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-   - 6 Li 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) Width (MeV/c) Our “femstoscopes” - How to use them? q (MeV/c) 1+R(q) G. Verde et al., PRC65, (2002) q (MeV/c) 1+R(q) p-p d-  Size (fm) Width (MeV/c) 1 st Peak (resolution) 2 nd Peak

Doing femtoscopy with Imaging (a.a.) Source size Source size from peak shape/width Y total =Dynamical + Sec. Decays Y fast + Y slow Images of of the dynamically emitting source (pre-equil.) Slow sources (Sec. decays) 14 N+ 197 Au E/A=75 MeV P. Danielewicz, D.A. Brown qe G. Verde et al., PRC (2002)

Output of imaging femtoscopy Size (fm) (Fast) Source Sizes Total momentum Long-lived source (%) Total momentum Fast/Slow contributions Probing the dynamical proton emitting source No shape analyses

Probing dynamical sources in BUU S imaging (r) vs S BUU (r) Long-lived emissions not handled properly by BUU BUU sources require renormalization

Probing transport theories Ar+Sc central e q 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-Stiff Asy-Soft n/p emmission times Correlation functions neutron-neutron proton-proton proton-neutron q (MeV/c) 1+R(q) IBUU: 52 Ca+ 48 Ca E/A=80 MeV Asy-Stiff Asy-Soft

Neutron-proton correlation exps neutron-proton q (MeV/c) 1+R(q) Asy-stiff Asy-soft 112,124 Sn+ 58,64 Ni E/A=35 MeV Neutrons Protons LNS-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-stiff r 1/2 ~3.6 fm Asy-soft r 1/2 ~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 collisionsSources Protons from secondary decays: more in 112 Sn+ 112 Sn Preliminary LASSA 112 Sn+ 112 Sn vs 124 Sn+ 124 SnE/A=50 MeV, central

Isospin effects - energy gated correlations q (MeV/c) 1+R(q) E 1,E 2 >60 MeVE 1,E 2 <50 MeV 124 Sn+ 124 Sn 112 Sn+ 112 Sn 124 Sn+ 124 Sn 112 Sn+ 112 Sn Need higher resolution Explore the shape at low q-values Slow sources dominate Dynamical sources dominate

- experiment in ,48 Ca + 40,48 Ca E/A=80 MeV HiRA & MSU-4  Correlation 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 Sensitive to geometry only Correlation function Numerator (coinc) Sensitive to T: thermometer

d-  correlations in pure-thermal models Problems in reproducing the line shape of R(q)! J. Pochodzalla et al., PRC35, 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

Beam z x y Elongated source in quasi-central events Xe+Au collisions, E/A=50 MeV Comparison to data improves with v rad ~ c and emission densities  ~   The correlation functions depends on the interplay temperature/collective motion ! Thermal only V rad = 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 ~ 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: 8 B*---> p+ 7 Be, 10 C--->2p+2 , etc. Relative heights of peak heights sensitive to spin of 8 Be states LASSA data W.P.Tan, PRC (2004) States of 8 B p+ 7 Be (?) 1.4 (?) B8B

Sequential decay modes of 12 C and 10 C Peripheral collisions 12 C+ 24 MgE/A=53, 95 MeV Decay of 12 C and 10 C quasi projectiles (QP*) 12 C*-->  part. correlations 10 C*-->  +p+p4-part. Correlations

Event mixing Modified event mixing 3  correlation function - 12 C* decays E* = E k + Q( 12 C-->3  ) Sequential decay through 8 Be contributes strongly 12 C  8 Be+   2  Sequential decays

10 C states excited states Final state: Always 2  +2p … but different paths are possible 10 C  6 Be+   (2p+  )  10 C  8 Be+  p   (  +  )  p 10 C  9 B+p   (  +  p)  p

E* = E k + Q( 10 C-->2  p) 2  +2p correlations - states in 10 C Evidence for sequential decays - 9 B channel the most favored F. Grenier, Laval Univ, PhD Thesis, 2006 F. Grenier, A. Chbihi, G. Verde et al., submitted E k (MeV) 9 B+p 8 Be+2p 6 Be+ 

High angular resolution experiment Dedicated experiment with radioactive beams: 10 C+ 9 Be  p+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. ΔE1ΔE2 Si 300μm 700μm mm ? FAZIA - Four-  A-Z Identif Array R&D phase (Working groups already active) Europe, India

Monolitic detector telescopes  E stage directly implemented on the E detector Very low identification thresholds (~ AKeV for N isotopes!) Position sensitivity ~ 0.1 mm : high angular resolution F. Amorini et al., INFN-LNS, Catania