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Cluster-Orbital Shell Model と Gamow Shell Model

Aug. 1-3, 2006, KEK 研究会 「現代の原子核物理　ー多様化し進化する原子核の描像ー」. Cluster-Orbital Shell Model と Gamow Shell Model. Hiroshi MASUI Kitami Institute of Technology. Introduction. Study of nuclei in the core and valence nucleons model space. Cluster-Orbital Shell Model Pole- and Continuum-contributions.

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Cluster-Orbital Shell Model と Gamow Shell Model

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  1. Aug. 1-3, 2006, KEK研究会 「現代の原子核物理　ー多様化し進化する原子核の描像ー」 Cluster-Orbital Shell ModelとGamow Shell Model Hiroshi MASUI Kitami Institute of Technology

  2. Introduction Study of nuclei in the core and valence nucleons model space • Cluster-Orbital Shell Model • Pole- and Continuum-contributions Neo-COSM approach Comparison with Gamow Shell Model

  3. core 1-body 2-body 1. Cluster-Orbital Shell Model(COSM) Y. Suzuki and K. Ikeda, PRC38(1998) • Hamiltonian • Model space

  4. Neo-COSM approach H.M, K. Kato and K. Ikeda, PRC73(2006), 034318 • Dynamics of the total system Size-parameter of the core: b • Stochastically chosen basis sets Radial function: Gaussian

  5. 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)

  6. 16O+XN systems Energies are almost reproduced

  7. Dynamics of the core T. Ando, K. Ikeda, and A. Tohsaki-Suzuki, PTP64 (1980). Energy of 16O-core Additional 3-body force

  8. Core-N interaction Core+n Core+p

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

  10. COSM is a CO“SM” What is the relation to GSM?

  11. 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

  12. Im.k Bound states Re. k Anti-bound states (Virtual states) Complex momentum plane Resonant states

  13. Poles, Continua, Contour path Contour path: Discretized R. Id Betan, et al., PRC67(2003)

  14. 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

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

  16. Core-N: Folding+exchange+OCM N-N: Volkov No.2 (m=0.58, h=b=0.07) Angular momentum: L=5 Core-N: “KKNN[1]”+OCM N-N: Minnesota (u=1.00) Angular momentum: L=5 [1] H. Kanada, et al., PTP61 (1979), 1327. 18O and 6He • 18O: well-bound system • 6He: weakly bound system (a halo nucleus)

  17. 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

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

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

  20. Convergence N. Michel et al., PRC67 (2003) S. Aoyama et al. PTP93 (1995) GSM: Surface Delta COSM: Minnesota (finite)

  21. If we restrict the model space as L=1 [26] G. Hagen et al., PRC71 (2005) Poles and continua: Details are changed

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

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

  24. Summary • COSM Useful method to study stable and unstable nuclei within the same footing Truncation of the model space • Comparison to GSM Same as GSM Stable nuclei: Weakly bound nuclei: Different from GSM Even though the model space is truncated, Correlations of poles and continua are included at a maximum

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