EoS)
• Find pace-time probes of the reaction:… Taking “photographs”
• Volume, density, shape, lifetime of fragmenting system
• Probe reaction models (transport, dynamics/EoS)
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Intensity interferometry: from large scales ...Star
R
d << R
Static systems: exploring the geometry (size, R)
HBT: R. Hanbury Brown, R.Q. Twiss, Phil. Mag., Ser. 7 45 (1954) 663
… to subatomic physic scales (, K-K, , p-p, n-n, IMF-IMF, …)
Fast evolving systems: 10-23-10-15 sec: geometry changing in time
DetectorsNuclear reaction
d >> RR+V
G. Goldhaber et al., PR 120 (1960) 300
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Measuring correlation functions
112Sn
22112112 )(1, pYpYqRppY
R(q) probes space-time properties of source
d p
p
1+R
(q) 1+
R(q)
q (MeV/c) q (MeV/c)
p-p d-6Li2.19
6Li4.31
LASSA (IU, MSU, WU)
124Sn
E/A=50 MeV/u
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Koonin-Pratt Eqn and Source functionS.E. Koonin, PLB70 (1977) 43S.Pratt et al., PRC42 (1990) 2646
rdqRqCPP
1)(1)( ),( rqK
)(rS
P
212
1ppq
21 ppP
21 rrr
• = Source function
Probability distribution of emitting a pair separated bywhen last particle is emitted
)(rSP
• If (not simultaneous)21 tt Space-time ambiguity in )(rSP
Directional correlations to reduce space-time ambiguity… … only if
r0
VrRL 0
P
fmVr 200
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Very-Long-Lived emitting sources
Directional correlation functions insensitive
proton
proton
Detectors
… such as secondary decays, evaporation, …
Source elongated up to fmfmV 32 1010
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Angle-averaged correlation functionsP
q
1p
2p
Angle-averaging over
• Spherical symmetric Gaussian profiles extensively used
20
2 2/exp)( rrrS
r0=3.4 fm
4.2
5.9
14N+197Au E/A=75 MeV ~25o
Gaussian spherical sources
“Common wisdom”…
R(20 MeV/c) Size
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• Low q region not accessible experimentally: probing only fast source
Fast and slow emitting sources in HIC
f1)(0
cr
rdrS
Fast SlowSlowFastTOT YYY Proton emission:
Fast: Pre-equilibriumTOTFAST YfY
Slow: Evaporation, Secondary Decays
TOTSLOW YfY )1(
1Fast SlowContribution from:
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Size of two-proton sources
• Width (not height!!) of peak at 20 MeV/c measures uniquely the size of the source
20
23
0
2/exp2
)( rrr
rS
1)( 2 frdrS
G. Verde at al., PRC65, 054609 (2002)
Slope~ 2.7 MeV/c/fmC(q)=
Size (r0)
Wid
th – F
WH
M (M
eV/c)
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Fast and slow d- sources
1+R
(q)
S(r
) (f
m-3)
r (fm) q (MeV/c)
d- source d- correlation
slowfast SSrS )(
2
1
Pea
k w
idth
(M
eV/c
)Size (fm)
Peak 2
Peak 1
• Size of fast source from width of peak 2
6Li (2.19)
6Li (4.31)
Peak 1 dominated by detector resolution
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q (MeV/c)
1+R
(q)
p-p correlations: physics information content
Ytotal=Pre-eq. + Sec. Decays Yfast + Yslow
Peak HeightRelative contribution from fast pre-eq. source Yfast/Ytotal
Peak width (shape)Size (shape) of two-proton fast source S(r)
G. Verde et al., PRC65, 054609 (2002)
Shape analysis required!
G. Verde at al., PRC65, 054609 (2002)
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Imaging two-proton sourcesD.A. Brown, P. Danielewicz PRC57 (1998) 2474, PRC64 (2001) 014902G. Verde et al., PRC65 (2002) 054609
drrrSrqKqRqC 2
0)(),(41)(1)(
Source FunctionImaging = Inverting KP Eqn )(rS
KP Eqn
• Model independent and multi-dimensional approach
All the points deviating from 1 contain information about S(r), not only C(q=20 MeV/c)
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• Imaging: profile of the short-lived dynamical source size from r1/2
relative contribution from long- emissions:
14N+197Au E/A=75 MeV ave~25o
Imaging
3.4
4.2
5.9
r0 (fm)=
Zero-lifetimeGaussian sources
frdrScr 1)(1
0
3
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• r1/2 weakly sensitive to Psum: size of fast dynamical sources
• Long-lifetime contributions 1-f strongly depend on Psum
Properties of two-proton sources
7
54
2.53.1
2.9
r 1/2(f
m)
f
)/( cMeVPsum )/( cMeVPsum
Source Sizes Long-lived contributions
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Imaging p-p correlations
• Relative contributions from FAST and SLOW emitting sources
Constraints on secondary decays
• Size of emitting sources – from peak width (shape), not from peak height!
