Pairing Correlations in Nuclei on Neutron Drip Line

Transcription

1 Pairing Correlations in Nuclei on Neutron Drip Line INT Workshop on Pairing degrees of freedom in nuclei and the nuclear medium Nov , 2005 Hiroyuki Sagawa (University of Aizu) Introduction Three-body model Di-neutron and H 2 O molecule (cigar) -type configurations Summary collaborator: K. Hagino (Tohoku University)

2 Nuclear Landscape stable nuclei Z=113 RIKEN 126 superheavy nuclei protons known nuclei proton halo p-n pairing rp-process 50 neutrons proton drip line neutron drip line continuum correlations neutron halo, skin, di-neutrons r-process unknown region neutron stars

3 skin nucleus 24 O

4 Pairing correlations in nuclei on the neutron drip line - Borromean systems - K. Hagino and H. Sagawa Phys. Rev. C72,044321(2005) 1. Three body model with a density-dependent delta-interaction 2. Ground states of borromean nuclei 6 Heand 11 Li and a skin nucleus halo vs. skin di-neutron vs. molecule configurations 3. Dipole excitations 4. Summary 24 O S=0 S=0 or 1 di-neutron H 2 O moleculetype cigar-type)

5 Three-body model (Bertsch-Esbensen, Ann.Phys.209,327(1991), Nucl.Phys.A542, 310 (1992). ) where a nn = -15fm is nn scattering length and k c is determined by the effective range, while vρ, Rρ and aρ are adjusted in order to reproduce known ground state properties of each nucleus.

6 V nc Parameters of V n-c ans V n-n interactions r 2 1 d 1 V nc() r V ( r = fsoro l s) rdr 1+ exp(( r R)/ a) with R = ra o 1/3 C fm. V o (MeV) r o (fm) a (fm) f so 6 He Li (-parity) (+parity) O V nn 6 He v v ρ Rρ a ρ o (MeVfm 3 ) (MeVfm 3 ) (fm) (fm) E cut (MeV) Li O

7 Two neutron state for ground state where is the eigenstates of single-particle Hamiltonian h nc. Neutron separation Di-neutron-core distance

8 Ground State Properties 2 1/2 2 1/2 2n nn c-2n nucleus S (MeV) r (fm) r (fm) configuration (%) He (p ) /2 Li (p ) / /2 (ε s1/2 = 2.739MeV, ε d5/2 = 3.806MeV) 2 (s 1/2) 22.7 O (s ) 93.6 Li (p ) /2 S 2n is still controversial in 11 Li. C. Bachelet et al., S 2n =376+/-5keV (ENAM,2004) 2 (s 1/2 ) 22.1

9

10 Two-body Density ρ uuvuv uuvuv ( r, r, θ ) = Ψ ( rr, ) Ψ ( rr, ) gs 1 2 gs 1 2 = ρ ( r, r, θ ) + ρ ( r, r, θ ) S = 0 S = One-body density as a function of angle rdr 1 1 r2 dr2 2 r1 r ρθ ( ) 4 π ρ (,, θ )

11 Spin decomposition of two-body density ρ $$ ' ' 1 ll L l l L ( r, r, θ ) = $ 8π ' ' Ll,, jlj, 4π S = ' ' l+ l 2j+ 1 2j + 1 ( ) Φ ( ' lj r1, r2) Φ ' '( r1, r2) YL0( θ12) lj 2l+ 1 2l + 1 ρ $$ ' ' ' 1 ll L l l L l l L ( r, r, θ ) = $ 8π ' ' Ll,, jlj, 4π S = ' ' j+ j 2j+ 1 2j + 1 ( ) 2 2 Φ ( ' lj r1, r2) Φ ' '( r1, r2) YL0( θ12) lj 2l+ 1 2l + 1 2

