Statistical Theory of Nuclear Reactions
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Statistical Theory of Nuclear Reactions
UNEDF SciDAC Annual Meeting
MSU, June 21-24, 2010
Goran Arbanas (ORNL)Kenny Roche (PNNL)Arthur Kerman (MIT/UT)Carlos Bertulani (TAMU)David Dean (ORNL)
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HPC numerical simulation of formal theories ofstatistical nuclearreactions
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Year 5 Progress Report
• Year 5 Reaction Deliverable #55:– “Examine energy-dependence of eigensolutions in the expansion
for the KKM theory.”
• Year 5 Progress Report:– Prototyped energy dependence in KKM:
• Intel MKL implementation of complex symmetric eigensolver on 12 cores
– Massively parallel code in “ensemble” eigensolver of complex symmetric matrices (K. Roche).• In the meantime: loop through energies on the parallel code.
• Related HPC contribution:– Massively Parallel eigensolver for large (ensembles) of complex
symmetric matrices
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Why KKM?
• A framework based on Feshbach’s projection operators
• Central result:– T = Tbackground + Tresonant = Taverage + Tfluctuating
• A foundation for derived statistical theories:– Kerman-McVoy
• Designed for two step processes like A(d,p)B*, B*A+n
• Could be used for statistical (d,p) reactions at FRIB
– Feshbach-Kerman-Koonin (FKK)• Multistep reactions, used for nuclear data analysis
• Similar expressions were derived later by other methods
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Physical picture
E
…
Q
d q
P
continuum bound
PHQ
dHq
P d q
Q
compounddoorway
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Feshbach’s projection operators
EH
PHQHPPQPQP PQ 20;1
Two-potential formula yields
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KKM subtraction
Use Hopt to
rewrite Eq. (3)
Kawai, Kerman, and McVoyAnn. of Phys. 75, 156 (1973)
Energy averaging of the T-matrix yields this expression for opticalpotential and opt.wave-f.(for Lorentzian averaging)
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KKM Fluctuation T-matrix
Two-potential formula yields
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Expand the T-matrix by eigenfunctions
Lorentzian weight function width .
This E-dependence nowtreated explicitly.
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Preliminary Results:Eigenvalues/vectors Average Ratio SQRT(Variance)
E-independent 0.0037 0.0053
E-dependent 0.0042 0.0049
Computation parameters:• Eigenvalues/vectors computed at 100
energies spanning 18-22 MeV • 1600 equidistant Q-levels• 40 channels• 20 equidistant radial points where
HPQ set to a Gaussian-distributed random interaction
• E = 20 MeV• 100 E’ points for Lorentzian
averaging between 18 and 22 MeV• Lorentzian averaging width I = 0.5
MeV• s-wave only• Strongly overlapping resoances
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Test approximations in KKM derivation
• The E-dependence makes E-averaging more accurate
Preliminary results areanalyzed.
Random Phase Hypothesis
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HPC progress report (by K. Roche)
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Year 5 plan
• Complete parallel KKM with E-dep. eigenvalues/vectors
• Test approximations in derivation of KKM cross sections
• Publish the KKM work (including the work on doorways)