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Three-pion correlations for studying partial coherence in nuclear collisions

Three-pion correlations for studying partial coherence in nuclear collisions. E. Ikonen Metrology Research Institute, Aalto University and Centre for Metrology and Accreditation (MIKES) Espoo, Finland. Contents. I. SOURCE MODELS FOR PARTICLES AND PHOTONS

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Three-pion correlations for studying partial coherence in nuclear collisions

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  1. Three-pion correlations for studying partial coherence in nuclear collisions E. Ikonen Metrology Research Institute, Aalto University and Centre for Metrology and Accreditation (MIKES) Espoo, Finland

  2. Contents I. SOURCE MODELS FOR PARTICLES AND PHOTONS Partial coherence in nuclear collisions? II. PARTICLE CORRELATIONS Three-particle correlations Multiple coherent components III. PHOTON CORRELATIONS IN OPTICS Coherent (free-electron laser) Incoherent (chaotic) IV. CONCLUSIONS

  3. Source current models for particles and photons Particles: M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys. Rev. C 20, 2267 (1979) => two-pion correlations of partially coherent source U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997) => three-pion correlations of partially coherent source (heavy ion collisions) coherent chaotic

  4. Source current models for particles and photons Particles: M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys. Rev. C 20, 2267 (1979) => two-pion correlations of partially coherent source U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997) => three-pion correlations of partially coherent source (heavy ion collisions) coherent chaotic multiple coherent components chaotic Photons: R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994) => analysis of free-electron laser (FEL)

  5. Source current models for particles and photons Particles: M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys. Rev. C 20, 2267 (1979) => two-pion correlations of partially coherent source U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997) => three-pion correlations of partially coherent source (heavy ion collisions) coherent chaotic multiple coherent components chaotic Photons: R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994) => analysis of free-electron laser (FEL) E. Ikonen, J. Opt. Soc. Am. B 21, 1403 (2004) => analysis of x-ray free-electron laser (XFEL) number of co-operating electrons in XFEL insertion device (collision of bunch of electrons with magnetic field of an undulator)

  6. Partial coherence in Au+Au collisions? J. Adams et al., Phys. Rev. Lett. 91, 262301 (2003). central collisions non-central collisions central collisions non-central collisions

  7. central collisions non-central collisions central collisions non-central collisions Partial coherence in Au+Au collisions? J. Adams et al., Phys. Rev. Lett. 91, 262301 (2003). r3/2 < 1 indicates partially coherent source (especially for non-central collisions)

  8. Challenges in extrapolation to zero momentum Conventional analysis method U. Heinz and A. Sugarbaker, Phys. Rev. C 70, 054908 (2004)

  9. Challenges in extrapolation to zero momentum Conventional analysis method Proposed analysis method (more realistic source model could produce larger deviation at low momentum difference) U. Heinz and A. Sugarbaker, Phys. Rev. C 70, 054908 (2004)

  10. Contents I. SOURCE MODELS FOR PARTICLES AND PHOTONS Partial coherence in nuclear collisions? II. PARTICLE CORRELATIONS Three-particle correlations Multiple coherent components III. PHOTON CORRELATIONS IN OPTICS Coherent (free-electron laser) Incoherent (chaotic) IV. CONCLUSIONS

  11. Three-particle correlations • Zero-momentum-difference • intercept R2(p, p) is affected by • - long-lived resonances • - particle misidentification • experimental binning effect • these effects are cancelled in the normalized three-particle correlation function r3 = R3(p, p, p) / [R2(p, p)]3/2 • where R3(p, p, p) is the zero-momentum-difference intercept • of genuine three-particle correlations

  12. Three-particle correlations R3(p, p, p) • Zero-momentum-difference • intercept R2(p, p) is affected by • - long-lived resonances • - particle misidentification • experimental binning effect • these effects are cancelled in the normalized three-particle correlation function r3 = R3(p, p, p) / [R2(p, p)]3/2 • where R3(p, p, p) is the zero-momentum-difference intercept • of genuine three-particle correlations H. Bøggild et al., Phys. Lett. B455, 77 (1999). fully incoherent fully coherent

  13. Au+Au collisions Normalized three-particle correlator r3/2 eliminates experimental difficulties in source coherence studies r3 = R3(p, p, p)/[R2(p, p)]3/2 r3/2 < 1 indicates partially coherent source (especially for non-central collisions) central collisions non-central collisions central collisions non-central collisions J. Adams et al., Phys. Rev. Lett. 91, 262301 (2003).

