Tensor Interaction and Cluster Structure H Toki RCNPOsaka

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Tensor Interaction and Cluster Structure H. Toki RCNP/Osaka 09. 4. 24 toki@rcnp 1

Tensor Interaction and Cluster Structure H. Toki RCNP/Osaka 09. 4. 24 toki@rcnp 1

Pion exchange interaction (Chiral symmetry) Tensor interaction: 50% of V 2 attraction Central interaction:

Pion exchange interaction (Chiral symmetry) Tensor interaction: 50% of V 2 attraction Central interaction: 30% of V 2 attraction in 4 He r>0. 5 fm TOSM 09. 4. 24 toki@rcnp 2

What is TOSM? Brueckner-Hartree-Fock model High momentum components are included in G-matrix. = Self-consistent

What is TOSM? Brueckner-Hartree-Fock model High momentum components are included in G-matrix. = Self-consistent 09. 4. 24 Pauli Brueckner G-matrix toki@rcnp Wave function contains only low momentum component 3

TOSM vs BHF Hartree-Fock Tensor correlation In shell model basis UCOM for Short range

TOSM vs BHF Hartree-Fock Tensor correlation In shell model basis UCOM for Short range part 09. 4. 24 toki@rcnp 4

Bruckner-Hartree-Fock result Delta Brockmann-Machleidt: PRC 42(1990) 09. 4. 24 toki@rcnp Anti-nucleon 5

Bruckner-Hartree-Fock result Delta Brockmann-Machleidt: PRC 42(1990) 09. 4. 24 toki@rcnp Anti-nucleon 5

4 He+4 He 4 He+n and 4 He+n is the gateway to cluster structure.

4 He+4 He 4 He+n and 4 He+n is the gateway to cluster structure. is the gateway to shell structure. About 50% of two body attraction comes from tensor interaction in 4 He. 09. 4. 24 toki@rcnp 6

TOSM wave function Basic wave function (Suzuki method) This wave function can handle short

TOSM wave function Basic wave function (Suzuki method) This wave function can handle short range correlation. The spirit of TOSM is to introduce Y 2 component. The second term takes care of the tensor correlation. 09. 4. 24 toki@rcnp 7

4 He+4 He RGM wave function We have to calculate the norm and energy

4 He+4 He RGM wave function We have to calculate the norm and energy kernel. and 09. 4. 24 are highly complicated!! toki@rcnp 8

Suzuki global vector method Permutation 09. 4. 24 toki@rcnp 9

Suzuki global vector method Permutation 09. 4. 24 toki@rcnp 9

Suzuki global vector method II Generating function If we know integral of GF, we

Suzuki global vector method II Generating function If we know integral of GF, we get ME of FV. 09. 4. 24 toki@rcnp 10

4 He+n Fundamental shell model state TOSM The matrix elements can be calculated by

4 He+n Fundamental shell model state TOSM The matrix elements can be calculated by using the global vector method and generating functions. 09. 4. 24 toki@rcnp 11

Numerical results We use stochastic variational method (SVM) We calculate only s-wave states at

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) 09. 4. 24 toki@rcnp 12

Results We calculate for s-wave states with Volkov force. We calculate d, 3 He

Results We calculate for s-wave states with Volkov force. We calculate d, 3 He and 4 He. The energies are obtained at once. E(d)=-0. 543 Me. V E(3 He)=-8. 42 Me. V E(4 He)=-30. 4 Me. V 09. 4. 24 toki@rcnp 13

Conclusion (1) TOSM is close to BHF method. TOSM can have high momentum components.

Conclusion (1) TOSM is close to BHF method. TOSM can have high momentum components. He+4 He is gateway to cluster structure. We construct 4 He TOSM wave function in Jacobi coordinates. We formulate RGM wave function by using two 4 He TOSM wave functions. 4 09. 4. 24 toki@rcnp 14

Conclusion (2) Suzuki global vector method is powerful. We use generating function method to

Conclusion (2) Suzuki global vector method is powerful. We use generating function method to get RGM kernels. 4 He+n 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. 09. 4. 24 toki@rcnp 15

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