1. Space-time characterization in a complex dynamical system
Projectile
Target
Expansion
Fragmentation
Secondary decays
t ~ fm/c
~ s
t~ fm/c
~ s and more
Pre-equilibrium
Compression g
r/r0~1.5?
r/r0~0.3?
Different particles produced by different sources/densities/times
What achievements?

2. We have tools to… measure distances as small as 10-15 m
measure times as short as sec

3. Observables  Physics
Dynamics
Space-time properties
LP-LP correlation functions (g, n, p, d, t, 3He, 4He)
Giuseppe Verde
IMF-IMF correlation functions
Arnaud Le Fevre
LP-IMF correlation functions
Abdou Chbihi
Size, shape, lifetime, densities
Disentangle different sources
Images of emitting sources
Probes of reaction models
Chronology of emissions
Thermodynamics
Internal excitation energy
Internal emission temperatures
Structure
Spin of unbound states
Halo nuclei, exotic decay modes

4. Light-particle correlations
C. Schwartz, GSI
proton-proton 1 2
Detector
Emitting Source
Sensitive to space-time properties of the emitting system 5 2
< Z
< 4 4 B 3 d l e i y 2 c o i n c i d e n c e s 1 m i x e d e v e n t s 1 . 3
S.E. Koonin, PL 70B (1977) 43
S. Pratt et al., PRC 36 (1987) 2390
D.H. Boal et al., RMP 62 (1990) 553
W.G. Gong et al., PRC 43 (1991)
W. Bauer et al., ARNPS (1992)
U. Heinz et al., ARNPS 49 (1999) 1 . 2 ) q 1 . 1 ( R + 1 . 1 . 9 . 8 2 4 6 8 1 q ( M e V / c )
Bosonic/Fermionic nature of 1 and 2
Symmetrization/Anti-symmetrization of y
Final State Interactions
Coulomb (repulsive, long-range ~ )
Nuclear (attractive, short-range ~ 1-2 fm)

5. Koonin-Pratt Eqn and Source function
S.E. Koonin,
PLB70 (1977) 43
S.Pratt et al.,
PRC42 (1990) 2646
Kernel =
= Source function Probability distribution of emitting a pair separated by
when last particle is emitted
If (not simultaneous)
Space-time ambiguity in
S. Pratt, PRL
53 (1984) 1219
S. Pratt et al.,
PRC (1987) 2390 r0

6. Directional correlation functions: sizes and lifetimes

7. Directional correlations: size-lifetime
S. Pratt, PRL
53 (1984) 1219
S. Pratt et al.,
PRC (1987) 2390 r0
Effect of the anti-symmetrization of y
Ar+Sc E/A=80 MeV, Central
M. Lisa et al., PRL71 (1993) 2863
D.O. Handzy et al., PRC50 (1994)
Reduce space-time ambiguity if
20-25 fm
It means the following. If there is a lifetime effect in the emission of the two proton that cannot be considered simultaneous, then we must expect that the two particle source is more elongated in the direction parallel to the direction of the total momentum of the pair. This longitudinal direction contains the information about the lifetime of the emission while the transverse direction contains mainly the information about the space portion of the separation. What one can do is to study directional correlations and build the correlation function for the pairs with P parallel to q and the one with P perpendicular to q. These two correlation functions will be different. The difference is due to the Pauli exclusion prinsiple that will suppress the correlation when the total momentum is perpendicular to the relative momentum.
By studying the correlations in this way you can decouple the space and time information. But there are some limitation to be taken into account.
First of all these studies require a lot of statistics (so they are not easy). And then, however, they are able to reduce the space-time ambiguity if R(q) is not dominated by fast pre-equilibrium emissions and only if …
But this not the case unfortunately for heavy ion collisions at intermediate energies.

