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Study of Weakly Bound Nuclei with an Extended
Cluster-Orbital Shell Model
Hiroshi MASUI
Kitami Institute of Technology, Kitami, Japan
K. KatoHokkaido University, Sapporo, Japan
K. IkedaRIKEN, Wako, Japan
18th International IUPAP Conference on Few-Body Problems in Physics “FB18”
August 21-26, 2006, Santos, Sao-Paulo, BRAZIL
2. New aspects for the halo structure
An extended Cluster-orbital shell model
1. A model to describe weakly bound, “many-nucleon” systems
Introduction
Gamow shell-model picture
Difference from typical halo nuclei: 6He, 11Be, 11Li
Core + Multi-valence neutrons(?)Core+n (+2n)
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)
Weak-bound neutrons (Relatively) Strong-bound neutrons
16O22O
From experiments: part 1 RIKEN (R. Kanungo et al., PLB512(2001) )
Reaction cross-section deduced by the Glauber model
22O alone < 22O in 23O
22O の Rrms
“Core” is soft enough
22O is not appropriate to be considered as a Core
23O ground state : 5/2+ (Lowest config. :1/2+)
(0d5/2)6 is no good picture of 22O = Not a “inert” core
From experiments: part 2RIKEN ( R. Kanungo et al., PRL88(2002) )
Momentum distribution fitted by the Glauber model
Gives the best fit
d5/2
s1/2
d5/2
s1/2
J5/2+ J1/2+
From experiments: part 3
23O-ground state is 1/2+
GSI (D. Cortina-Gil et al., PRL93(2004) )
Analysis using the Eikonal model
Still this picture is true
d5/2J1/2+
What we need is
a model to describe weakly bound, “many-nucleon” systems
An extended Cluster-Orbital Shell Model
Cluster-Orbital shell model (COSM)
Y. Suzuki and K. Ikeda, PRC38(1998)
Original: study of He-isotopes
•Shell-model Matrix elements (TBME) For many-particles
COSM is suitable to describe systems:
Weakly bound nucleons around a core
•Cluster-model Center of mass motion
−Neo Cluster-Orbital Shell-Model−
We extend the model space
2. Dynamics of the total system
Microscopic treatment of the core and valence nucleons
•Structure of the core
•Interaction between the core and a valence nucleon
H.M, K. Kato and K. Ikeda, PRC73(2006), 034318
1. Description of weakly bound systems
•Gaussian basis function
•Stochastically chosened basis sets
A sort of full-space calculation
Basis function for valence nucleons in COSM
i-th basis function
Gaussian
k l klShell model:
k Single-particle states
COSM: kllk Non-orthogonal
1. Description of weakly bound systems
“exact” method
SVM-like approachV. 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
18O (16O+2n) : N=2000Stochastic approach: N=138
2. Dynamics of the total system
Size-parameter of the core: b
0p3/2
0p1/2
0s1/2
h.o. config.
We change core-size parameter b
•Microscopic Core-N interaction
NN-int. : Volkov No.2
17O
(Mk=0.58, Hk=Bk=0.07)
direct exchange Pauli (OCM)
18O 19O
20O
Calculated levels of O-isotopes
Order of levels: good
GSM : N. Michel, et al., PRC67 (2003)
Dynamics of the core
T. Ando, K. Ikeda, and A. Tohsaki-Suzuki, PTP64 (1980).
Additional 3-body force
Energy of 16O-core Core-N potential
Described by the same core-size parameter b
Different minima of b
b: 18Ne case is larger
2.64
2.66
18O
18Ne
fixed-b
2.65
2.68
changed
2.81 ±0.14
2.61 ±0.08
Exp.
Energy of the total system
core valence
What is the difference?
Change of Core - N interaction:
Effect for the S-wave potential is different
This could be a key to solve the structure of 23O and 24O
If d5/2 is closed in 22O, s-wave becomes dominant in 23O
Core+n Core+p
0d5/2
1s1/2
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) )
calc. Ref.1 Ref.24He 1.48 1.57 1.49 6He 2.48 2.48 2.30 2.468He 2.66 2.52 2.46 2.67
[1] I. Tanihata et al., PRL55(1985)[2] G. D. Alkhazov et al. PRL78 (1997)
Rrmss
Tail part of wave function
2. Comparison with GSM
“Gamow Shell Model (GSM)”
Single-particle states
Bound states (h.o. base)
Pole (bound and resonant ) + Continuum
1b,r,a
dk L
R. Id Betan, et al., PRC67(2003)
N. Michel, et al., PRC67 (2003)
G. Hagen, et al., PRC71 (2005)
“Gamow” state
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 comparison1. Completeness relation
2. Expansion of the wave function
Solved by CSM
Single-particle COSM
18O
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
Poles and Continua of 6He
0p1/2 :
0p3/2 : Almost the same
Different
[21] N. Michel et al., PRC67 (2003)
[26] G. Hagen et al., PRC71 (2005)
“SM” approaches:
Even though angular momentaIn the basis set increase
Contributions of the sum of p3/2 and p1/2 do not change
Summary1. An extended COSM (Neo-COSM)
•Energies, Rrms are reasonably reproduced•Dynamics of the core is a key to study multi-valence nucleon sytems
2. Comparison to GSM
Stable nuclei:
Weakly bound nuclei:
Same as GSM
Different from GSM
Correlations of poles and continua are included at a maximum
Useful method to study stable and unstable nucleiwithin the same footing
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