  14. Contents I. SOURCE MODELS FOR PARTICLES AND PHOTONS Partial coherence in nuclear collisions? II. PARTICLE CORRELATIONS Three-particle correlations Multiple coherent components III. PHOTON CORRELATIONS IN OPTICS Coherent (free-electron laser) Incoherent (chaotic) IV. CONCLUSIONS

  15. Examples of ”macroscopic coherence” milk drop bullet through apple forward splash backward splash From the HCP2009 talk by Axel Drees (Stony Brook University)

  16. Theory: E. Ikonen, PRC 78, 051901 (2008) multiple coherent components + chaotic component

  17. Theory: E. Ikonen, PRC 78, 051901 (2008) multiple coherent components + chaotic component

  18. Theory: E. Ikonen, PRC 78, 051901 (2008) multiple coherent components + chaotic component

  19. Data and models for S+Pb and Au+Au collisions Relation between r3/2 and R2(p, p)for different numbers N of coherent source components and related experimental data from S+Pb (Boggild et al) and Au+Au (Adams et al) collisions. central non-central

  20. Data and models for S+Pb and Au+Au collisions Relation between r3/2 and R2(p, p)for different numbers N of coherent source components and related experimental data from S+Pb (Boggild et al) and Au+Au (Adams et al) collisions. The result with a single coherent component, used in the analysis by Adams et al, is shown by the curve labeled N = 1. Tentatively, experimental data from S+Pb and Au+Au collisions seem to be in agreement with the curve N = 2 (or N = 3). central non-central

  21. Contents I. SOURCE MODELS FOR PARTICLES AND PHOTONS Partial coherence in nuclear collisions? II. PARTICLE CORRELATIONS Three-particle correlations Multiple coherent components III. PHOTON CORRELATIONS IN OPTICS Coherent (free-electron laser) Incoherent (chaotic) IV. CONCLUSIONS

  22. Pulsed photon correlations in XFEL multiple coherent components distance in undulator

  23. Simulation of free-electron laser operation R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).

  24. Simulation of free-electron laser operation electron bunch length electron co-operation length R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).

  25. Experimental FEL results Collision of bunch of electrons with the sinusoidal magnetic field of undulator T. Shintake et al., Nature Photon. 2, 555 (2008)

  26. Experimental FEL results Collision of bunch of electrons with the sinusoidal magnetic field of undulator A single-shot spectrum (blue solid curve) and averaged spectrum over 100 shots (red solid curve) T. Shintake et al., Nature Photon. 2, 555 (2008)

  27. Incoherent (chaotic) photon spectra Collision of bunch of electrons with the magnetic field of wiggler P. Catravas et al., Phys. Rev. Lett. 82, 5261 (1999)

  28. Si 1 1 1 beam splitter APD1 from mono- chromator APD2 moving slit Incoherent photon correlations (x rays) Si beam splitter dy

  29. Si 1 1 1 beam splitter APD1 from mono- chromator APD2 moving slit Incoherent photon correlations (x rays) Si beam splitter dy SPring-8, Japan

  30. C2/CB - 1 Si 1 1 1 beam splitter APD1 from mono- chromator APD2 moving slit Incoherent photon correlations (x rays) Si beam splitter dy Excess coincidences C2/CB - 1 E. Ikonen et al., Phys. Rev. A 74, 013816 (2006) SPring-8, Japan

  31. C2/CB - 1 Photon and particle correlations Zero-momentum-difference intercept R2(p, p) E. Ikonen et al., Phys. Rev. A 74, 013816 (2006)

  32. C2/CB - 1 Photon and particle correlations Zero-momentum-difference intercept R2(p, p) H. Boggild et al., Phys. Lett B 349, 386 (1995) E. Ikonen et al., Phys. Rev. A 74, 013816 (2006)

  33. C2/CB - 1 Photon and particle correlations HBT 1956 (light from Hg lamp and star Sirius) Zero-momentum-difference intercept R2(p, p) H. Boggild et al., Phys. Lett B 349, 386 (1995) E. Ikonen et al., Phys. Rev. A 74, 013816 (2006)

  34. Conclusions • A model of a fully incoherent contribution, combined with a single coherent component (N = 1), is used in conventional heavy-ion collision analyses

  35. Conclusions • A model of a fully incoherent contribution, combined with a single coherent component (N = 1), is used in conventional heavy-ion collision analyses • Another possibility is to have multiple coherent components (N > 1), combined with fully incoherent contribution (as used with free-electron lasers)

  36. Conclusions • A model of a fully incoherent contribution, combined with a single coherent component (N = 1), is used in conventional heavy-ion collision analyses • Another possibility is to have multiple coherent components (N > 1), combined with fully incoherent contribution (as used with free-electron lasers) • Tentatively, experimental data from S+Pb and Au+Au collisions support the concept of multiple coherent components

  37. Conclusions • A model of a fully incoherent contribution, combined with a single coherent component (N = 1), is used in conventional heavy-ion collision analyses • Another possibility is to have multiple coherent components (N > 1), combined with fully incoherent contribution (as used with free-electron lasers) • Tentatively, experimental data from S+Pb and Au+Au collisions support the concept of multiple coherent components • Three-pion correlation data from new experiments could give more information on the collision process

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