Many-Body Resonances of Nuclear Cluster Systems and Unstable Nuclei

Transcription

1 Many-Body Resonances of Nuclear Cluster Systems and Unstable Nuclei Contents of the lecture 1. Resonances and complex scaling method 2. Many-body resonances of He-isotopes and their mirror nuclei 3. Coulomb breakup reactions of Borromean Nuclei 6 He and 11 Li 4. New 3α resonant states in 12 C References: S. Aoyama, T. Myo, K. Kato and K. Ikeda, Prog. Theor. Phys. 116 (2006), H. Horiuchi, K. Ikeda and K. Kato, Prog. Theor. Phys. Suppl. 192 (2012),

2 Proton-rich Z PRC 84 (2011) PRC 85 (2012) Nuclear Chart stable nuclei Z N, τ= β-unstable nuclei Z>N or N>Z unbound & particle emission Neutron-rich unbound nuclei PRC 80 (2009) PLB 691 (2010) 150 Mirror symmetry between proton-rich & neuron-rich (with Coulomb) N

3 Neutron-rich He isotopes : experiment 3-body resonance 4-body resonance TUNL Nuclear Data Evaluation 5-body resonance 1/2? halo E ~ 8MeV/A α n n skin α E 1MeV/A 3

4 Proton-rich 7 B & 8 C Proton-rich unbound nucleus 4 He- 5 Li- 6 Be- 7 B- 8 C, decay into α+p+p+p(+p) systems Experiments Only the ground states are observed. 7 B: L. R. McGrath & J. Cerny, Phys. Rev. Lett. 19, 1442 (1967). 8 C: R. G. H. Robertson, S. Martin, W. R. Falk, D. Ingham, A. Djaloeis, Phys. Rev. Lett. 32, 1207 (1974). 8 C & 20 Mg R. J. Charity et al., Phys. Rev. C 84, (2011). 9 C beam: 7 B, 8 B*, 8 NO theory describes resonances of 7 B & 8 C, so far. Mirror symmetry of p-rich & n-rich unstable nuclei 7 B- 7 He, 8 C- 8 He : energies levels, configurations

5 Complex-Scaled Cluster Orbital Shell Model Cluster Orbital Shell Model (COSM) Include open channel effects. 8 He : 7 He+n, 6 He+n+n, 5 He+n+n+n,... Complex Scaling Method iθ r re, k ke iθ Obtain resonance w.f. with correct α boundary condition as Gamow states E=E r iγ/2 Give the continuum level density, E resonance+continuum, Green s function strength function, Lippmann-Schwinger Eq., T-matrix n r 1 r 2 r 3 r 4 A.T. Kruppa, R.G. Lovas, B. Gyarmati, PRC37(1988) 383 ( 8 Be as 2α) S. Aoyama, Myo, K. Kato, K. Ikeda, PTP116(2006) 1 (CSM review) C. Kurokawa, K. Kato, PRC71 (2005) ( 12 C as 3α) Kikuchi (LS eq.) 5 5 Matsumoto (CDCC)

6 He isotopes : Expt vs. Complex Scaling 3-body resonance 4-body resonance 5-body resonance n α Myo, K.Kato, K.Ikeda PRC76( 07) Myo, R.Ando, K.Kato PRC80( 09) Myo, R.Ando, K.Kato, PLB691( 10)150 TUNL Nuclear Data Evaluation 6 6

7 Matter & Charge radii of 6,8 He [fm] [fm] Expt Theor R m R ch I. Tanihata et al., PLB289( 92)261 G. D. Alkhazov et al., PRL78( 97)2313 O. A. Kiselev et al., EPJA 25, Suppl. 1( 05)215. P. Mueller et al., PRL99(2007)

8 Energy of 8 He with complex scaling 5-body resonance Eigenvalue problem with 32,000 dim. Full diagonalization of complex SX8R of NEC 8

9 Proton-rich side : 4 He+4p 3-body resonance 4-body resonance 5-body resonance p α Charity et al. PRC84(2011) TUNL Nuclear Data Evaluation Γ(exp) ~ 0.130(50) MeV

10 Mirror symmetry in resonances n-rich vs. p-rich Myo, Kikuchi, Kato PRC84 (2011) PRC85 (2012) Good symmetry 10

11 neutron removal 6 7 S 0 + a n J π J ', J J ', J = nlj S-factors of 7 He & 7 B He( ) ( ) He( ) 6 7 S 0 a p J π = nlj + nlj Be( ) ( ) B( ) nlj 2 2 α 6 He (halo) n 7 He 7 B Expt. of 7 He : F. Beck et al., Phys. Lett. B 645 (2007)

