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

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

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

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:

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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

Summary Application of three-body model to Borromean nuclei 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

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

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

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