1. Di-nucleon correlations and soft dipole excitations in exotic nuclei
Institute of Theoretical Physics, CAS
September 24, 2010
Hiroyuki Sagawa
Center for Mathematics and Physics, University of Aizu
Introduction
BCS-BEC crossover
Three-body model and di-neutron correlations in exotic nuclei
Soft dipole excitations and three-body breakup in 6He and 11Li
Di-proton correlations in 17Ne
Summary

2. Quasi-particle excitations

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

6. (large coherence length) Interacting “diatomic molecules”
Weakly interacting
fermions
Correlation in p space
(large coherence length)
Interacting
“diatomic molecules”
Correlation in r space
(small coherence length)
cf. BEC of molecules in 40K
M. Greiner et al., Nature 426(’04)537

12. BCS
Crossover region

13. -

15. Messages from Nuclear Matter Calculations
76, (2007)

16. 16C
18C
Borromian Nuclei
(any two body systems are not bound, but three body system is bound)

17. Three-body model H. Esbensen, G.F. Bertsch, K. Hencken,
Phys. Rev. C56(’99)3054 n r1
Density-dependent delta-force
VWS
VWS r2
v ann
a S2n
core n
(note) recoil kinetic energy of the core nucleus
Hamitonian diagonalization with WS basis
Continuum can be included by solving Green’s functions
Pauli blocking is properly taken into account.
Important for
dipole excitation
Application to 11Li, 6He

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

19. Application to 11Li, and 6He
11Li, 6He: Typical Borromean nuclei
11Li:
(Efimov states ?)
WS: adjusted to p3/2 energy in 8Li & n-9Li elastic scattering
Parity-dependence to increase the s-wave component
6He:
WS: adjusted to n-a elastic scattering

20. Two-particle density for 11Li
q12
9Li r2 n
Set r1=r2=r, and plot r2 as a
function of r and q12
two-peaked structure
Long tail for “di-neutron”
S=0
S=0 or 1
di-neutron
cigar-type)

21. Comparison among three nuclei
11Li
6He
(p1/2)2 :59.1%
(s1/2)2 :22.7% (d5/2)2 :11.5%
(p3/2)2 :83.0 %
(d5/2)2 :6.11 %, (p1/2)2 :4.85 %
(s1/2)2 :3.04 %, (d3/2)2 :1.47 %
for (p1/2)2 or (p3/2)2
for (s1/2)2

22. Probing the behavior at several densities
Coexistence of BCS-BEC like behaviour of Cooper Pair in 11Li
Probing the behavior
at several densities

23. : di-neutron
configurations
: cigar-like