Acknowledgements

• NSCL/MSU (USA): P. Danielewicz, C.K. Gelbke, W.G. Lynch, M.B. Tsang, W.P. Tan, REU students

• INFN-Catania (Europe)

• LLNL (USA): D.A. Brown

• IU and WU (USA) :HiRA groups

• GANIL (Europe): A. Chbihi, J. Frankland

• Laval Univ. (Canada): F. Grenier, R. Roy

Our “femtoscopes”

1+R

(E* )

E*(MeV)

p-p

d-

-6Li

How to get sizes?

Different sizes from different particle species?

Role of (N/Z) degree of freedom?

Can we isolate and study exotic unbound states (astrophysics and physics at-and-beyond the drip lines)?

G. Verde at al., PRC65 (2002)

C(q

)=

Size (fm)

Wid

th (M

eV/c)

Our “femstoscopes” - How to use them?

q (MeV/c)

1+R

(q)

G. Verde et al., PRC65, 054609 (2002)

q (MeV/c) q (MeV/c)

1+R

(q)

p-p

d-

Size (fm)

Wid

th (M

eV/c)

1st Peak (resolution)

2nd Peak

Doing femtoscopy with Imaging (a.a.)

Source size

• Source size from peak shape/widthYtotal=Dynamical + Sec. Decays

Yfast + Yslow

Images of of the dynamically emitting source (pre-equil.)

Slow sources (Sec. decays)

14N+197Au E/A=75 MeV

P. Danielewicz, D.A. Brown

∫ ⋅⋅⋅= ),()(4)( 2 qrKrSrdrqR π

q e

G. V

erde et al., PR

C (20

02)

Output of imaging femtoscopy

7

54

2.53.1

2.9

Siz

e (f

m)

(Fast) Source Sizes

Total momentum

Lon

g-li

ved

sou

rce

(%)

Total momentum

Fast/Slow contributions

Probing the dynamical proton emitting source

No shape analyses

Probing dynamical sources in BUU Simaging(r) vs SBUU(r)

• Long-lived emissions not handled properly by BUU

BUU sources require renormalization

Imaging

Sou

rces

( )rSBUU

( ) ( )rSrS BUUBUU ⋅= λλ,

( )rSBUU⋅λ

Probing transport theoriesAr+Sc central

eq

r (fm)

S(r)

(fm

-3)

Imaging Data

BUU free NN

BUU red NN

Models

E/A=120 MeV

G. Verde et al., PRC (2003)

Isospin-dependent BUU (IBUU)Density dependence of the symmetry energy

Asy-StiffAsy-Soft

n/p emmission times

Correlation functions

neutron-neutron

proton-proton

proton-neutron0.0

0.5

1.0

1.5

1

2

3

4

1

3

5

7

q (MeV/c)

1+R

(q)

IBUU: 52Ca+48Ca E/A=80 MeV

Asy-Stiff

Asy-Soft

Neutron-proton correlation exps

1

2

3

4

neutron-proton

q (MeV/c)

1+

R(q

)

Asy-stiff

Asy-soft

112,124Sn+58,64Ni E/A=35 MeV

Neutrons

ProtonsLNS-Catania, INFN-Catania, INFN-Bari, Lund University

Protons

Neutrons

Future programs - higher resolution and efficiency? (GANIL, MSU, programs in progress)

Asy-BUU predictions

Difficult experiments - neutron detection!

n/p chronology, R. Ghetti et al.

p-p source shape and Asy-EOS

• Asy-soft: larger 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.)

p-p Sources

1+R

(q)

q (MeV/c)

Asy-stiff

Asy-soft

Correlations

Isospin effects in Two-proton sources

Central collisions Sources

Protons from secondary decays: more in 112Sn+112Sn

Preliminary

Preliminary

LASSA

112Sn+112Sn vs 124Sn+124Sn E/A=50 MeV, central

Isospin effects - energy gated correlations

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

•Need higher resolution

•Explore the shape at low q-values

Slow sources dominateDynamical sources dominate

HiRA@MSU - experiment in 2006 40,48Ca + 40,48Ca E/A=80 MeV

HiRA & MSU-4Correlation functions

Isotopic effects on high resolution correlation functions - low q-values measured

Extend to several particle species… but collective motion and event characterization need to be controlled (MSU 4)

Si strips X-Y CsI

Angular resolution !

Event characterization

Complex particles: HBT and nuclear thermometers

€

1+ R(q) =Ycoinc

Yuncor

Sensitive to geometry only

Correlation functionNumerator (coinc)

Sensitive to T: thermometer

d- correlations in pure-thermal models

Problems in reproducing the line shape of R(q)!

