1. Unified Studies of the exotic structures in 12 Be and the  + 8 He slow scattering Makoto Ito, Naoyuki Itagaki Theoretical Nuclear Physics Lab., RIKEN Nishina Center Department of Physics, Tokyo University I. Introduction II. Formulation : Extended microscopic cluster model III.  + 8 He scattering and exotic structures in 12 Be IV. Monopole transition of 12 Be V. Summary and Future perspectives

2. Cluster effects in reactions 1. Molecular Resonances (MRs) are typical examples : 12 C+ 12 C, 16 O+ 16 O, 12 C+ 16 O Val. N : tight binding Transfers of a valence neutron → No sharp resonances Val. N : weak binding Transfer of “active” neutrons → Sharp resonances are generated ? A (Cores) >> XN A (Cores) ～ XN ⇒ Collective excitation of individual nuclei is essential. 2. MR system + one valence neutron : 12 C+ 13 C, 16 O+ 17 O, etc… Transfer process is extensively investigated ⇒ NO clear resonances !! Transfer effect in neutron-rich systems Previous studies ( 12 C+ 13 C etc)Neutrons’ drip-line case N～ZN～Z N >> Z An additional neutron

3. Our interest : transfer reaction by a neutrons’ drip line nucleus Ex. energy Orthogonality Low-lying B.S. states Molecular Orbitals (MOs):  ― 、  ＋ ‥ Resonance formation Slow RI beam Transfer channels Today’s report N AB E ( A+B ) Unbound region Bound region + 8 He + 4 He (= 12 Be) 4 He + 4N + 4 He Scattering and structure ⇒ Transfer effects shall be strong !! We should combine MO and asymptotic channels. ( ) ( Exp. at GANIL )

4. 12 Be (experiments) 12 Be+  → ( 6 He+ 6 He)+  A. Saito et al. 6 He + 6 He (Atomic) Moleculue Structural changes Low-lying (Breaking of N=8 Magicity)High-lying states (Atomic) (Important system before proceeding systematic studies) E(sd-0p) ～ 1MeV Def. Length ～ 2fm

5.  1/2+ (sd) -- ++ -- ++ 3/2+ (sd) 1/2- (0p) 3/2- (0p) 1/2+ (sd) 1/2- (pf) ＋ ― ― ＋ Formulation ( I ) : Single particle motion in two centers  ( s.p.) =  (L) ±  (R) : LCAO  L (0p) ±  R (0p) Y(1,0) Y(1,±1)  (0p) S Z Config. Mixing Distance : S  (0s) 4 ( 10 Be=  +  +N+N )

6.  (  + ) 2 = ( P z (L) ― P z (R) ) 2 Formulation (II)  + 6 He 6 He +  5 He + 5 He Linear Combination of Atomic Orbital (LCAO)   + 6 He(0 + ) = P z (L) ・ P z (L) + P z (R) ・ P z (R) － 2P z (L) ・ P z (R) = P x (R) ・ P x (R) + P y (R) ・ P y (R) +P z (R) ・ P z (R) Total wave function Pm(a)・Pn(b)Pm(a)・Pn(b) (m,n)=x,y,z(a,b) = L,R Variational PRM S Z General MO: ( C(L)P i (L) + C(R)P j (R) ) 2

7. Energy surfaces in 12 Be =  +  +4N (0p 3/2 ) 2 (sd) 2 (  - ) 2 (  + ) 2 (0p) 6 (  - ) 4 Adiabatic Energy surfaces 2 MeV Atomic-Molecular Hybrid configuration 6 He Covalent SD S ～ 5fm V NN : Volkov No.2+G3RS J  = 0 +  + 8 He 6 He + 6 He 5 He + 7 He  + 8 He Continuum Energy R(  ) ～ 1.4fm

8. Coupling to open channels in continuum Open channels Compound states (Closed) Bound state approximation with Atomic Orbital Basis Scattering B.C. Rearrangement channels :  + 8 He g.s. 、 6 He g.s. + 6 He g.s. 、 5 He g.s. + 7 He g.s. Closed states method : Prof. Kamimura, Prog. Part. Nucl. Phys. 51 (2003) 400 ～ 500 S.D. with J  projection

9.  + 8 He ⇒ 6 He + 6 He Cross sections ( mb ) E c.m. ( MeV ) Cross sections of neutron transfers E c.m. ( MeV )  + 8 He ⇒ x He + y He (J  =0 + ) Elastic 6 He + 6 He 5 He + 7 He Dotted curves : Three open channels only Solid curves: Open + closed chanels This is a prediction for recent experiments at GANIL.

