Can a cluster model explain halo structure of exotic nuclei

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Can a cluster model explain halo structure of
exotic nuclei ?

• M. Tomaselli, L.C. Liu, S. Fritzsche,
• Th. Kuehl, D. Ursescu, A. Gluzicka

GSI-Darmstadt, Germany LANL, USA University of
Kassel, Germany IFD, Warsaw, Poland
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Motivation

• Clusterisation universal receipt for N-body
  problem
• Interaction of clusters at high pressure
• Importance of the dynamic evolution of clusters
• Modern physics in a dynamic world
• Necessity to describe interacting clusters of
  different species

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Topics

• Review of cluster model in nuclear physics
• From cluster to a dynamic model
• Interacting cluster model solvable in terms of
  cluster coefficients
• Nuclear physics with interacting clusters DCM
  and BDCM
• (Fermion- and Boson- Dynamic Correlation Model)
• Momentum distribution in exotic nuclei

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Elementary clusters in nuclear physics
Rest nucleus
Rest nucleus
p or n
3He or 3H
Rest nucleus
Rest nucleus
2H
4He
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Shape coexistence in vacuum Example 6He
In the ground state of 6He two different clusters
coexist
4He
3H
3H
2 n
4He
2 n
particle-hole cluster
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Interaction between clusters deformation of the
vacuum
In the ground state of 6He two different clusters
coexist
4He
3H
3H
2 n
4He
Two body interaction
2 n
Three body interaction
Cluster interaction
particle-hole cluster
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From interacting clusters to DCM
Macroscopic cluster interaction 2H
cluster move in the optical potential formed by
the alpha particle optical model.
Microscopic cluster interaction
N-particles which were partitioned in small and
big clusters interact.
4He
3H
3H
2 n
Can the dynamic correlation model reproduce the
interacting cluster picture?
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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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Simmetry properties of the configuration mixing
wavefunction (CMWF)
Define operators
k mk
J1 M1
J2 M2
Destroy a hole-particle pair and create a
particle-hole pair
ukmk
k mk
J1 M1
J2 M2
Destroy a hole-hole pair and create a
particle-particle pair
pkmk
k mk
J1 M1
J2 M2
Destroy a particle-particle pair and create a
hole-hole pair
hkmk
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Group property of the defined operators
Action of the operator on totally antisymetric
wavefunction
k mk
J
J2 M2
J1 M1

ukmk(3)
Norm
The same action is valid for pkmk and hkmk
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Unitary operator
J
ukmk(3)/Norm

ukmk(3)

Commutator relation
uk1mk1(3) uk2mk2(3)geometric factor uk3mk3(3)
Therefore the unitary operators are generators of
the SU2J1(3)
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Cluster transformation coefficients

ukmk(3)
ukmk(3)
J
J1 M1
J2M2
all possible partitions 3gt2
M
Cluster Transformation Coefficients
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Factorisation of the model CMWFs (for electrons
and nucleons) in terms of cluster coefficients
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In medium G-matrix elements and corresponding two
body potentials for 18O
Matrix elements for the first three positive 0
levels.
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Spectrum of the positive and negative parity
state of 18O
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Nuclear results for Li isotopes
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Two models - two distributions

• Distribution in the cluster model is resulting
  from the sum of 0 groundstate of 4He and two non
  interacting particles
• In the DCM the distribution is given by the
  center of mass distribution of the total number
  of particles
• In DCM , the 4He distribution is given by L0
  center of mass component.
• In the calculations we present, this component
  could not be very well described within 3p-1h
  core excitation mechanism.
• Calculation of the 4He distribution in dressed
  p-h states is under calculation to improve the
  L0 terms which are giving determinant
  contribution at small R.

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Distributions in BDCM
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Perturbation versus DCM for 11Li
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Distribution and proton scattering cross-section
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Nuclear results for 6Li isotopes momentum
distribution
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Nuclear results for 6Li isotopesMomentum
integrands
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Wave functions of the in medium proton-neutron
wavefunction in 6Li
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Momentum components of the in medium proton
neutron wavefunction in 6Li
Dressed Wood-Saxon
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Nuclear results for 6Li isotopes
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Nuclear results for 6Li isotopes
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Conclusions

• Dynamic correlation model is not reproducing
  cluster structure at the energy scale
  investigated
• Clusters are strongly interacting
• An experimental test of the microscopic method
  introduced is desiderable
• More still to be analysed (especially at high
  energies)