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Probing two-particle sources in HIC

d- a. 1+R(E * ). p-p. a - 6 Li. E * (MeV). Probing two-particle sources in HIC. Giuseppe Verde, NSCL/Michigan State University. HIC03, Montreal, 25-28 June, 2003. Outline p-p correlation functions: physics information content Imaging

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Probing two-particle sources in HIC

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  1. d-a 1+R(E*) p-p a-6Li E*(MeV) Probing two-particle sources in HIC Giuseppe Verde, NSCL/Michigan State University HIC03, Montreal, 25-28 June, 2003 • Outline • p-p correlation functions: physics information content • Imaging • Complex particle correlations (d-a), effects of collective flow • Conclusions

  2. Secondary decays Fragmentation Projectile Target Pre-equilibrium Compression Expansion Long time scales Short time scales HIC at intermediate energies Probe nuclear equation of state (EoS) • Volume, density, shape, lifetime of fragmenting system • Probe reaction models (transport, dynamics/EoS) • Find pace-time probes of the reaction:… Taking “photographs”

  3. HBT: R. Hanbury Brown, R.Q. Twiss, Phil. Mag., Ser. 7 45 (1954) 663 R d << R Static systems: exploring the geometry (size, R) Intensity interferometry: from large scales ... Star … to subatomic physic scales (p-p, K-K, g-g, p-p, n-n, IMF-IMF, …) G. Goldhaber et al., PR 120 (1960) 300 Detectors Nuclear reaction R+Vt d >> R Fast evolving systems: 10-23-10-15 sec: geometry changing in time

  4. 1+R(q) 1+R(q) q (MeV/c) q (MeV/c) Measuring correlation functions LASSA (IU, MSU, WU) p-p d-a 6Li2.19 6Li4.31 124Sn E/A=50 MeV/u R(q) probes space-time properties of source 112Sn

  5. = Source function Probability distribution of emitting a pair separated by • when last particle is emitted • If (not simultaneous) Space-time ambiguity in Directional correlations to reduce space-time ambiguity… … only if r0 Koonin-Pratt Eqn and Source function S.E. Koonin, PLB70 (1977) 43 S.Pratt et al., PRC42 (1990) 2646

  6. Detectors Very-Long-Lived emitting sources … such as secondary decays, evaporation, … proton proton Source elongated up to Directional correlation functions insensitive

  7. Angle-averaging over 14N+197Au E/A=75 MeV q~25o r0=3.4 fm 4.2 5.9 “Common wisdom”… R(20 MeV/c) Size Angle-averaged correlation functions • Spherical symmetric Gaussian profiles extensively used Gaussian spherical sources

  8. Proton emission: Fast Slow Fast: Pre-equilibrium Slow: Evaporation, Secondary Decays Fast and slow emitting sources in HIC • Low q region not accessible experimentally: probing only fast source Fast Slow Contribution from:

  9. G. Verde at al., PRC65, 054609 (2002) Slope~ 2.7 MeV/c/fm Width – FWHM (MeV/c) C(q)= Size (r0) • Width (not height!!) of peak at 20 MeV/c measures uniquely the size of the source Size of two-proton sources

  10. Peak 2 Peak width (MeV/c) Peak 1 Size (fm) Fast and slow d-a sources • Size of fast source from width of peak 2 d-a source d-a correlation 1 6Li (2.19) 1+R(q) S(r) (fm-3) 2 6Li (4.31) r (fm) q (MeV/c) Peak 1 dominated by detector resolution

  11. p-p correlations: physics information content Ytotal=Pre-eq. + Sec. Decays Yfast + Yslow G. Verde at al., PRC65, 054609 (2002) Peak width (shape) Size (shape) of two-proton fast source S(r) G. Verde et al., PRC65, 054609 (2002) 1+R(q) Peak Height Relative contribution from fast pre-eq. source Yfast/Ytotal q (MeV/c) Shape analysis required!

