UCRL-PRES-?????? orAL and the Future of Imagin This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. Outline: What is CorAL Tour of components: A test problem Imaging New bases
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UCRL-PRES-??????
CorAL and the Future of Imaging
This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.
Outline: What is CorAL Tour of components: A test problem Imaging New bases
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What is CorAL?• The Correlation
Algorithm Library– Source & correlation data
structures• Various 1d• Cartesian harmonics• Spherical harmonics• 3d histograms
– OSCAR formatted input– Various model sources– Imaging tools– Fitting tools in development– Kernels– Oodles of wavefunctions– Sample codes
• Status:– It (sortof) runs, but we’re
still cleaning it up – Documentation in progress– Code collaboration
agreements available (see me later)
– Official GPL release “any time now”
• Platforms:– Linux, Unix, MacOSX– Written in C++– Requires Gnu Scientific
Library
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CorAL components• Core libraries
– libcoral: core CorAL library
– libcoralutils: utility codes CorAL uses
• Binaries– CHUM: freeze-out point (emission function)
generator
– SHARK: precompute the kernels for CRAB and DIVER
– CRAB: constructs correlations and sources from OSCAR data
– DIVER: imaging code
– plotting codes (bfplot, scplot, converts2c)
•Various component tests
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Core Halo Ur-Model (CHUM)Variation of the Core-Halo model of Nickerson, Csörgo˝, Kiang, Phys. Rev. C 57, 3251 (1998), etc.
• Blast-wave like flow profile• Gaussian source with finite source lifetime• production from source and resonance decay
The emission function:
f is fraction of ’s emitted directly from core, i.e. = f 2 in source.
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CHUM cont.• From exploding core, with Gaussian shape:
• Use full 3-body decay kinematics and lifetime of =23 fm/c:
• Blast-wave like flow profile:
where , and
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CHUM source is non-Gaussian in 3d
Set Rx=Ry=Rz=4 fm, f/o=10 fm/c, T=165 MeV, f=0.5
Difference in side, out and long directions mean tail in higher lm terms as well as the 00 term. The out-long tail due to lifetime of source.
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Source function is related to emission function:
Work in Bertsch-Pratt coordinates in pair Centre of Mass (CM) frame
The Koonin-Pratt equation:
Pair final state relative wave-function, q(r), defines the kernel:
K(q,r)=|q(r)|2-1.
CoRrelation AfterBurner (CRAB)
CRAB’s role has increased: it now computes sources and correlations from OSCAR data
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Breaking Problem into 1d Problems
Where
Expand in Ylm’s and Legendre polynomials:
Cartesian harmonics give analogous expressions
• l = 0 : Angle averaged correlation, get access to Rinv
• l = 1 : Access to Lednicky offset, i.e. who emitted first (unlike only)• l = 2 : Shape information, access to RO, RS, RL:
C20 RL
C00-(C20±C22) RS, RO
• l = 3 : Boomerang/triaxial deformation (unlike only)• l = 4 : Squares off shape
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Use CRAB to generate Slm(r)
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Use CRAB to generate Clm(q)
Note: Coulomb turned off
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Demonstration InVERter (DIVER)
• kernel not square & may be singular• noisy data• error propagation
imaging is an ill-posed problem
Practical solution to linear inverse problem, minimize :
Most probable source is:
With covariance matrix:
Convert Koonin-Pratt equation to matrix form:
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What about radial basis?
• Radial dependence of each term in terms of basis functions:
• Basis choice affects sensitivity to correlation. Characterize with l=0 kernel:
A crappy basis gives bad source with small uncertainty