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

Quasi-particle excitations

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

(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

BCS Crossover region

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Messages from Nuclear Matter Calculations 76, 064316(2007)

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

Three-body model H. Esbensen, G.F. Bertsch, K. Hencken, Phys. Rev. C56(’99)3054 n r1 Density-dependent delta-force VWS VWS r2 v0 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

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

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

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)

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

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

: di-neutron configurations : cigar-like