Tensor Interaction and Cluster Structure

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Tensor Interaction and Cluster Structure

• H. Toki
• RCNP/Osaka

2
Pion exchange interaction
(Chiral symmetry)

• Tensor interaction 50 of V2 attraction
• Central interaction 30 of V2 attraction
• in 4He

rgt0.5fm
TOSM
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What is TOSM?
Brueckner-Hartree-Fock model
High momentum components are included in G-matrix.

Pauli
Wave function contains only low momentum
component
Self-consistent
Brueckner G-matrix
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TOSM vs BHF
Hartree-Fock
Tensor correlation In shell model basis
UCOM for Short range part
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Bruckner-Hartree-Fock result
Delta
Brockmann-MachleidtPRC42(1990)
Anti-nucleon
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4He4He and 4Hen
4He4He is the gateway to cluster structure.
4Hen is the gateway to shell structure.
About 50 of two body attraction comes from
tensor interaction in 4He.
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TOSM wave function
Basic wave function
(Suzuki method)
This wave function can handle short range
correlation.
The spirit of TOSM is to introduce Y2 component.
The second term takes care of the tensor
correlation.
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4He4He
RGM wave function
We have to calculate the norm and energy kernel.
and are highly complicated!!
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Suzuki global vector method
Permutation
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Suzuki global vector method II
Generating function
If we know integral of GF, we get ME of FV.
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4Hen
Fundamental shell model state
TOSM
The matrix elements can be calculated by using
the global vector method and generating functions.
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Numerical results

• We use stochastic variational method (SVM)
• We calculate only s-wave states at this moment
• We take Volkov force with only the central
  interaction
• We have to choose wave functions in clever way
  (iteratively in most suitable way)

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Results

• We calculate for s-wave states with Volkov force.
• We calculate d, 3He and 4He.
• The energies are obtained at once.
• E(d)-0.543MeV
• E(3He)-8.42MeV
• E(4He)-30.4MeV

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Conclusion (1)

• TOSM is close to BHF method.
• TOSM can have high momentum components.
• 4He4He is gateway to cluster structure.
• We construct 4He TOSM wave function in Jacobi
  coordinates.
• We formulate RGM wave function by using two 4He
  TOSM wave functions.

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Conclusion (2)

• Suzuki global vector method is powerful.
• We use generating function method to get RGM
  kernels.
• 4Hen is formulated in TSOM.
• The Suzuki method becomes highly complicated to
  add more shell model states.
• We can work out diagonalization by stochastic
  variational method.