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Study of Weakly Bound Nuclei with an Extended Cluster-Orbital Shell Model

18 th International IUPAP Conference on Few-Body Problems in Physics “FB18”. August 21-26, 2006, Santos, Sao-Paulo, BRAZIL. Study of Weakly Bound Nuclei with an Extended Cluster-Orbital Shell Model. Hiroshi MASUI Kitami Institute of Technology, Kitami, Japan. K. Kato

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Study of Weakly Bound Nuclei with an Extended Cluster-Orbital Shell Model

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  1. 18th International IUPAP Conference on Few-Body Problems in Physics “FB18” August 21-26, 2006, Santos, Sao-Paulo, BRAZIL Study of Weakly Bound Nuclei with an Extended Cluster-Orbital Shell Model Hiroshi MASUI Kitami Institute of Technology, Kitami, Japan K. Kato Hokkaido University, Sapporo, Japan K. Ikeda RIKEN, Wako, Japan

  2. Introduction A model to describe weakly bound, “many-nucleon” systems An extended Cluster-orbital shell model 2. New aspects for the halo structure Gamow shell-model picture

  3. From experiments: Widening of Rrms near the drip-lines A. Ozawa, from UEC-Workshop@RIKEN

  4. Abrupt changes happen near the neutron drip-line O-isotopes Rrms Separation Energy

  5. 16O 22O Difference from typical halo nuclei: 6He, 11Be, 11Li Large Sn values of 23O and 24O ( 2.7MeV and 3.7MeV ) 6He : 4He+2n (Sn: 0.98MeV)11Li : 9Li+2n (Sn: 0.33MeV) 11Be: 10Be+n (Sn: 0.50MeV) 23O : 22O+n (Sn: 2.7MeV)24O : 22O+2n (Sn: 3.7MeV) (Relatively) Strong-bound neutrons Weak-bound neutrons Core+n (+2n) Core + Multi-valence neutrons(?)

  6. From experiments: part 1 RIKEN (R. Kanungo et al., PLB512(2001) ) Reaction cross-section deduced by the Glauber model 22OのRrms 22O alone ＜ 22O in 23O “Core” is soft enough 22O is not appropriate to be considered as a Core

  7. From experiments: part 2 RIKEN ( R. Kanungo et al., PRL88(2002) ) Momentum distribution fitted by the Glauber model Gives the best fit 23O ground state : 5/2+ (Lowest config. :1/2+) s1/2 s1/2 J=5/2+ Jp = 1/2+ d5/2 d5/2 (0d5/2)6 is no good picture of 22O = Not a “inert” core

  8. From experiments: part 3 GSI (D. Cortina-Gil et al., PRL93(2004) ) Analysis using the Eikonal model 23O-ground state is 1/2+ Jp = 1/2+ d5/2 Still this picture is true

  9. What we need is a model to describe weakly bound, “many-nucleon” systems An extended Cluster-Orbital Shell Model

  10. Cluster-Orbital shell model (COSM) Original: study of He-isotopes Y. Suzuki and K. Ikeda, PRC38(1998) • Shell-model • Matrix elements (TBME) • For many-particles • Cluster-model • Center of mass motion COSM is suitable to describe systems: Weakly bound nucleons around a core

  11. Gaussian basis function • Stochastically chosened basis sets • Structure of the core • Interaction between the core and a valence nucleon We extend the model space −Neo Cluster-Orbital Shell-Model− H.M, K. Kato and K. Ikeda, PRC73(2006), 034318 1. Description of weakly bound systems A sort of full-space calculation 2. Dynamics of the total system Microscopic treatment of the core and valence nucleons

  12. Single-particle states Shell model: COSM: 1. Description of weakly bound systems Basis function for valence nucleons in COSM i-th basis function Gaussian Non-orthogonal

  13. Anti-symmetrized wave function C.F.P.-like coefficients

  14. SVM-like approach V. I. Kukulin and V. M. Krasnopol’sky, J. Phys. G3 (1977) K. Varga and Y. Suzuki, Phys. Rev. C52(1995) “exact” method 18O (16O+2n) : N=2000 Stochastic approach: N=138 “Refinement” procedure H. Nemura, Y. Akaishi and Y. Suzuki, Phys. Rev. Lett. 89(2002)

