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 Partial coherence in nuclear collisions?

II. PARTICLE CORRELATIONSThree-particle correlationsMultiple coherent components

III. PHOTON CORRELATIONS IN OPTICSCoherent (free-electron laser) Incoherent (chaotic)

IV. CONCLUSIONS

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


Particles:



coherent 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)

multiple coherent components

chaotic


Particles:



coherent 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)


chaotic

number of co-operating electrons in XFEL insertion device(collision of bunch of electrons with magneticfield of an undulator)

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

central collisions

non-central collisions

central collisions


r3/2 < 1 indicates partially coherent source (especially for non-central collisions)

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

central collisions


central collisions


Challenges in extrapolation to zero momentum

U. Heinz and A. Sugarbaker, Phys. Rev. C 70, 054908 (2004)

Conventional analysis method

Challenges in extrapolation to zero momentum

U. Heinz and A. Sugarbaker, Phys. Rev. C 70, 054908 (2004)

Conventional analysis method

Proposed analysis method

(more realistic source model could produce larger deviationat low momentum difference)

Contents




IV. CONCLUSIONS

Three-particle correlations

Zero-momentum-differenceintercept 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 interceptof genuine three-particle correlations

Three-particle correlations

H. Bøggild et al., Phys. Lett. B455, 77 (1999).

Zero-momentum-differenceintercept 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 interceptof genuine three-particle correlations

R3(p, p, p)

fully coherent

fully incoherent

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)

J. Adams et al., Phys. Rev. Lett. 91, 262301 (2003).

central collisions


Au+Au collisions

central collisions


Contents




IV. CONCLUSIONS

Examples of ”macroscopic coherence”

backward splash

bullet through apple

forward splash

milk drop

From the HCP2009 talk by Axel Drees (Stony Brook University)

Theory: E. Ikonen, PRC 78, 051901 (2008)

multiple coherent components + chaotic component

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.

Data and models for S+Pb and Au+Au collisions

central

non-central

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).

Data and models for S+Pb and Au+Au collisions

central

non-central

Contents




IV. CONCLUSIONS

Pulsed photon correlations in XFEL

distance in undulator


Simulation of free-electron laser operation

R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).

Simulation of free-electron laser operation

R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).

electron bunch length

electron co-operationlength

Experimental FEL results

T. Shintake et al., Nature Photon. 2, 555 (2008)

Collision of bunch of electrons with thesinusoidal magnetic field of undulator

Experimental FEL results

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)

Collision of bunch of electrons with thesinusoidal magnetic field of undulator

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)

Si 1 1 1 beam splitter

APD1

APD2moving slit

from mono-chromator

dy

Incoherent photon correlations (x rays)

Si beam splitter


APD1

APD2moving slit

from mono-chromator

dy


Si beam splitter

SPring-8, Japan


APD1

APD2moving slit

from mono-chromator

dy


Si beam splitter

Excess coincidences C2/CB - 1

C2/CB -

1

SPring-8, Japan

E. Ikonen et al., Phys. Rev. A 74, 013816 (2006)

Photon and particle correlations

Zero-momentum-differenceintercept R2(p, p)

C2/CB -

1



H. Boggild et al., Phys. Lett B 349, 386 (1995)


C2/CB -

1



H. Boggild et al., Phys. Lett B 349, 386 (1995)

HBT 1956(light from Hg lamp and star Sirius)


C2/CB -

1


Conclusions

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

Conclusions


• Another possibility is to have multiple coherent components (N > 1), combined with fully incoherent contribution (as used with free-electron lasers)

Conclusions



• Tentatively, experimental data from S+Pb and Au+Au collisions support the concept of multiple coherent components

Conclusions



• 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

Three-pion correlations for studying partial coherence in nuclear collisions

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