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軽い中性子過剰核と BCS-BEC クロスオーバー

軽い中性子過剰核と BCS-BEC クロスオーバー. K. Hagino (Tohoku University) H. Sagawa (University of Aizu). 11 Li, 6 He. Motivation: Pairing correlation in nuclei Ground state properties of 11 Li and 6 He Di-neutron correlation and BCS-BEC crossover LL 6 He ? Summary.

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軽い中性子過剰核と BCS-BEC クロスオーバー

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  1. 軽い中性子過剰核と BCS-BEC クロスオーバー K. Hagino (Tohoku University) H. Sagawa (University of Aizu) 11Li, 6He • Motivation: Pairing correlation in nuclei • Ground state properties of 11Li and 6He • Di-neutron correlation and BCS-BEC crossover • LL6He ? • Summary

  2. Introduction: Pairing correlations in nuclei Mean-field approximation closed shell nuclei + + ….. + open shell nuclei weakly bound nuclei

  3. Introduction: Pairing correlations in nuclei Coherence length of a Cooper pair: much larger than the nuclear size (note) x = 55.6 fm (for A=140) R = 1.2 x 1401/3 = 6.23 fm

  4. Introduction: Pairing correlations in nuclei Coherence length of a Cooper pair: much larger than the nuclear size ? Di-neutron correlations in neutron-rich nuclei cf. HFB calculations for 18-24O, 50-58Ca, 80-86Ni: M. Matsuo, K. Mizuyama, Y. Serizawa, PRC71(’05)064326 Coul. b.u. of 11Li 11Li K.H. and H. Sagawa, PRC72(’05)044321 T. Nakamura et al., PRL96(’06)252502

  5. BCS-BEC crossover crossover BCS (weak coupling) BEC (strong coupling) • Weakly interacting • fermions • Correlation in p space • (large coherence length) • Weakly interacting • “diatomic molecules” • Correlation in r space • (small coherence length) cf. BEC of 40K molecules M. Greiner et al., Nature 426(’04)537 cf. BCS-BEC crossover in color superconductivity: Y. Nishida and H. Abuki, PRD72(’05)096004

  6. BCS-BEC crossover Cooper pair wave function: crossover BEC (strong coupling) BCS (weak coupling) Correlation in r space (small coherence length) Correlation in p space (large coherence length) x x

  7. BCS-BEC crossover crossover BCS (weak coupling) BEC (strong coupling) • Weakly interacting • fermions • Correlation in p space • (large coherence length) • Weakly interacting • “diatomic molecules” • Correlation in r space • (small coherence length) ?? ?? Di-neutron correlations in neutron-rich nuclei Pairing in stable nuclei

  8. BCS-BEC crossover behavior in infinite nuclear matter Neutron-rich nuclei • Weakly bound levels • Unsaturated density around surface (halo/skin) pairing gap in infinite nuclear matter M. Matsuo, PRC73(’06)044309

  9. Spatial structure of neutron Cooper pair in infinite matter BCS Crossover region M. Matsuo, PRC73(’06)044309

  10. Spatial structure of neutron Cooper pair in infinite matter Our Motivations • How can this behavior be seen in finite nuclei? • Relation to di-neutron • correlation? 11Li = 9Li + n + n M. Matsuo, PRC73(’06)044309

  11. Three-body model with density-dependent delta force G.F. Bertsch and H. Esbensen, Ann. of Phys. 209(’91)327 H. Esbensen, G.F. Bertsch, K. Hencken, Phys. Rev. C56(’99)3054 11Li, 6He n r1 VWS Density-dependent delta-force VWS r2 core n Diagonalization:

  12. r Two-particle density for the ground state q12 r 「水分子型」 中性子ハロー 「強相関型」 「水分子型」と「強相関型」 の共存 K. Hagino and H. Sagawa, Phys. Rev. C72(’05)044321

  13. r q12 r Two-particle density for the ground state strong di-neutron correlation 11Li 6He K.H. and H. Sagawa, PRC72(’05)044321

  14. Geometry of Borromean nuclei 11Li “experimental” mean opening angle B(E1) matter radius or HBT 6He (11Li) (6He) K.H. and H. Sagawa, PRC76(’07)047302

  15. Dipole excitations Response to the dipole field: K.H. and H. Sagawa,PRC76(’07)047302

  16. Relation to BCS-BEC crossover 11Li S=L=0 probing the behaviour of 2n-wf at several densities

  17. K.H., H. Sagawa, J. Carbonell, and P. Schuck, PRL99(’07)022506

  18. good correspondence 11Li Nulcear Matter Calc. K.H., H. Sagawa, J. Carbonell, and P. Schuck, PRL99(’07)022506. M. Matsuo, PRC73(’06)044309

  19. 2-neutron rms distance Matter Calc. 11Li M. Matsuo, PRC73(’06)044309 cf. Free n-n system virtual state around zero energy < r > ~ 12 fm (Nijmegen potential)

  20. 3-body structure of LL6He LL6He L Set R=1.25*41/3 fm and a=0.65 fm, and adjust V0 so that e1s1/2 = -BL(L5He) = -3.12 MeV V0 = 24.67 MeV a L adjust g so that E(LL6He) = Eexp = -7.25 MeV

  21. r q12 r (s1/2)2 : 98.5 %

  22. Summary • Application of three-body model to Borromean nuclei 11Li • Di-neutron wave function for each R • Close correspondence to the matter calculations • BCS/BEC crossover phenomenon • Concentration of a Cooper pair on the nuclear surface • Also in other superfulid nuclei (universality) very different from the conventional view of pairing 6He, 16C, 24O cf. see also N. Pillet et al., PRC76(’07)024310

  23. Gogny HFB calculations N. Pillet, N. Sandulescu, and P. Schuck, PRC76(’07)024310

  24. Density-dependent delta interaction H. Esbensen, G.F. Bertsch, K. Hencken, Phys. Rev. C56(’99)3054 • Two neutron system in the vacuum: • Two neutron system in the medium: : adjust so that S2n can be reproduced

  25. M. Matsuo, K. Mizuyama, Y. Serizawa, PRC71(’05)064326

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