Microscopic correlations in the Charge Radii of Exotic Nuclei

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Microscopic correlations in the Charge Radii of
Exotic Nuclei

• M. Tomasellia,b
• Th. Kühla D. Ursescua

a Gesellschaft für Schwerionenforschung, D-64291
Darmstadt,Germany b Technical University
Darmstadt, D-64289 Darmstadt, Germany
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Contents

• Motivation
• The Boson Dynamic Correlation Model (BDCM) and
  Charge Radii
• Charge Distributions of 6He and 6Li
• Charge Radii from Isotope Shift
• The HFS in the Mass Shift
• Outlook

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Motivation

• Correlation effects in nuclei via the cluster
  model eiS (S scattering operator)
• Open shell nuclei
• Correlation effect in charge distributions
• Analysis of the isotopic shift (IS) data in terms
  of correlated wave function
• Test of the method with measured nuclei
  extrapolation to exotic nuclei

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Unitarity Model Operator (UMO)
.....
Disadvantage

• Perturbative
• No Pauli Principle
• Works with effective operator

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Nuclear model based on Dynamic Correlation Model
(DCM)
......
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Boson Dynamic Correlation Model (BDCM)
......
Advantage

• The commutator chain reduced to an eigenvalue
  problem by introducing dynamic linearisation
  aproximation
• Pauli Principle
• Microscopic calculation without effective
  operators

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Example for linearisation approximation
In this work we are mainly concerned with
calculating admixture coefficients for the ground
state wavefunction.
That means that vacuum boiling configuration of
higher complexity are poorly admixed. Under
these considerations we introduce the following
aproximations
With the linearisation the 4 particle 2 holes
configuration are approximated with effective 3
particle 1 hole configurations
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Effect of linearisation on commutator chain
Use the linearisation approximation defined in
the previous transparency
Collect the resulting terms
Dynamic eigenvalue equations for mixed mode
amplitudes 2 particles gt 3 particles 1 hole
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Dynamics eigenvalue equation for one dressed
boson which is solvable self-consistently
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Configuration mixing wave functions
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Degree of spuriousity
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Energy of the single particle-hole states
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Cluster factorization theory (CFT)
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Unitary transformation operators
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Casimir operator
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Example of calculation
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Factorisation of the model CMWFs (electrons and
nucleons) in terms of cluster coefficients
The factorisation method is presently applied to
reduce complex Feynman diagrams to simple form
Particle line
Hole line
Interaction between nucleons or electrons
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Single particle energies
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CMWF for the ground states of 6He and 6Li
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Spectrum of 6Li, 9Be and 13C
Boson Dynamic Correlation Model and Dynamic
Correlation Model
reproduce the low lying spectra of light nuclei
reasonably well
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Single particle distribution
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Distribution in BDCM
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Charge distributions of 6He
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Charge radii of 6He
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Charge distributions of 6Li
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Nuclear results for Li isotopes
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Summary of Charge Radii
Rc charge radius
Rp point radius
References Method 1 I. Tanihata, Phys. Lett B
206,592 (1988) Interaction Cross Sections with
Glauber model, HO distributions 2 P.
Navratil, PRC 57,3119 (1998) Large-basis
shell-model calculations 3 S. Pieper,
Annu.Rev.Nucl.Part.Sci. 51, 53 (2001) Greens
Function Monte Carlo AV18/IL2 4 S. Pieper, PRC
66, 044310 (2002) Greens Function Monte Carlo
AV18/IL2 5 Suzuki, Progr.Theo.Phys.Suppl. 146,
413 (2002) Stochastic Variational Multicluster
Method on a correlated gaussian basis 6 M.
Tomaselli et al., Can. J. Phys. 80, 1347
(2002) Dynamic Correlation model 7
Penionzhkevich, Nucl.Phys. A 616, 247
(1997) coupled channel calculations,
double-folding optical potential, M3Y effective
interaction 8 C.W. de Jager, At.Dat.Nucl.Dat.Tab
. 14, 479 (1974) Electron Scattering
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Matter- and folded charge-radii of 7Be and 9Be
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Experimental and calculated electromagnetic
transitions of 9Be
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Principle of Lithium Charge Radius Determination
Using Perturbation Theory
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Correlations effect in 7Li
Preliminary results
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Conclusion and outlook for Li study

• Nuclear physics and atomic physics may be
  combined to calculate the charge radius of exotic
  isotopes
• In nuclear physics the charge radii can be
  calculated with or without the use of correlated
  wave functions
• Inclusion of correlation effect generate larger
  radii than those obtained in single particle
  models
• Correlation are therefore also important in the
  analysis of the IS data
• Preliminary results obtained with DCM for 7Li
  show that core polarization is playing an
  important role in the isotopic shift theory
• Motivation for calculating the charge radii of
  other exotic nuclei

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Thank You!