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. 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

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. Two-particle density for the ground state strong di-neutron
correlation
11Li r
q12
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. Response to the dipole field:
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. 11Li good correspondence Nulcear Matter Calc.
K.H., H. Sagawa, J. Carbonell, and P. Schuck,
PRL99(’07)
M. Matsuo, PRC73(’06)044309

16. 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)

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. 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

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:

21. Ec=40 MeV
hs as hn an
bare
screened
J. Margueron, H. Sagawa, and K.H., arXiv:

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

23. 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

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
H. Esbensen, K.H., P. Mueller, and H. Sagawa,
PRC76(’07)924302

26. 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)