12 One-neutron removal strength of 7 He GS 6 J' ν 7 J S 6 J ' 7 J J'J (E) = J ', J ( E) = He (E He α) a ( E) njl He δ (E E ) anlj ( n) He α α njl nlj njl 2 2 Myo, Ando, Kato PRC80(2009) He+n+n ν complete set with CSM ν 1 1 = Im He (E ) a He (E ) He (E ) a He π α 7 J 6 J' 6 J' 7 J α njl α α njl E Eα 7 He(3/2 ) α n 6 He ( * ) n 1 5 He+n 4 He+n+n 4 He+n+n 12 12

13 One-neutron removal strength of 7 He GS 6 J ' 7 SJ ', J ( E) = He ( E) anlj ( n) He nlj J 2 Myo, Ando, Kato PRC80(2009) He+n+n complete set using CSM He+n 4 He+n+n He(3/2 ) α 6 He ( * ) n n 1 5 He+n 4 He+n+n 4 He+n+n 5 He+n 13 13

14 Configuration weights of 8 C, 8 He G.S. 0p0h p2h 8 C (4p) 8 He (4n) (p 3/2 ) (p 3/2 ) 2 (p 1/2 ) (p 3/2 ) 2 (d 5/2 ) C (4p) 8 He (4n) (p 3/2 ) (p 3/2 ) 2 (p 1/2 ) (p 3/2 ) 2 (d 3/2 ) Good symmetry between 8 C & 8 He 14

15 Continuum effect in 8 He (r n < 6 fm) G.S. 0p0h Full No continuum (p 3/2 ) (p 3/2 ) 2 (p 1/2 ) (p 3/2 ) 2 (d 5/2 ) p2h Full No continuum (p 3/2 ) (p 3/2 ) 2 (p 1/2 ) (p 3/2 ) 2 (1s 1/2 ) (p 3/2 ) 2 (d 3/2 ) (p 3/2 ) 2 (d 5/2 )

16 Radial properties of 8 C, 8 He G.S. 8 C 8 He 10%-15% increase due to Coulomb repulsion I. Tanihata et al., PLB289( 92)261 G. D. Alkhazov et al., PRL78( 97)2313 O. A. Kiselev et al., EPJA 25, Suppl. 1( 05)215 cf. 6 Be- 6 He, 20% increase (2p) (2n)

17 Radial properties of 8 C, 8 He C 8 He 30% decrease due to Coulomb barrier C (E r, Γ) = (8.9, 6.4) (MeV) 8 He (E r, Γ) = (3.1, 3.2) comparable 17

18 Summary and conclusion of Section 2 The complex-scaled cluster orbital shell model (CS-COSM) calculations well describe many-body resonant states of He isotopes (n-rich) & Mirror nuclei (p-rich). Observed levels are well reproduced and many excited resonant states are predicted. Observed matter and charge radii for halo and skin nuclei are well explained. Mirror symmetry breaking due to Coulomb interaction and difference of threshold energies. 18

19 3. Coulomb Breakup Reactions of Borromean Borromean systems Nuclei 6 He and 11 Li three-body system whose any two-body subsystem has no bound states Borromean Family Symbol Two-Neutron Halo Systems: 11 Li= 9 Li+n+n, 6 He= 4 He+n+n

20 Coulomb breakup reactions are good means to investigate structures of weakly-binding systems such as halo nuclei: s-wave components and di-neutron correlation. 9 Li, 11 Li Electro-Magnetic interactions

21 of 11 Li, ( 6 He)

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23 The COSM bases have to be taken up to l=16 in order to obtain a good convergence of the ground state energy. This means that the n-n correlation is important.

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25 Strength Functions and Coulomb Breakup Reaction T. Myo, A. Ohnishi and K. Kato, Prog. Thepr. Phys. 99, (1998) 801

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27 ~ " ~ ' ~ ~ ~ 1 " " 1 ' ' 1 1 " ' θ θ π θ θ π θ θ π θ θ θ θ ψ ψ ψ ψ ψ ψ θ θ θ θ k k L k k L k k L N r n n n n n b n k k k r dk dk dk u u u u = = = 4 He+n+n 5 He(3/2 - )+n 5 He(1/2 - )+n Resonances T. Myo, A. Ohnishi and K. Kato, Prog. Theor. Phys. 99 (1998), 801. Extended Completenes Relation in CSM Complex Scaling Resolution of Continuum States 5 He(1/2 - )+n 5 He(3/2 - )+n 4 He+n+n

28 E1 Strength Components of Continuum States T. Myo, K. Kato, S. Aoyama and K. Ikeda, PRC63(2001),

29 Coulomb breakup strength of 6 He d σ E (, ) NE ( E) db E E λ λ λ NEλ ( E) : virtual photon number de de 6 He : 240MeV/A, Pb Target (T. Aumann et.al, PRC59(1999)1252) T.Myo, K. Kato, S. Aoyama and K. Ikeda PRC63(2001)