probing two-particle sources in hic giuseppe verde, nscl/michigan state university hic03, montreal,...
Post on 03-Jan-2016
214 Views
Preview:
TRANSCRIPT
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
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)
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
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
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
Very-Long-Lived emitting sources
Directional correlation functions insensitive
proton
proton
Detectors
… such as secondary decays, evaporation, …
Source elongated up to fmfmV 32 1010
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
• 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:
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)
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
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)
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)
• 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
• 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
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
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)
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)
• 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
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
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
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
Complex particle correlations1+R(E
* )
E*(MeV)
p-p
d-
-6Li
• Densities, fast/slow contributions, source profiles and test of reaction models
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
Collective motion requires special considerations
• Reduction of source size
• Shape of correlation functions between complex particles (d-) strongly distorted.
collth vvv
mTvth 3
Source size reduction
Only thermal motion
thvv
Detectors
Thermal + Collective motion
)(rvvv collth
Position-momentum correlations
Size reduction enhanced with heavier particles
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.
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.
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
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!
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
top related