8. Size and lifetimes in spectator matter
C. Schwartz, ALADiN
Aladin data
<E0>/<A0> increasing  Size Decreasing
Size relevant to nuclear caloric curves
Zbound, Size

9. s Chi2 test Directional analysis dominated by dynamical stage ?
C. Schwartz, ALADiN: 1000 MeV/u – Target spectators
0<Z
<20
20<Z
<40
40<Z
<60
60<Z
<79
bound
bound
bound
bound 10 9 9 8 8 7 6
(fm) 7 5
uniform 4 R 6 3 2 5 s 1 4 10 20 30 10 20 30 10 20 30 10 20 30 40 t
(fm/c)
Gaussian
Emission times are short
comparable with
passing time of spectator
Directional analysis dominated by dynamical stage ?
tp-p ≤ 20 fm/c
b = 0.87 c
2*6.5 fm
Dt=15 fm/c
R ~ 8 fm  r/r0 ~ (?)

10. FOPI @ GSI – central collisions
Ru(Zr) + Ru(Zr) @ 400 MeV/u, Central
Angle-averaged correlations
Directional correlations
Eur. Phys. J. A 6, 185 (1999)
Dominated by short-lived component
very short t

11. Secondary decays, evaporation… …very Long-Lived emitting sources
Detectors
proton
Source elongated up to
Directional correlation functions not sensitive to very long-lived emissions

12. Directional correlation functions: size and lifetime
p-p extensively studied
Short lifetimes (t ≤ 25fm/c)
Dominated by dynamical sources (secondary decays out of the game)

13. A clear probe of early dynamical stage: Direct hard photons
Pre-equilibrium
TAPS data
r/r0~1.5?
t ~ fm/c
~ s
np  npg Bremsstrahlung

14. Hard photons & pre-equilibrium protons (MEDEA)
Common features:
source velocity bsource= bN-N
Large inverse slope parameter
mean multiplicity  surface of the overlap region: same impact parameter dependence
44A MeV Ar+V
photons
Inverse slope:
~ 14 MeV
44A MeV Ar+V
protons
photons
Overlap surface Mg
protons
Overlap surface
1+Rg-p
If energetic protons and g are produced in first chance nucleon-nucleon collisions in the overlap region at the very beginning of the reaction
P. Sapienza et al. PRL73 (1994) 1769

15. Hard g-g intensity interferometry
Bose-Einstein correlations (no mutual interactions and no interactions with the medium)
E>25-30 MeV
qrel (MeV/c)
1+R(qrel)
1+R(E1-E2) 50
100
150
E1-E2 (MeV)
TAPS, M. Marques et al., PRL73 (1994) 34
Kr+Ni, 60 MeV/u
MEDEA, A. Badala’ et al., PRL74 (1995) 4779
Ar+Al, 95 MeV/u
Space and Time disentangled (analysis difficult)
Rrms ~ 1.73 ± 0.86 fm ~ Roverlap ~ 1.9 fm
t ~ 5 fm/c

16. Angle-averaged correlation functions: sizes and densities

17. Angle-averaged correlation functions
Angle-averaging over
14N+197Au E/A=75 MeV q~25o
Spherically symmetric Gaussian profiles extensively used
r0=3.4 fm
High Psum
(Fast protons)
4.2
Peak Height Size
5.9
Low Psum
(Slow protons)
W.G. Gong et al., PRC41 (1991) 71
W.G. Gong et al., PRC43 (1991) 1804 …

18. Systematics of gaussian sizes
Target=197Au
Proj
(AP)
r0 (fm)
Vp/Vbeam
Pre-equlibrium
Long t
AP=3
AP~15
AP=40
3He
14N,16O
40Ar
What happens when long-lived emitting sources dominate?

19. Angle-averaged correlation functions
Gaussian sizes extensively used: peak height to extract source size
Difficult to reproduce the shape of correlation functions
Understand better long-lifetime emissions

20. Shape analysis Imaging and its physics

21. p-p correlations: physics information
q (MeV/c)
1+R(q)
G. Verde et al., PRC65, (2002)
Ytotal=Pre-eq. + Sec. Decays Yfast Yslow
Peak width (shape)
Size (shape) of two-proton fast source S(r)
Peak Height
Relative contribution from fast pre-eq. source Yfast/Ytotal
Shape analysis required!

