Cluster-Orbital Shell Model と Gamow Shell Model Hiroshi MASUI Kitami Institute of Technology 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」

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

1. Cluster-Orbital Shell Model(COSM) Y. Suzuki and K. Ikeda, PRC38(1998) Hamiltonian Model space core1-body2-body

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

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

16 O+XN systems Energies are almost reproduced

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

Core+nCore+p Core-N interaction

R rms are improved Inclusion of the dynamics of the core:

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

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

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

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

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

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

18 O and 6 He 18 O: well-bound system 6 He: weakly bound system (a halo nucleus) 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.

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

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

Poles and Continua of 6 He 0p 1/2 : 0p 3/2 : Almost the same Different [21] N. Michel et al., PRC67 (2003) [26] G. Hagen et al., PRC71 (2005) “SM” approaches:Truncated

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

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

Even though angular momenta In the basis set increase Contributions of the sum of p 3/2 and p 1/2 do not change

Details of poles and continua p 3/2 p 1/2 Almost the same Changes drastically!!

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