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Pairing Correlation in neutron-rich nuclei

Pairing Correlation in neutron-rich nuclei. K. Hagino (Tohoku University) H. Sagawa (University of Aizu). 11 Li. Motivation: BCS-BEC crossover Three-body model with density-dependent delta interaction Ground state properties of 11 Li and 6 He Relation to BCS-BEC crossover

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Pairing Correlation in neutron-rich nuclei

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  1. Pairing Correlation in neutron-rich nuclei K. Hagino (Tohoku University) H. Sagawa (University of Aizu) 11Li • Motivation: BCS-BEC crossover • Three-body model with density-dependent delta interaction • Ground state properties of 11Li and 6He • Relation to BCS-BEC crossover • Di-neutron correlation in 8He and in heavier nuclei • Parametrization of density-dependent pairing interaction • Summary

  2. Introduction: 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

  3. Implication to finite nuclei? Relation to di-neutron correlation? Spatial structure of neutron Cooper pair in infinite matter BCS Crossover region M. Matsuo, PRC73(’06)044309

  4. 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:

  5. 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

  6. Two-particle wave functions (J=0 pairs) Hamiltonian diagonalization • Continuum: box discretization • Energy cut-off:

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

  8. Geometry of Borromean nuclei “experimental” mean opening angle (note) forbidden transition H. Esbensen, K.H., P. Mueller, and H. Sagawa, PRC76(’07)924302

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

  10. Dipole excitations K.H. and H. Sagawa,PRC76(’07)047302

  11. Geometry of Borromean nuclei “experimental” mean opening angle (note) forbidden transition H. Esbensen, K.H., P. Mueller, and H. Sagawa, PRC76(’07)924302 or also from HBT-type 2n correlation study

  12. 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

  13. Relation to BCS-BEC crossover 11Li probing the behaviour of 2n-wf at several densities

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

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

  16. 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)

  17. Di-neutron correlation in 8He a + 4n model Vna: Woods-Saxon vnn: density-dependent contact force Hartree-Fock-Bogoliubov (HFB) + PNP (VBP) two-body correlation density 4 particle density (dineutron-dineutron configuration)

  18. r q12 r Di-neutron correlation in 8He two-body correlation density 4 particle density (dineutron-dineutron configuration) r q12 r K.H. and N. Takahashi, in preparation

  19. Surface di-neutron condensation? canonical basis representation (wf for condensation) 8He (core + 4n) 84Ni (WS-HFB) (contribution from v2 < 0.9)

  20. Density-dependent pairing interaction? “standard” parametrization: : volume pairing fm-3 : surface pairing fm-3 : mix pairing another parametrization? I=(N-Z)/(N+Z) J. Margueron, H. Sagawa, and K.H., arXiv: 0710.4241

  21. Ec=40 MeV hs as hn an bare 0.664 0.522 1.01 0.525 screened 1.80 0.27 1.61 0.122 J. Margueron, H. Sagawa, and K.H., arXiv: 0710.4241

  22. isotope dependence of pairing properties in finite nuclei(HFB calculation)? J. Margueron, H. Sagawa, and K.H., arXiv: 0710.4241

  23. 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

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

  25. charge radius 11Li 1.175(124) fm2 (exp) 0.789 fm2 (3body model) 6He 2.054(14) fm2 (exp) 2.036 fm2 (3body model) H. Esbensen, K.H., P. Mueller, and H. Sagawa, PRC76(’07)924302

  26. for 84Ni q (deg) r (fm) contribution from the “core” (v2 > 0.9) contribution from the valence (v2 < 0.9)

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