1 / 32

Unified Studies of the exotic structures in 12 Be and the a + 8 He slow scattering

Unified Studies of the exotic structures in 12 Be and the a + 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.

marv
Télécharger la présentation

Unified Studies of the exotic structures in 12 Be and the a + 8 He slow scattering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unified Studies of the exotic structures in 12Be and the a+8He 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. a+8He scattering and exotic structures in 12Be IV. Monopole transition of 12Be V. Summary and Future perspectives

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

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

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

  5. j(0p) Formulation ( I ) : Single particle motion in two centers F ( s.p.) =j(L) ± j(R) : LCAO jL(0p) ± jR(0p) Y(1,±1) s- ＋ 1/2- (pf) 1/2+ (sd) Y(1,0) p+ ― 3/2+ (sd) Z 1/2- (0p) s+ ― 1/2+ (sd) 3/2- (0p) (10Be=a+a+N+N ) a a p- ＋ S Config. Mixing Distance : S a(0s)4

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

  7. Energy surfaces in 12Be = a+a+4N VNN : Volkov No.2+G3RS 6He 6He Adiabatic Energy surfaces n(0p)6 Jp = 0+ Continuum Energy 5He + 7He (p-)4 6He + 6He a + 8He 6He + 6He R(a)～1.4fm a + 8He Covalent SD n(0p3/2)2(sd) 2 2 MeV S～5fm Atomic-Molecular Hybrid configuration (p-)2 (s+)2

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

  9. Cross sections of neutron transfers a + 8He ⇒ xHe + yHe (Jp=0+) a + 8He ⇒ 6He + 6He Elastic Cross sections ( mb ) 6He + 6He 5He + 7He Ec.m. ( MeV ) Ec.m. ( MeV ) Dotted curves : Three open channels only This is a prediction for recent experiments at GANIL. Solid curves: Open + closed chanels

  10. Effects of the transfer coupling : Minimum coupling Solid : Full calculation Dotted curves a+8He ⇒ xHe+yHe a + 8Heg.s. a + 8He(21+) Elastic 5He(3/2－) + 7He(3/21－) 6He+6He 5He(3/2－) + 7He(1/21－) 5He+7He I=0 5He(3/2－) + 7He(5/21－) 5He(1/2－) + 7He(3/21－) 5He+7He I=2 6Heg.s.+ 6Heg.s. 6Heg.s.+ 6He(21+) 6He(21+) + 6He(21+) Sharp resonant structures are generated by Transfer Coupling → New aspects !!

  11. Schematic picture of excitation modes

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

  13. Coexistence in A=12 systems : Coexistence phenomena 6Heg.s.+ 6Beg.s. Coexistence becomes prominent. 8.8 MeV a a 5Heg.s.+ 7Beg.s. 6Heg.s.+ 6Lig.s. Vn-n、Va-n is Weak. 5.4 MeV 19.8 MeV ～4 MeV 5Heg.s.+ 7Lig.s. 06+ 5Heg.s.+ 7Heg.s. Hoyle state 05+ 2.9 MeV 6Heg.s.+ 6Heg.s. 04+ 02+ a + 8Lig.s. 03+ a + 8Heg.s. a + 8Beg.s. 12C 12B 12Be

  14. Comparison of 12Be and 12C 12C + a→ (a+a+a) + a ( M. Itoh et al. at Tohoku Univ. ) 12Be + a→ (6He+6He) + a ( A. Saito et al. at Tokyo Univ. ) There appear many resonances !! 0+ 7.5 12 No decays to a+8He

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

  16. Monopole Transition Why monopole ? Cluster structure There is a possibility that monopole transitions are enhanced If cluster structures are developed. ( Ex < 10MeV ) Pioneering work on monopole transition Cluster correlation in a ground state(Yamada et al., PTP, inpress) Excitation of clusters’ relative motion (2hw) 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 Simple shell model (1p-1h, 2hw) ： No strength around low-lying region, Ex<10MeV

  17. Adiabatic energy surfaces in 12Be 3rd 0+ VNN : Volkov No.2+G3RS Adiabatic Energy surfaces 8He GCM (03+) Cluster Excitation 1st 0+ a + 8He (p-)2 (s+)2 GCM (01+) a – a Distance a – a Distance

  18. Monopole transition of 12Be Adiabatic connection enhances the Monopole transition ! ( a.u. ) 8He 03+ 01+ → 03+ is enhanced. (p-)2 (s+)2 01+ a – a distance ( fm )

  19. 10Be case : M.I., PLB636, 236 (2006) Energy spectra ( Jp = 0+ ) Adiabatic surfaces (Jp = 0+) a+6He(21+) Cluster ｰi W(R)

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

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

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

  23. Generalized Two-center Cluster Model (GTCM) M. Ito et al., PLB588(04), PLB636(06), PRL100(08) 12Be=a+a+4N a 8He 6He 7He 6He 5He Mol. Orbit Combine Combined model of mol. orbit and asymptotic channels ... S + + Y = C2 C3 C1 0Pi (i=x,y,z) coupled channel with atomic basis S, Ci: Variational PRM Absorbing BC Scattering BC Tr. Density <Yf | r| Yi> Resonance PRM PTP113 (05) 12Be(01+)→12Be(0ex+) Monopole Transition a+8He Scattering PRC78(R) (08) ｰi W(R)

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

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

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

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

  28. Enhancement of the two neutron transfer Strong decay into 6He+6He Open Closed Covalent SD, | Sf,i |2=1 Unitary condition of S-matrix 5He + 7He 4He + 6He 6He + 6He a+8He ⇒ 6He+6He Jp = 0+ Large part of the flux flows to 6He+6He.

  29. 本研究の背景 クラスター構造 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。 単極遷移とクラスター構造に関する先行研究 基底状態におけるクラスター相関 (山田) 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 ) クラスター基底 = N (最低許容数) + N (高節数) 殻模型 + クラスター + + N = N low N> N low 基底状態にクラスターの種があり、それが2hw励起する 下浦 ： 単純な殻模型の場合、Ex<10MeVに単極遷移の強度はない

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

More Related