1. 2011.11.3toki@beihangpionsym1 Tensor interaction in Extended Brueckner-Hartree-Fock theory Hiroshi Toki (RCNP, Osaka) In collaboration with Yoko Ogawa (RCNP) Jinniu Hu (RCNP) Kaori Horii (RCNP) Takayuki Myo (Osaka Inst. of Technology) Kiyomi Ikeda (RIKEN)

2. 2011.11.3toki@beihangpionsym2 Pion is important in Nuclear Physics ！ Yukawa （１９３４） predicted pion as a mediator of nuclear interaction to form nucleus Meyer-Jansen （１９４９） introduced shell model ー beginning of Nuclear Physics Nambu （１９６０） introduced the NJL model with chiral symmetry for mass generation and pseudo-scalar pion.

3. 2011.11.3toki@beihangpionsym3 Shell model (Meyer-Jensen) Phenomenological Strong spin-orbit interaction added by hand Magic number 2,8,20,28,50,82 2 8 20 40 70 Harmonic oscillator

4. 2011.11.3toki@beihangpionsym4 The importance of pion is clear in deuteron Deuteron (1 + ) NN interaction S=1 and L=0 or 2

5. 2011.11.3toki@beihangpionsym5 Variational calculation of few body system with NN interaction C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001) VMC+GFMC V NNN Fujita-Miyazawa Relativistic Pion is keyHeavy nuclei (Super model)

6. 2011.11.3toki@beihangpionsym6 Pion is important in nucleus ８０％ of attraction is due to pion Tensor interaction is particularly important Pion Tensor spin-spin

7. 2011.11.3toki@beihangpionsym7 The importance of pion is clear in deuteron Deuteron (1 + ) NN interaction S=1 and L=0 or 2

8. 2011.11.3toki@beihangpionsym8

9. 2011.11.3toki@beihangpionsym9 ******* 9 Jacobi coordinate x 1,x 2,x 3 Tensor Optimized Few-body Model (TOFM) For 4 He Total J=0, S-wave (L=0,S=0) D-wave(L=2,S=2) S-wave (L=0) D-wave (L=2)

10. 2011.11.3toki@beihangpionsym10 Comparison of TOFM with rigorous calculation (SVM) K LS E Vc Vt 3 H with AV8’ 46.68 47.57 -7.76-7.54 -22.30-22.49 -29.96 -30.84 -1.91-2.00 ＴＯＦＭ ＳＶＭ 4 He with AV8’ (w/o Coulomb) K LS E Vc Vt 95.37 102.35 -4.05 -4.71 -24.05 -25.92 -54.58 -55.22 -60.79 -68.32 ＴＯＦＭＳＶＭ

11. 2011.11.3toki@beihangpionsym11 TOFM concept should be used for nuclear many body problem G.S. Spin-saturated The spin flipped states are already occupied by other nucleons. Pauli forbidden

12. 2011.11.3toki@beihangpionsym12 (2011) Hartree-Fock theory cannot handle tensor interaction

13. 2011.11.3toki@beihangpionsym13 Total energy Variational principle Equation for finite nuclei

14. 2011.11.3toki@beihangpionsym14 TOSM space : three body interaction iteration Not allowed Nucleus Hyper nucleus

15. 2011.11.3toki@beihangpionsym15 EBHF equation Extended BHF equation Effective Hamiltonian in HF method

16. 2011.11.3toki@beihangpionsym16 Comparison of BHF and EBHF theories EBHF 1 2

17. 2011.11.3toki@beihangpionsym17 Feshbach projection method Variational method and Feshbach theory completely agree.

18. 2011.11.3toki@beihangpionsym18 Nuclear matter J. Hu, H. Toki and Y. Ogawa Calculating finite nuclei Bonn B

19. 2011.11.3toki@beihangpionsym19 Momentum distribution in nuclear matter EBHF BHF

20. 2011.11.3toki@beihangpionsym20 Tensor interaction A B C small medium large

21. 2011.11.3toki@beihangpionsym21 Neutron matter No difference among three Bonn potentials

22. 2011.11.3toki@beihangpionsym22 Conclusion We have developed Extended Brueckner-Hartree- Fock (EBHF) theory for tensor interaction. We are able to calculate many body system by using bare nucleon-nucleon interaction. We calculate nuclear matter with Bonn potential. We can work out many body system with chiral symmetric Lagrangian. We have a framework to connect nuclear physics with quark-gluon dynamics. We begin totally a new nuclear physics.

23. 2011.11.3toki@beihangpionsym23 Monden