10. Effects of the transfer coupling : Minimum coupling  + 8 He g.s.  + 8 He(2 1 + ) 6 He g.s. + 6 He(2 1 + ) 6 He(2 1 + ) + 6 He(2 1 + ) 5 He(3/2 － ) + 7 He(3/2 1 － ) 5 He(3/2 － ) + 7 He(1/2 1 － ) 5 He(3/2 － ) + 7 He(5/2 1 － ) 5 He(1/2 － ) + 7 He(3/2 1 － ) 6 He g.s. + 6 He g.s. Dotted curves Sharp resonant structures are generated by Transfer Coupling → New aspects !!  + 8 He ⇒ x He+ y He Elastic 6He+6He 5He+7He I=0 5He+7He I=2 Solid : Full calculation

11. Schematic picture of excitation modes

12. Excitation modes in 12 Be 7 He 5 He 6 He 8 He 6 He Excitation from the 0 2 + state. Excitation from the 0 1 + state. Cluster + S. P. Excitation 01+01+ 02+02+ Cluster’s relative Motion is excited. Single particle Excitation (-)2(-)2 (-)2(-)2 (  - ) 2 (  + ) 2 (0p R )(0p L ) (  + ) 2 05+05+ 03+03+ 04+04+ 06+06+  + 8 He ⇒ 6 He+ 6 He Covalent SD  -  REL. + S.P. of 4N 6 He + 6 He  + 8 He

13. Coexistence in A=12 systems : Coexistence phenomena  + 8 He g.s. 6 He g.s. + 6 He g.s. 5 He g.s. + 7 He g.s. 12 C  12 B  + 8 Be g.s. 5 He g.s. + 7 Be g.s. 6 He g.s. + 6 Be g.s.  + 8 Li g.s. 6 He g.s. + 6 Li g.s. 5 He g.s. + 7 Li g.s. 12 Be 02+02+ Hoyle state 03+03+ 04+04+ 05+05+ 06+06+ 19.8 MeV 8.8 MeV 5.4 MeV 2.9 MeV ～ 4 MeV Coexistence becomes prominent. Vn-n 、 V  -n is Weak.

14. Comparison of 12 Be and 12 C 12 Be +  → ( 6 He+ 6 He) +  12 C +  → (  +  +  ) +  There appear many resonances !! ( A. Saito et al. at Tokyo Univ. ) ( M. Itoh et al. at Tohoku Univ. ) 0+0+ No decays to  + 8 He 7.512

15. Rotational bands : Coexistence of MRs and covalent SD Exp. at RIKEN (Saito) Red : Covalent SD Pink : 5 He + 7 He Green : 6 He + 6 He Blue :  + 8 He Green squares: (  - ) 2 (  + ) 2 White square: (  - ) 2 (  - ) 2 Exp. by Freer Exp. at RIKEN (Shimoura) Bound region Scattering region

16. Monopole Transition Pioneering work on monopole transition Simple shell model (1p-1h, 2hw) ： No strength around low-lying region, Ex<10MeV Cluster correlation in a ground state (Yamada et al., PTP, inpress) There is a possibility that monopole transitions are enhanced If cluster structures are developed. ( Ex < 10MeV ) Excitation of clusters’ relative motion (2hw) Cluster structure If has large cluster components, the monopole matrix elements will be enhanced ! Large cluster components in G.S. can be always justified by Bayman-Bohr Theorem Why monopole ?

17. Adiabatic energy surfaces in 12 Be Adiabatic Energy surfaces V NN : Volkov No.2+G3RS  + 8 He 8 He (  - ) 2 (  + ) 2  –  Distance 3 rd 0 + 1 st 0 + GCM (0 1 + ) GCM (0 3 + ) Cluster Excitation  –  Distance

18. Monopole transition of 12 Be (  - ) 2 (  + ) 2 8 He 01+01+ 03+03+ Adiabatic connection enhances the Monopole transition ! 0 1 + → 0 3 + is enhanced.  –  distance ( fm ) ( a.u. )

19. Adiabatic surfaces (J  = 0 + ) Energy spectra ( J  = 0 + ) ｰ i W(R)  + 6 He(2 1 + ) 10 Be case : M.I., PLB636, 236 (2006) Cluster

20. Contents Unified description of the  + 8 He reactions and the exotic structures in 12 Be Results New features 2. Exited (resonance) states are characterized in terms of the excitation degree of freedoms included in the ground state. (Val. neutrons or cluster relative motion) 1. Comparison with the recent experiment of the  + 8 He scattering (GANIL) Future studies M. I., N. Itagaki, H.Sakurai, K. Ikeda, PRL 100, 182502 (2008). M. I., N. Itagaki, PRC78, 011602(R) (2008). 1. Transfer coupling is important for the formation of the sharp resonances. 2. Systematic studies on the resonant scattering of neutrons’ drip-line nuclei M. I., N. Itagaki, Phys. Rev. Focus Vol.22, Story4 (2008). (Resonance formation by neutron transfers ) 3. The energy spacing of the resonances becomes quite small. 4. The monopole transition is enhanced with a development of the cluster.