J. Pochodzalla et al., P

RC

35, 1695 (1987)

Effects of position-momentum correlations

• Apparent source size reduction

• Shape of correlation functions depends on both source size and temperature

More relevant for massive particles

Position - relative momentum correlations

Thermal

Thermal+Collective

Beamz

x

y

Elongated source in quasi-central events

Xe+Au collisions, E/A=50 MeV

€

vcoll = vrad

r

RZ

Comparison to data improves with

vrad ~ 0.1-0.2 c

and emission densities

~ 0.1-0.4

The correlation functions depends on the interplay temperature/collective motion !

Thermal onlyVrad=0

0.1

0.2

0.3

G. Verde et al., Physics Letters B, (2007), in press

T=4 MeV

Sizes/Densities from correlations

Higher densities from more energetic particles

p-p 0 ~ 0.5

d- 0 ~ 0-1-0.4

p-p sources more localized than d- sources!

Particle emission hierarchy (EES model, W. Friedman)

p-p d-

HIC as a spectroscopic tool• Several unbound states are produced in just one single HIC

experiment - reconstruct unbound species with correlations– Ex: 8B*---> p+7Be, 10C--->2p+2, etc.

Relative heights of peak heights sensitive to spin of 8Be states

LASSA data

W.P.Tan, PRC (2004)

States of 8B

p+7Be

0.774 (?)

1.4 (?)

2.32

8B

1+

3+

Sequential decay modes of 12C and 10C

• Peripheral collisions12C+24Mg E/A=53, 95 MeV (Indra@GANIL)

Decay of 12C and 10C quasi projectiles (QP*)

• 12C*--> part. correlations10C*--> +p+p 4-part. Correlations

Event mixingModified event mixing

3 correlation function - 12C* decays

E* = Ek + Q(12C-->3)

Sequential decay through 8Be contributes strongly 12C 8Be+ 2

Sequential decays

10C states excited states

Final state:

Always 2+2p

… but different paths are possible

10C 6Be+ (2p+)10C 8Be+p (+)p

10C 9B+p (+p)p

E* = Ek + Q(10C-->2p)

2+2p correlations - states in 10C

Evidence for sequential decays- 9B channel the most favored

F. Grenier, Laval Univ, PhD Thesis, 2006

F. Grenier, A. Chbihi, G. Verde et al., submitted

Ek(MeV)

9B+p8Be+2p

6Be+

High angular resolution experiment

Dedicated experiment with radioactive beams:

10C+9Bep+p+E/A=10.7 MeV

• HiRA: 4-body correlations

High high angular resolution

• Results in agreement with HIC experiment with stable beams!

Charity et al., PRC (R) (2007)

Conclusions

• Femtoscopes at intermediate energies• Imaging: sizes, probes of transport theories,

symmetry energy in Asy-EOS• Complex particles correlations: 1+R sensitive to both

Temperature and Volume (collective motion)• Multi-particle correlations in HIC as a spectroscopic

tool: Several nuclear exotic species in one single experiment!

• Femtoscopy/correlations require high resolution… but it is worth the money!

Tools to access dynamics/thermodynamics/structure

Detector:

•Three stage ΔE1-ΔE2-E - nTD Si-Si-CsI telescope

E2 used as a silicon det and as a photodiode for CsI(Tl)

•Pulse Shape Analysis in E1 nTD Silicon detector to extract Z and A with low thresholds

Full Digital Electronics

•On-line fast DSP / on-line calibration procedures

•Granularity and angular resolution

•Compactness, flexibility, transportability and… Neutrons capabilities(?)

Detector:

•Three stage ΔE1-ΔE2-E - nTD Si-Si-CsI telescope

E2 used as a silicon det and as a photodiode for CsI(Tl)

•Pulse Shape Analysis in E1 nTD Silicon detector to extract Z and A with low thresholds

Full Digital Electronics

•On-line fast DSP / on-line calibration procedures

•Granularity and angular resolution

•Compactness, flexibility, transportability and… Neutrons capabilities(?)

G.Poggi – XVColloque-Ganil-2006

CsI(Tl)H.I.

ΔE1 ΔE2

Si Si

300μm 700μm 30-100 mm

?

FAZIA - Four- A-Z Identif Array

•R&D phase (Working groups already active)

•Europe, India

Monolitic detector telescopes

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

E stage directly implemented on the E detector

Qu

ickTim

e™

an

d a

TIF

F (U

nco

mp

ress

ed

) decom

pre

sso

rare

need

ed

to s

ee th

is pictu

re.

• Very low identification thresholds (~300-400 AKeV for N isotopes!)

• Position sensitivity ~ 0.1 mm : high angular resolution

F. Amorini et al., INFN-LNS, Catania