Theoretical Remarks

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Theoretical Remarks
http//unedf.org

• N. Schunck
• Department of Physics ? Astronomy, University of
  Tennessee, Knoxville, TN-37996, USA
• Physics Division, Oak Ridge National Laboratory,
  Oak Ridge, TN-37831, USA

Gretina Science Workshop, LBNL, April 23-24 2009
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Theoretical Nuclear Structure
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Inter-Nucleon NN, NNN Interactions AV18, EFT,
Vlow-k
Theory of Light Nuclei Verification
NCSMGFMCCC Validation Nuclei with A 6
Density functional Theory Improved
functionals Remove computationally-imposed
constraints Global properties of nuclei with A gt
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Low-energy Reactions Hauser-Feshbach Feshbach-Kerm
an-Koonin Fission Mass and energy distributions
Dynamic Extensions of DFT LACM, GCM, TDDFT, QRPA,
CI, CC Level densities
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Modern Challenges in DFT
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• Development of new generations of energy
  functionals
• Explore functionals that go beyond Skyrme or
  Gogny
• Use of a larger, more constraining, experimental
  dataset
• Remove artificial CPU limitations by using
  high-performance computing
• Construction of a sound theoretical framework
• Kohn-Sham theorem for self-bound systems
• Passage from NN, NNN, etc. interaction to
  functional form
• Inclusion of beyond mean-field correlations on a
  large scale
• Clarify their role formal aspects as well as
  practical ones
• Systematically benchmark with experiment

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On the relevance of shell structure
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• Among other things, shell structure is behind
• Magicity
• Existence of deformed nuclei (Jahn-Teller
  effect), including exotic ones (like tetrahedral
  nuclei)
• Position of rotational bands with respect to g.s.
  band
• Gives fine-tuning correction to masses
• Evolution of s.p. levels with respect to any
  symmetry-breaking term dictated, to a large
  extent, by symmetries, i.e. quantum numbers, and
  relative position of levels

Remark Shell structure directly impacts pairing
correlations large shell gaps cause pairing
collapse
Tensor
Spin-orbit
Skyrme Functional
Vanishes for even-even nuclei
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Why odd nuclei are useful
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• Probe time-odd terms
• Give detailed, relatively model-independent
  information on shell structure near the Fermi
  level
• Help probe pairing properties
• What could help
• Have bandhead excitation energies in superheavies
  (limit of large A)
• Have spectroscopic information (Nilsson labels)

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Why deformed nuclei are useful
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• Good old Strutinsky theorem
• EHF Emacro dEshell
• How to disantangle the macroscopic and
  microscopic contribution ?
• Poor deformation properties of current
  functionals
• Fission, hyper-deformation, exotic deformations
  like tetrahedral, hindered by macroscopic effects

• What could help
• Spins of the Jacobi shape transition (critically
  dominated by macroscopic behavior)
• Discrete ? transitions in the HD well probe
  extreme deformations
• More linking transitions from (HD), SD to g.s.
  band

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Why superheavy nuclei are useful
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M. Bender et al., Phys. Rev. C 60, 034304 (1999)
Macroscopic Deformation Energy ELD(def)
Z122

• SH good playground to test
• Extrapolability of interactions
• Bulk properties vs. shell effects
• What could help
• Single-particle structure in odd-mass SH gives a
  snapshot of the shell structure
• Rotational bands up to very high spins exploring
  collective properties

Z124
Z126
Z128
Z130
N184
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Experimental data
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• Bottom lines are
• We want to be sure that every term of the
  functional is properly constrained
• We need to control errors (experimental and
  theoretical)
• We want as much data as possible at the DFT
  level, but some of it clearly will have to go
  beyond

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