21. Coverage by APS American Phys. Society WEB Journal Phys. Rev. Focus See also, RIKEN RESEARCH 5 September (2008) (http://focus.aps.org/story/v22/st4) http://www.rikenresearch.riken.jp/research/517/

23. Extension of Cluster Concept Rigid cluster 8 He 6 He 7 He 5 He 0+0+ 0S 0+0+ 1S ～ 3MeV 02+02+ 03+03+ 12 Be =  +  + 4N 0+0+ 12 C = (  +  ) +  16 O =  + 12 C 0S 2+2+ 0D ～ 7MeV 02+02+ 05+05+ ・・・・ Excitation : 8 Be-  Rel. motion 6 He 5 He Excitation : 12 C-  Rel. + 12 C Rot. ～ 4 MeV Loose cluster Clusters are rigid. Neutron rearrangements with small energy increasing Clusters are loose !! dE ～ 2 MeV dE ～ 1 MeV (N ～ Z : dE>10 MeV)

24. Generalized Two-center Cluster Model (GTCM) Combined model of mol. orbit and asymptotic channels ++... C1 C2C3  0Pi (i=x,y,z) coupled channel with atomic basis Mol. Orbit  8 He Resonance PRM PTP113 (05)  + 8 He Scattering PRC78(R) (08) 12 Be=  +  +4N ｰ i W(R) S, Ci : Variational PRM S Combine Absorbing BCScattering BCTr. Density 12 Be(0 1 + )  → 12 Be(0 ex + ) Monopole Transition 7 He 5 He 6 He M. Ito et al., PLB588(04), PLB636(06), PRL100(08)

25. Molecular structures will appear close to the respective cluster threshold. α-Particle ⇒ Stable Systematic Appearance of  cluster structures 3 H+p ～ 20 MeV Cluster structures in 4N nuclei IKEDA Diagram Ikeda’s Threshold rules Be isotopes Molecular Orbital : Itagaki et al. ― ― + + PRC61,62 (2000)

26. Studies on Exotic Nuclear Systems in (E x,N, Z) Space ( N,Z ) : Two Dimensions Ex. energy Structural Change Low-lying Molecular Orbital :  ― 、  ＋ ‥ Unbound Nuclear Systems Slow RI beam Decays in Continuum Is Threshold Rule valid ?? N

27. H. Voit et al.,NPA476,491 (1988) E. Almqvist et al., PRL4, 515 (1960) Molecular resonance phenomena in stable systems 12 C+ 12 C at Coulomb barrier ⇒ Sharp resonances 13 C+ 12 C at Coulomb barrier ⇒ NO clear resonances

28.  (  + ) 2 = ( P z (L) ― P z (R) ) 2 Formulation : 10 Be=  +  +N+N  + 6 He 6 He +  5 He + 5 He Linear Combination of Atomic Orbital (LCAO)   + 6 He(0 + ) = P z (L) ・ P z (L) + P z (R) ・ P z (R) － 2P z (L) ・ P z (R) = P x (R) ・ P x (R) + P y (R) ・ P y (R) +P z (R) ・ P z (R) Total wave function : Fully anti-symmetrized Pm(a)・Pn(b)Pm(a)・Pn(b) (m,n)=x,y,z(a,b) = L,R Variational PRM S Z ( 12 Be=  +  +4N: 38 AOs,K=0 )  : (0s) 4

29. Enhancement of the two neutron transfer Unitary condition of S-matrix Open Closed 5 He + 7 He 6 He + 6 He 4 He + 6 He Covalent SD, | S f,i | 2 =1  + 8 He ⇒ 6 He+ 6 He Strong decay into 6 He+ 6 He J  = 0 + Large part of the flux flows to 6 He+ 6 He.

31. 本研究の背景 単極遷移とクラスター構造に関する先行研究 下浦 ： 単純な殻模型の場合、 Ex<10MeV に単極遷移の強度はない 基底状態におけるクラスター相関 ( 山田 ) クラスター構造の発達に伴い、低励起領域に強い単極遷移強度 が現れることが指摘されている。 クラスターの相対運動を 2hw 励起 ( N : クラスター相対運動の量子 ) 殻模型 + クラスター 基底状態にクラスターの種があり、それが 2hw 励起する クラスター基底 = N ( 最低許容数 ) + N ( 高節数 ) クラスター構造 ++ N = N low N > N low

32. Why monopole ? Pioneering work on monopole transition Simple shell model (1p-1h, 2hw) ： No strength around low-lying region, Ex<10MeV Cluster correlation in a ground state (Yamada et al., PTP, inpress) There is a possibility that monopole transitions are enhanced If cluster structures are developed. ( Ex < 10MeV ) Excitation of clusters’ relative motion (2hw) ( N : Quanta for relative motions ) Shell model + Cluster 2hw excitation of the seed of clusters in a ground state Cluster basis = N (Lowest arrowed) + N (Higher quanta) Cluster structure ++ N = N low N > N low