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Tensor Interaction and Cluster Structure

Tensor Interaction and Cluster Structure. H. Toki RCNP/ Osaka. Pion exchange interaction. (Chiral symmetry). Tensor interaction: 50% of V 2 attraction Central interaction: 30% of V 2 attraction in 4 He. r>0.5fm. TOSM. What is TOSM?. Brueckner-Hartree-Fock model.

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Tensor Interaction and Cluster Structure

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

  2. Pion exchange interaction (Chiral symmetry) • Tensor interaction: 50% of V2 attraction • Central interaction: 30% of V2 attraction in 4He r>0.5fm TOSM toki@rcnp

  3. 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 toki@rcnp

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

  5. Bruckner-Hartree-Fock result Delta Brockmann-Machleidt:PRC42(1990) Anti-nucleon toki@rcnp

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

  7. 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. toki@rcnp

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

  9. Suzuki global vector method Permutation toki@rcnp

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

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

  12. 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) toki@rcnp

  13. 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 toki@rcnp

  14. Conclusion (1) • TOSM is close to BHF method. • TOSM can have high momentum components. • 4He+4He 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. toki@rcnp

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

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