Correlation functions and characterization of emitting sources. A. Chbihi GANIL

Transcription

1 Correlation functions and characterization of emitting sources A. Chbihi GANIL

2 Outline Intensity interferometry Directional correlations : size-lifetime Angle-averaged correlation functions Imaging, model independent technique Size-lifetime of emitting source Probes of reaction transport models Emission Chronology Neutron-proton, proton-deuteron Chronology to constraind Asy-EOS Fragment-fragment correlations Access the time-scales of fragments emission and densities at freeze-out Mechanisms of fragment emission Correlation function to study spectroscopy of exotic nuclei Thermal characterization of emitting sources LP-IMF correlations

3 Measurements of the correlation functions 1+ R(x) = Y coin Y evt.mixing x 1, x 2, x 3,... x 1, x 2, x 3,... ( ) ( ) x = q,v rel,e k,...

4 Intensity interferometry Koonin-Pratt equation S(r) is unknown source function Probability of emitting 2-particles at relative dist r calculated at the time when the last part is emitted Kernel function K(r,q) = ψ 2 q (r) 1 Contains antisymmetrization of pp wave function and mutual Coulomb interactions (FSI) Peak is due to the attractive S-wave nuclear interaction of pp scattering and depends on the volume of source. Peak height decreases with size increase

5 Directional correlation functions If the 2 particles are not emitted simultanously, S(r) is affected by the space-time ambiguity. S appears deformed. Larger Pauli suppression for transverse than longitudinal Directional-gated correl allow to disentangle the space and time information in S(r)

6 Directional correlation functions at high energy MeV FOPI data Central collisions Dominated by very short-lived component, very short τ R. Kotte et al., EPJ A6, 185 (1999)

7 Koonin-Pratt eq. Angle-averaged correlation functions Gaussian fit S p (r) α exp(-r 2 /2r 02 ) Contains information about its spatial extend and its lifetimes folded in relative distance r Difficult to disentangle space-time ambiguity in S(r) W.G. Gong et al., PR C43, 1804 (1991)

8 Systematic of Gaussian sizes Long τ Pre-equilibrium (40/14) 1/3 For High velocity / Pre-equilibrium r0 decreases independently of E inc Scale with the radius of projectile r0 defines the overlap of proj-target. (3/14) 1/3 For low velocity / long τ r0 comparable for all sys A p =40 40 Ar Ap N, 16 O A p =3 3 He F. Zhu et al., PR C44, R582 (1991)

9 Angle-averaged and directionalgated correlation functions Gaussian sizes extensively used:peak height to extract source size Difficult to reproduce the shape of correlation functions Understand better long-lifetime emissions

10 Particle emission time scales in HIC Fast emissions Pre-equilibrium Long lifetime emissions Evaporation, expansion, secondary decays Yields: Y TOT = Y fast + Y slow

11 R(q) = 4π Imaging p-p correlations dr r 2 S(r) K(r,q) 14 N+ 197 Au E/A=75 MeV G. Verde et al., PRC65, (2002) Fast pre-equilibrium emitting sources Slow late emissions q Source size e Space-time pictures Imaging technique consists of extracting the source profile by numerical inversion of Koonin-Pratt eq.

12 Information content

13 Comparison imaging & Gaussian

14 Imaging and its physics Shape analysis required to measure the size/density of the emitting source Relative contributions from dynamical/secondary decay sources (fast/slow) Entire profile of the source

15 Probes of reaction models Experimental functions vs microscopic models predictions (BUU, QMD, AMD) Imaging : Correct for contributions from long-lived emissions Compare directly the profiles of emitting source. Sensitivity to details of σ NN,inmedium

16 Shape analysis of BUU sources renormalization of BUU constraints long lived contributions to the source function High P : BUU reproduce the shape Low P : shapes sensitive to σ NN observations Reduced σ NN ->smaller sources G.Verde et al., PRC67 (2003)

17 Chronology of the emitted particles

18 Deuteron - proton chronology from QP E/A=50 MeV QuickTime et un décompresseur sont requis pour visionner cette image. D. Gourio et al., EPJA 7 (2000) 245 When the first emitted particle is slower than the second, the average distance will be reduced and the coulomb suppression enhanced and vise-versa

19 Neutron-proton chronology MeV/u Backward enhances the dyn source emission for reversed kinematics forward evaporation of QP Interplay of isospin part of mean field and Cb for protons will yield more protons than neutrons --> τ p >τ n Due to the absence of Cb for neutrons, large fraction of low energy neutrons decay from QP --> τ p <τ n

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21 QuickTime et un décompresseur BMP sont requis pour visionner cette image.

