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