Configuration interaction model for open quantum systems

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Configuration interaction model for open quantum
systems
Nicolas Michel (Kyoto University) Witek
Nazarewicz (ORNL - University of
Tennessee) Marek Ploszajczak (GANIL) Jimmy
Rotureau (ORNL University of Tennessee)
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Plan

• Gamow states
• Complex scaling method
• Completeness relations
• Gamow Shell Model (GSM) matrix diagonalization
• Spectroscopic factors and overlap functions in He
  chain
• Realistic interactions with GSM
• Conclusion and perspectives

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Gamow states

• Georg Gamow a decay
• G.A. Gamow, Zs f. Phys. 51 (1928) 204 52
  (1928) 510
• Definition
• Straightforward extension to non local potentials
  (HF)

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Complex scaling method

• Radial integral calculation complex scaling
• Analytic continuation integral independent of R
  and ?
• Long range O(r) cases of divergence with
  scattering states
• Practical for one-body operators only.

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Gamow states location
Choice of contour arbitrary
narrow
broad
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Completeness relations with Gamow states

• Berggren completeness relation (l,j)
• T. Berggren, Nucl. Phys. A 109, (1967) 205
• Continuum discretization
• N-body discretized completeness relation (all
  l,j)

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GSM matrix diagonalization

• GSM matrix large complex symmetric matrices
• Lanczos method insufficient resonances hidden
  among scattering states

Resonant states ? Scattering states ?
20O 0 states
Overlap method 1 GSM pole app. 2
Full GSM space so
maximal
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N. Michel et al., Phys. Rev. C 67, 054311 (2003)
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4He core valence neutrons
N. Michel et al., Phys. Rev C, 67 054311 (2003)
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Spectroscopic factor

Nucleon-nucleon correlations measure
N. Michel et al., Phys. Rev. C, (Rap. Comm.), 75
031301(R) (2007)
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Real WS fit
Complex WS fit
O(r)
Overlap function
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Realistic interactions in GSM

• Matrix elements complex scaling for infinite
  integrals
• Problems very long (2D integrals), divergences
  still occur
• Solution HO expansion for nuclear interaction
• Weak convergence with number of HO states
• HO matrix elements Fast calculation (Moshinsky
  transformation)
• No complex scaling HO / Gamow states overlaps
  only

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Examples

• 6He 2n 4He core
• core HF basis, sdp model space

• N3LO with Vlow-k
• L 1.9 fm-1, b 2 fm

6He
G. Hagen et al., Phys. Rev. C 73 064307 (2006)
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Examples

• 6He halo density
• 
  fast convergence with number of HO states

G. Hagen et al., Phys. Rev. C 73 064307 (2006)
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Conclusion and perspectives

• Conclusion
• GSM Standard shell model simplicity and power
  beyond Hilbert space.
• Complete description of loosely bound and
  resonant states.
• No limitation to the number of particles in the
  continuum.
• Spectroscopic factors, overlap functions
• strong modification of observables due to
  continuum coupling
• Realistic interactions in GSM HO efficiency even
  with continuous bases
• Perspectives
• Coherent framework unifying structure and
  reaction.
• Many body open channels.
• No-core shell model with realistic interactions
  shell model matrix in HF basis.
• Gamow HFB-QRPA medium and heavy nuclei
  drip-lines (next presentation).
• Molecular states, quantum dots