  15. 0p1/2 0p3/2 0s1/2 h.o. config. Size-parameter of the core: b 2. Dynamics of the total system We change core-size parameter b

  16. 16O+XN systems

  17. Microscopic Core-N interaction NN-int. : Volkov No.2 (Mk=0.58, Hk=Bk=0.07) 17O Pauli (OCM) direct exchange

  18. 16O+XN systems Energies are almost reproduced

  19. Calculated levels of O-isotopes 18O 19O 20O Order of levels: good GSM : N. Michel, et al., PRC67 (2003)

  20. Rrms radius

  21. Additional 3-body force T. Ando, K. Ikeda, and A. Tohsaki-Suzuki, PTP64 (1980). Dynamics of the core Described by the same core-size parameter b Energy of 16O-core Core-N potential

  22. Different minima of b b: 18Ne case is larger fixed-b Exp. changed 18O 2.64 2.61 ±0.08 2.65 2.66 2.81 ±0.14 18Ne 2.68 Energy of the total system core valence

  23. Inclusion of the dynamics of the core: Rrms are improved

  24. What is the difference? Core+n Core+p Change of Core - N interaction: Effect for the S-wave potential is different If d5/2 is closed in 22O, s-wave becomes dominant in 23O This could be a key to solve the structure of 23O and 24O 1s1/2 0d5/2

  25. He-isotopes • Core-N: KKNN potential ( H. Kanada et al., PTP61(1979) ) • N-N: Minnesota (u=1.0) ( T.C. Tang et al. PR47(1978) ) • An effective 3-body force ( T. Myo et al. PRC63(2001) ) Rrmss calc. Ref.1 Ref.2 4He 1.48 1.57 1.49 6He 2.48 2.48 2.30 2.46 8He 2.66 2.52 2.46 2.67 [1] I. Tanihata et al., PRL55(1985) [2] G. D. Alkhazov et al. PRL78 (1997) Tail part of wave function

  26. 2. Comparison with GSM “Gamow Shell Model (GSM)” R. Id Betan, et al., PRC67(2003) N. Michel, et al., PRC67 (2003) G. Hagen, et al., PRC71 (2005) Single-particle states Bound states (h.o. base) Pole (bound and resonant ) + Continuum “Gamow” state

  27. Progresses • R. Id Betan, R. J. Liotta, N. Sandulescu, T. Vertse Many-body resonance, Virtual states • N. Michel, W. Nazarewicz, M. Ploszajczak, J. Okolowicz He-, O-isotopes (Core+Xn), Li-isotopes (Core+Xn+p) • G. Hagen, M. Hjorth-Jensen, J. S. Vaagen Effective interaction, Lee-Suzuki transformation

  28. Preparation for a comparison 1. Completeness relation Solved by CSM 2. Expansion of the wave function Single-particle COSM

  29. 18O [21] N. Michel et al., PRC67 (2003) [26] G. Hagen et al., PRC71 (2005) “SN” : N-particles in continuum Even though the NN-int. and model space are different, pole and continuum contributions are the same

  30. “ECM” T-base 6He S. Aoyama et al. PTP93 (1995) “COSM” V-base Correlation of n-n T-base is important

  31. Poles and Continua of 6He “SM” approaches: [21] N. Michel et al., PRC67 (2003) 0p3/2 : Almost the same [26] G. Hagen et al., PRC71 (2005) 0p1/2 : Different

  32. Even though angular momenta In the basis set increase Contributions of the sum of p3/2 and p1/2 do not change

  33. Details of poles and continua p3/2 p1/2 Almost the same Changes drastically!!

  34. 2. Comparison to GSM Same as GSM Stable nuclei: Weakly bound nuclei: Different from GSM Summary 1. An extended COSM (Neo-COSM) • Energies, Rrms are reasonably reproduced • Dynamics of the core is a key to study • multi-valence nucleon sytems Useful method to study stable and unstable nuclei within the same footing Correlations of poles and continua are included at a maximum

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