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Relativistic extended chiral mean field model for finite nuclei

This study presents a relativistic extended chiral mean field model for finite nuclei, emphasizing key elements such as chiral symmetry, NN interaction, and pion exchange. Variational calculations for light nuclei are conducted, highlighting tensor interactions and short-range repulsion. The model incorporates tensor correlation, short-range correlation, and shell structures. Applications to Deuteron wave functions and nucleon-nucleon interactions are explored, focusing on quark confinement and strong repulsion. The model demonstrates satisfactory results for 4He nuclei, with potential for medium-heavy nuclei studies.

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Relativistic extended chiral mean field model for finite nuclei

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  1. Relativistic extended chiral mean field model for finite nuclei Hiroshi Toki (RCNP/Osaka) Yoko Ogawa (RCNP/Osaka) Takayuki Myo (Osaka Inst. of Tech.) Kiyomi Ikeda (RIKEN) toki@riken

  2. Variational calculation of light nuclei with NN interaction VMC+GFMC VNNN Fujita-Miyazawa C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001) Relativistic Pion is a key element toki@riken

  3. V r 1fm General feature of nucleon-nucleon interaction Nucleus using NN interaction • Strong tensor interaction (pion: chiral symmetry) • Strong short range repulsion (quark: confinement) Deuteron wave function Strong short range repulsion (Quark structure) s d -50 (MeV) Strong tensor interaction (Pion exchange) toki@riken Central dip and D-wave component

  4. Tensor optimized shell model Myo Ikeda Toki • Tensor correlation TOSM • Short-range correlation UCOM toki@riken

  5. TOSM+UCOM with AV8’ (Myo Toki Ikeda) Kamada et al. PRC(2002) T Few body Framework Hiyama Suzuki VLS More Tensor!! E VC VT toki@riken V coordinate vs. T coordinate

  6. Picture of nucleus proton Snapshot neutron pionic pair toki@riken

  7. Nucleon is made of quarks • QCD -- Confinement + Chiral Symmetry • NJL(Nambu-Jona-Lasinio) Quarks massive + Pion (NG boson) • Hadronization (Eguchi-Sugawara:1976) • Chiral sigma model (Toki-Weise:2008) • Want to make nucleus with chiral symmetry toki@riken

  8. jj Relativistic chiral mean field model LS • Relativistic mean field model with pion Toki, Sugimoto, Ikeda, PTP(2002) • Relativistic charge and parity projected chiral mean field model Ogawa, Toki,.., PRC(2004),PRC(2006) Spin-orbit splitting and jj-closed shell nuclei Only surface effect of pion Ogawa Toki toki@riken

  9. p-h p-h L Pion has volume effect(Pion is important in nuclear matter) Kaiser, Fritsch, Weise, NPA697(2002) G. Brown, Book qmax~2kF~3fm-1 (Akaishi) Tensor force is important!! qmax R ~ Lmax toki@riken

  10. Relativistic extended chiral mean field model Ogawa,Toki (2008) Linear Sigma Model Lagrangian Sigma condensation (NJL mechanism) produces finite masses. toki@riken Weinberg transformation

  11. Hadrons get mass Non-linear sigma model Two free parameters: Sigma meson mass Omega-nucleon coupling toki@riken

  12. Relativistic extended chiral mean field model Nucleon + sigma and omega Sigma+omega model with one pion exchange p p’ h’ h qmax R ~ Lmax Pionic quantum number 6 for 4He toki@riken

  13. Self-consistent variational calculation Mean field equation Nucleon 2p-2h states Oset-Toki-Weise formulation, Phys.Rep.(1984) toki@riken

  14. RECMF model results bmax~0.7fm Jmax~6 bs=1.4fm toki@riken

  15. RECMF model results (2) toki@riken

  16. RECMF model results (3) M is reduced by 10~15% Chiral symmetry is partially recovered! toki@riken

  17. Conclusion • We construct Relativistic Extended Chiral Mean Field model for finite nuclei • We have calculated 4He in RECMF and found quantitatively satisfactory results • We can move to medium heavy nuclei toki@riken

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