22. Imaging: high precision shape analyses
D.A. Brown
P. Danielewicz
Ytotal=Pre-eq. + Sec. Decays Yfast Yslow
Fast source profiles
… photographs
Model-independent size
Contributions from pre-equilibrium and secondary decays

23. Properties of two-proton sources7 5 4
2.5
3.1
2.9
Size (fm)
1-f (%)
Source Sizes
Long-lived contributions
Model independent sizes
Imaging provides also the relative contributions fast/slow

24. Imaging and its physics
Shape analysis required to measure the size/density of dynamical source
Relative contributions from dynamical/secondary decay sources
New Experiments (high resolution)

25. Densities in central collisions -FOPI
Lifetimes very short (from directional correlations)
Densities
r/r0 ~ 0.3  0.6
Not taking into account the effects of collective flow (ex.: shrinking of emitting source, …)
Shape??
R. Kotte et al, EPJ A23, 2005

26. Densities in target spectators
Aladin data
C. Schwartz, ALADiN
t ~ 25 fm/c !
Zbound, Size
Different particles  Different densities

27. Densities (waiting for a shape analysis)
Densities of ~ r0…, but in a very short time < 20 fm/c ?
Different particles probe different emitting sources?

28. Systematics of Correlation Measurements: p-p vs d-a
p-p correlations
Vp /Vbeam
d correlations
Vp /Vbeam
Zhu et al., PRC, R582 (1991)
Radii ~ 30%
Smaller than pp
Different particles might come from different emitting sources
What about imaging?

29. Extending imaging to complex particles
1+R(E*)
E*(MeV)
p-p
d-a
a-6Li
Access space-time properties at the break-up stage
Different particles probe different emitting sources and densities
Isotopically resolved IMF-IMF correlations
~200 KeV
LASSA Data

30. Imaging for complex particles
Imaging for complex particles... Collective motion requires special considerations
…especially for heavier particles
Reduction of source size
Shape of correlation functions between complex particles strongly distorted.

31. Collective distortions
G. Verde et al., in prep.
Nuclear part of correlation function needs correction
q (MeV/c)
1+R(q)
No Flow
Flow
KP eq.
Data reproduced for Teff=5 MeV

32. Probes of reaction models
Exp correlation functions vs microscopic models predictions (BUU, QMD)
Imaging:
Correct for contributions from long-lived emissions
Compare directly the profiles of the emitting source. Sensitivity to details of sNN,in-medium

33. Emission Chronology

34. Emission Chronology (non-identical particles)
if emission time delay…
(suppose p first) P1 P1 P1 P1
Vp > Vn
Vp< Vn P2 P2
... difference in correlation !
R. Ghetti & J. Helgesson

35. Emission chronology
D. Gourio et al., INDRA - Eur. Phys. J. A 7, 245 (2000)
PLF in Xe+Sn at 50 MeV/u
Chronology of emission p-d: td<tp
R. Kotte et al., FOPI - Eur. Phys. J. A 6, 185 (1999)
Results depend on space-time ambiguity
R. Ghetti et al. - PRL (2003)
Chronology of n and p emission!!

36. Neutron-proton chronology KVI – Ar + Al @ 61 MeV
Backward enhances dynamical source emission for reversed kinematics
Backward
Forward
n < p
p < n
R. Ghetti & J. Helgesson
Ghetti et al, PRL 91 (2003)

37. Chronology and Asy-EOS
n-p relative emission times depend on stiffness of symmetry energy
Ghetti et al, PRC 69 (2004)
neutron-proton
Lie-Wen Chen et al., PRL (2003)
Some indications of isospin effects in E/A=61 MeV
More exclusive measurements required

38. Conclusions and perspectives
p-p correlations: space-time properties of early dynamical sources.
Imaging analyses (1D and 3D) required to deduce reliable densities and lifetimes.
High resolution experiments required – event characterization necessary.
Emission chronology: promising probe of Asy- EOS. n-n, n-p, p-p, and isotopically resolved IMF-IMF