12 Total S=0 S=1

13 ρ Two-body Density uuvuv uuvuv ( r, r, θ ) = Ψ ( rr, ) Ψ ( rr, ) gs 1 2 gs 1 2 = ρ ( r, r, θ ) + ρ ( r, r, θ ) S = 0 S = One-body density as a function of angle rdr 1 1 r2 dr2 2 r1 r ρθ ( ) 4 π ρ (,, θ ) 2 For (p) J=0 configuration, S=0 and S=1 contributions (Talmi-Moshinsky transformation ); sin( θ ) ρ ( θ ) sin( θ )con( θ ) S= sin( θ ) ρ ( θ ) sin( θ ) S= For (s) J=0 configuration, only S=0 is possible. Peaked at 35 o and 145 o 90 o

14 Total S=0 S=1

15 Total S=0 S=1

16 Average correlation angles 6 He 11 Li 24 O ϑ o 65.3 o 82.7 o Anti-halo effect in 24 O r m (2n)=4.45fm r(2s 1/2 )=4.65fm

17 How can we observe di-neutron and H 2 O-type configurations? Parity Violation Electron scattering (Polarized electron beam) Coulomb break-up reaction. (Electric Dipole Excitations) Two-neutron transfer reactions.

18 Dipole Response Transition density

19

20 T.Nakamura et al., RIKEN Accel.Prog.Rep.38(2005)

21 Sum rule strength in 11 Li Exp: Ex<3.3MeV B(E1)=(1.5 +/- 0.1)e 2 fm 2 Cal: Ex<3.3MeV B(E1)= 1.31 e 2 fm 2

22 Continuum Energy Spectrum of 6 He above alpha+2n threshold T. Aumann et al., PRC59, 1259(1999)

23

24 Present (E<5MeV) (E<10MeV)

25 Experimental proof of di-neutron and/or molecule-type configurations Coulomb breakup reactions 2n transfer reactions Dipole strength 6 ( α, He) ( p, t)

26 Elastic di-neutron transfer in the 4 He( 6 He, 6 He) 4 He reaction n a n n n a Molecule configuration Di-neutron configuration 6 He 5 He 4 He 6 He 4 He n n 2n 4 He 5 He 6 He 4 He 6 He Sequential (two-step) transfer Direct (one-step) transfer D.T. Khoa and W. von Oertzen, Phys. Lett. B595 (2004) 193

27 Coupled Reaction Channels(CRC) results obtained with FRESCO code Louvain-la-Neuve data: R. Raabe et al., Phys. Lett. B458 (1999) 1; Phys. Rev. C67 (2003) ES= Elastic scattering TF= 2n-transfer Dominance of the direct 2n-transfer!

28 Dubna data: G.M. Ter-Akopian et al., Phys. Lett. B426 (1998) 251. CRC analysis: D.T. Khoa and W. von Oertzen, Phys. Lett. B595 (2004) 193.

29 N.K. Timofeyuk, Phys. Rev. C63 (2001) S-wave J=L=0 P-wave J=L=1 Di-neutron Molecule (85%) (15%) Study using the hyperspherical basis [E. Nielsen et al., Phys. Rep. 347 (2001) 373]; Cluster model [D. Baye et al., Phys. Rev. C54 (1996) 2563].

30 CRC results obtained with the code FRESCO (I.J. Thompson) Direct 2n TF 2n 6 He+ 4 He 4 He+ 6 He Indirect 2n TF 6 He* He 4 He+ 6 He* 2+ 2n 6 He+ 4 He 4 He+ 6 He via unbound 2 + excitation of 6 He

31 Summary 1. We have studied a role of di-neutron correlations in weakly bound nuclei on the neutron drip line. 2. The two peak structure is found in the borromean nuclei: One peak with small open angle -> di-neutron Another peak with large open angle -> H 2 O molecule type correlation. 3. Di-neutron configuration is dominated by S=0, while the H 2 O depends on the nuclei having either S=1 or S=0. 4. A skin nucleus 24 O shows no clear separation of the two configurations. 5. Dipole excitations show strong threshold effect in the borromeans, while there is no clear sign of the continuum coupling in the skin nucleus. 6. The threshold effect is dominated by the S=0 wave functions on the other hand, the coherent sum of S=0 and S=1 states enhances the dipole strength in 24 O. 7. Possible experimental probe Coulomb excitation, 2n transfer,

32 Future Perspectives 1. S=1 correlations: parity doublets. 2. Angular correlations of two-neutron breakup reactions. 3. Two-proton halo 19 F.