IMFIMF Directionnal Correlations

1
IMF-IMF Directionnal Correlations

• Motivations
• Characterization of geometrical properties of the
  composite system, at the moment of fragment
  emissions (freeze-out) volume (density),
  elongation in real space.
• Provide additionnal inputs to nuclear stopping
  systematics in real space.

HI
HI
2
Already existing method directional cuts
weights.

• Hard cuts (S.E. Koonin, Phys. Lett. B 70
  (1977) 43
• M.A. Lisa et al., Phys. Rev. Let. 71 (1993)
  2863)
• longitudinal ? lt 30o
• transversal 60o lt ? lt 120o
• OR
• Weighted (C. Schwarz et al., Nucl. Phys. A 681
  (2001) 279)
• longitudinal cos2(?)
• transversal sin2(?)

light particle resonances
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Already existing method directional cuts
weights.
c2 - test
C. Schwarz et al., Nucl. Phys. A 681 (2001) 279
Emission times are short and comparable with
passing time of spectator (volume break up)
Radii ? 8 fm (expansion)
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Already existing method directional cuts
weights.
Application to IMF-IMF correlations
N-body Coulomb trajectory
Central XeSn _at_ 50 A.MeV INDRA_at_GSI
A. Le Fèvre, C. Schwarz et al., Bormio 2003
Conference Proceedings
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Second method (new) directional projections.
Longitudinal projections vrelcos(?) Transversa
l projections vrelsin(?)
A. Le Fèvre, C. Schwarz et al., Bormio 2003
Conference Proceedings
6
Summary

• IMF-IMF directionnal correlation functions allow
  to extract information on spatial extensions of
  the emitting source (volume and aspect ratios),
  assuming short emission times.
• Model independent.
• Needs a 4p detection of the composite system.

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Directional weights vs projections
N-body Coulomb trajectory
Data central XeSn 50 A.MeV (INDRA_at_GSI)
Directional weights
Projections
R(0.671)
Good sensitivity on density Broad minimum for
shape
Good sensitivity on shape and density.
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Weighted corr. func.
N-body Coulomb traj.
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Projected corr. func.
prolate
oblate
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Already existing method directional cuts
weights.
Application to IMF-IMF correlations
MMMC-NS calculations
?
vrel
r r0 / 6 E 6 A.MeV Ecoll 2.3 A.MeV INDRA
filtered
beam
A. Le Fèvre, C. Schwarz et al., Bormio 2003
Conference Proceedings
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Coulomb correlation functions for XeSn _at_ 50 AMeV
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Short fragment emission times

• lt 20-50 fm/c
• Cf. L. Beaulieu et al., PRL 84(2000)5971

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Experimental results
Ref. A. Le Fèvre et al. arXivnucl-ex/0309016
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MMMC central XeSn, 50 A.MeV phase space (Zgt4)
Coordinate space
Velocity space
Without Coulomb
With Coulomb
With Coulomb