22 Fragment-fragment correlation functions Access to time-scales of fragment emission and density at freeze-out stage Mechanisms of fragment emission Simultaneous multifragment emission (short τ) Growth of density fluctuations in spinodal region (bulk instabilities) Sequential evolutionary emission? (longer τ) Emission from surface of excited source (similar to fission) Evolutionary emission? EES predictions

23 IMF timescales Miniball data vs 2-Body Coulomb FSI, Y.D. Kim et al., PRL 67 (1991) 14 3-Body trajectories important. τ fm/c: Shorter than seq. evaporation Y.D. Kim et al., PRC45 (1992) 387 T. Glassmacher et al., PRC50 (1994) 952

24 τ IMF vs incident energy: onset of simultaneous multifragmentation Central Kr+Nb 35 AMeV 45 AMeV 55 AMeV 65 AMeV 75 AMeV τ IMF (fm/c) Onset of simultaneous multifragmentation (bulk instabilities) Beam Energy (A MeV) MSU 4π data, E. Bauge et al., PRL70 (1993) 3705

25 Evolutionary multifragmentation Kr + Au Emission times τ IMF depend on fragment velocities Not a single freeze-out condition. Evolutionary fragment emission mechanisms (EES predictions) Thermally decaying source Miniball data, E. Cornell et al., PRL75 (1995) 1475 E. Cornell et al., PRL77 (1996) 4508 C-Be time ordering measurement

26 Fragment emission time systematics D. Durand et., NPA630 (1998) 52

27 Comparison to microscopic model Brownian One-Body dynamics (BOB) Freeze-out time fm/c Frag. Spatial distr 3-4 V 0

28 Surface to Bulk emission in thermal π -, p + A 8.0, 8.2, 9.2, 10.2 GeV/c multifragmentation ISiS data, L. Beaulieu et al., PRL84 (2000) 5971 Analysis: N-Body Coulomb trajectories T. Glassmacher et al., PRC50 (1994) 952 R. Popescu et al., PRC58 (1998) 270 Thermally expanding and decaying source: τ IMF decreases with increasing E*/A Transition from surface emission to bulk emission around E*/A 5 MeV?

29 3-α correlations from 12 C* Reaction: 12 C+ 24 Mg E/A=53 MeV ---> 12 C* quasi-projectiles Nucl. Phys. A811 (2008) 233 Event mixing Modified event mixing Indra data 12 C 8 Be+α 2α+α 12 C+ 24 Mg

30 2α-2p correlations : states in 10 C* RIB expts: Charity et al., PRC (R) (2007) Mercurio et al., PRC(R) (2008) Curtis et al., PRC 77 (R) (2008) HIC expt with Indra 10 C 6 Be+α (2p+α)+α E k (MeV) Nucl. Phys. A811 (2008) C 8 Be+2p (α+α)+2p 10 C 9 B+p (α+α+p)+p

31 Primary fragment reconstruction method Xe + 32 A MeV N. Marie et al., PRC 58, 256 (1998) S. Hudan et al., PhD thesis and PRC67, (2003) IMF-LCP V rel Correlations 1+R(V rel ) = N c /N nc Background Parameterization A-1/(BV rel +C) Evaporated p, d, t, 3 He, α size, E* pr primary fragments

32 Excitation energy of the primary fragments Primary fragment mass hypothesis

33 Proportion of thermal contribution Excitation energy saturates at 3 AMeV M ev /M tot fraction reflects <E*/A> of the primary fragments The majority of LCP are not evaporated by excited primary fragments

34 Conclusions Space-time characteristics extracted from Gaussian fit give incoherent results Imaging is promising method to estimate the source size and the relative contributions from dynamical/secondary decay sources It should be applied for directional-gated CF frag-frag correlations give a good estimation of the time emission High angular and energy resolution (correlations) are needed Large solid-angle coverage (collective motion, characterize complex event shapes)