Tensor interaction in Extended Brueckner-Hartree-Fock theory Hiroshi Toki (RCNP, Osaka) In collaboration with Yoko Ogawa.

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Presentation transcript:

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)

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.

Shell model (Meyer-Jensen) Phenomenological Strong spin-orbit interaction added by hand Magic number 2,8,20,28,50, Harmonic oscillator

The importance of pion is clear in deuteron Deuteron (1 + ) NN interaction S=1 and L=0 or 2

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)

Pion is important in nucleus ８０％ of attraction is due to pion Tensor interaction is particularly important Pion Tensor spin-spin

The importance of pion is clear in deuteron Deuteron (1 + ) NN interaction S=1 and L=0 or 2

******* 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)

Comparison of TOFM with rigorous calculation (SVM) K LS E Vc Vt 3 H with AV8’ ＴＯＦＭＳＶＭ 4 He with AV8’ (w/o Coulomb) K LS E Vc Vt ＴＯＦＭＳＶＭ

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

(2011) Hartree-Fock theory cannot handle tensor interaction

Total energy Variational principle Equation for finite nuclei

TOSM space : three body interaction iteration Not allowed Nucleus Hyper nucleus

EBHF equation Extended BHF equation Effective Hamiltonian in HF method

Comparison of BHF and EBHF theories EBHF 1 2

Feshbach projection method Variational method and Feshbach theory completely agree.

Nuclear matter J. Hu, H. Toki and Y. Ogawa Calculating finite nuclei Bonn B

Momentum distribution in nuclear matter EBHF BHF

Tensor interaction A B C small medium large

Neutron matter No difference among three Bonn potentials

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.

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