  12. KP Eqn Source Function Imaging = Inverting 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 two-proton sources D.A. Brown, P. Danielewicz PRC57 (1998) 2474, PRC64 (2001) 014902 G. Verde et al., PRC65 (2002) 054609

  13. r0 (fm)= 3.4 4.2 5.9 Zero-lifetime Gaussian sources Imaging 14N+197Au E/A=75 MeV qave~25o • Imaging: profile of the short-lived dynamical source • size from r1/2 • relative contribution from long-t emissions:

  14. Source Sizes Long-lived contributions 7 5 1-f (%) r1/2(fm) 4 3.1 2.5 2.9 Properties of two-proton sources • r1/2 weakly sensitive to Psum: size of fast dynamical sources • Long-lifetime contributions 1-f strongly depend on Psum

  15. Imaging p-p correlations • Profile of dynamical two-proton emitting source • Size of emitting sources – from peak width (shape), not from peak height! • Measure densities • Relative contributions from FAST and SLOW emitting sources • Constraints on secondary decays

  16. BUU sin-med Height of the peak not reproduced Long-lived emissions not handled correctly BUU sfree Ar+Sc Imaging analysis • Constraints contributions from secondary decays with f-value Test of transport theories G. Verde et al., Phys. Rev. C 67, 034606 (2003)

  17. Model BUU red NN BUU free NN Source shape: probing transport models G. Verde et al., Phys. Rev. C 67, 034606 (2003) Ar+Sc, E/A=120 MeV Shape of BUU source probes probes details about sNN Imaging S(r) (fm-3) Reduced sNN favored r (fm)

  18. Lie-Wen Chen et al., nucl-th/0211002, Nov 2002 Asy-stiff Asy-stiff Asy-soft Vasy(MeV) 1+R(q) Asy-soft r/r0 q (MeV/c) IBUU: Isospin effects in p-p correlations 52Ca+48Ca, 80 MeV/u • Peak height sensitive to Vasy(r/r0): Shorter emission times for asy-stiff? • Peak height not reliable (long-lifetime decays)

  19. Asy-stiff Asy-soft r1/2~4.4 fm 1+R(q) Asy-soft S(r) (a.u.) Asy-stiff r1/2~3.6 fm q (MeV/c) r (MeV/c) IBUU: Source shape and Asy-EOS Lie-Wen Chen et al., nucl-th/0211002, Nov 2002 Sources 52Ca+48Ca, 80 MeV/u P>500 MeV/c • Shape of peak sensitive to Asy-EOS • Asy-soft: more extended source, longer proton emission times • Measure at q<15 MeV/c required!!

  20. Sources Isospin effects in Two-proton sources Central collisions Preliminary Preliminary LASSA • 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

  21. Two-proton correlations in 112Sn+112Sn and 124Sn+124Sn 124Sn+124Sn 124Sn+124Sn 112Sn+112Sn 1+R(q) 1+R(q) 112Sn+112Sn Fast protons Slow protons E1,E2>60 MeV E1,E2<50 MeV q (MeV/c) q (MeV/c)

  22. d-a p-p 1+R(E*) a-6Li E*(MeV) Complex particle correlations • Densities, fast/slow contributions, source profiles and test of reaction models

  23. d-a in 112Sn+124Sn reactions Sources Central 112Sn+124Sn, E/A=50 MeV d-a Size~3.5+-0.5 Size 1+R(q) S(r) (fm-3) p-p Size~5.5+-0.5 LASSA r (fm) q (MeV/c) • Good news: d-a can probe long-lived emitting source • Warning! Height of peak 2 overpredicted

  24. Collective motion requires special considerations • Reduction of source size • Shape of correlation functions between complex particles (d-a) strongly distorted.

  25. Thermal + Collective motion Only thermal motion Position-momentum correlations Detectors Source size reduction Size reduction enhanced with heavier particles

  26. Event mixing Event a Yields Coincidence Event b 1+R(Erel) Correlation Erel (MeV) Collective motion distortions G. Verde et al., in prep.

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

  28. Size correction: p-p vs d-a Central 112Sn+124Sn, E/A=50 MeV Before correction Source sizes p-p 5.50.2 fm d-a 3.5 0.5 fm S(r) (fm-3) p-p d-a After correction Source sizes p-p 7.50.5 fm d-a 6 1 fm S(r) (fm-3) p-p d-a • Differences p-p vs d-a reduced • p-p and d-a probe different sources r (fm)

  29. 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-a) • 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!

  30. 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

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