Measure densities
• Profile of dynamical two-proton emitting source
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Test of transport theories
• Constraints contributions from secondary decays with f-value
Imaging analysis
Height of the peak not reproduced
Long-lived emissions not
handled correctly
Ar+Sc
BUU in-med
BUU free
G. Verde et al., Phys. Rev. C 67, 034606 (2003)
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Source shape: probing transport models
Shape of BUU source probes probes details
about NN
r (fm)
S(r)
(fm
-3)
Imaging
BUU free NN
BUU red NN
Model
Ar+Sc, E/A=120 MeV
Reduced NN favored
G. Verde et al., Phys. Rev. C 67, 034606 (2003)
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• Peak height sensitive to Vasy(0): Shorter emission times for asy-stiff?
• Peak height not reliable (long-lifetime decays)
0
Vas
y(M
eV)
Asy-soft
Asy-stiff
Lie-Wen Chen et al., nucl-th/0211002, Nov 2002
1+R
(q)
q (MeV/c)
Asy-stiff
Asy-soft
IBUU: Isospin effects in p-p correlations52Ca+48Ca, 80 MeV/u
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IBUU: Source shape and Asy-EOS
• Shape of peak sensitive to Asy-EOS
• Asy-soft: more extended source, longer proton emission times
• Measure at q<15 MeV/c required!!
Asy-stiffr1/2~3.6 fm
Asy-softr1/2~4.4 fm
r (MeV/c)
S(r
) (a
.u.)1+
R(q
)
q (MeV/c)
Asy-stiff
Asy-soft
SourcesLie-Wen Chen et al.,nucl-th/0211002, Nov 2002
52Ca+48Ca, 80 MeV/u
P>500 MeV/c
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Isospin effects in Two-proton sourcesCentral collisions Sources
• Need more statistics and higher resolution (future experiments): explore the shape up to q<8 MeV/c
• Protons from secondary decays: more in 112Sn+112Sn
Preliminary
Preliminary
LASSA
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Two-proton correlations in 112Sn+112Sn and 124Sn+124Sn
q (MeV/c) q (MeV/c)
1+R
(q)
1+R
(q)
E1,E2>60 MeV E1,E2<50 MeV
124Sn+124Sn
112Sn+112Sn
124Sn+124Sn112Sn+112Sn
Fast protons Slow protons
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Complex particle correlations1+R(E
* )
E*(MeV)
p-p
d-
-6Li
• Densities, fast/slow contributions, source profiles and test of reaction models
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d-in 112Sn+124Sn reactions
q (MeV/c)
1+R
(q)
Central 112Sn+124Sn, E/A=50 MeV
S(r
) (f
m-3)
r (fm)
p-p Size~5.5+-0.5
d-Size~3.5+-0.5
Sources
• Good news: d- can probe long-lived emitting source
• Warning! Height of peak 2 overpredicted
LASSA
2,0
22,0
2 2/exp2/exp)()()( slowslowfastfastslowfast rrrrrSrSrS
Size
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Collective motion requires special considerations
• Reduction of source size
• Shape of correlation functions between complex particles (d-) strongly distorted.
collth vvv
mTvth 3
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Source size reduction
Only thermal motion
thvv
Detectors
Thermal + Collective motion
)(rvvv collth
Position-momentum correlations
Size reduction enhanced with heavier particles
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Collective motion distortions
Yie
lds
Coincidence
Event mixing
TErel /exp
mixrel TE /exp
Erel (MeV)
1+R
(Ere
l)
Correlation
effrel TE /exp
TTT mixeff 111
Event b3v
collectivethermalrel vvv
13,
collv
collv
Event a
1v
2v
thermalrel vv
12,
G. Verde et al., in prep.
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Effective temperature correction
effrelNucl
FlowNoNuclFlow TEqRR exp)(
q (MeV/c)
1+R
(q)
q (MeV/c)
1+R
(q)
No Flow
Flow
Nuclear part of correlation function needs correction
Data reproduced for Teff=5 MeV
KP eq.
G. Verde et al., in prep.
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Size correction: p-p vs d-S
(r)
(fm
-3)
S(r
) (f
m-3)
r (fm)
d-
d-
p-p
p-p
Before correction
Source sizes
p-p 5.50.2 fmd-0.5 fm
After correction
Source sizes
p-p 7.50.5 fmd-1 fm
• Differences p-p vs d- reduced• p-p and d- probe different sources
Central 112Sn+124Sn, E/A=50 MeV
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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-)
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