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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

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

slide2

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

slide5

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(?)

slide6

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

slide7

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

slide8

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

what we need is
What we need is

a model to describe weakly bound,

“many-nucleon” systems

An extended Cluster-Orbital Shell Model

cluster orbital shell model cosm
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

slide11

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

slide12

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

slide13

Anti-symmetrized wave function

C.F.P.-like coefficients

slide14

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)

slide15

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

slide17

Microscopic Core-N interaction

NN-int. : Volkov No.2

(Mk=0.58, Hk=Bk=0.07)

17O

Pauli (OCM)

direct

exchange

16 o xn systems18
16O+XN systems

Energies are almost reproduced

slide19

Calculated levels of O-isotopes

18O

19O

20O

Order of levels: good

GSM : N. Michel, et al., PRC67 (2003)

dynamics of the core

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

slide22

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

slide24

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

slide25

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

2 comparison with gsm
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

progresses
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

preparation for a comparison
Preparation for a comparison

1. Completeness relation

Solved by CSM

2. Expansion of the wave function

Single-particle

COSM

slide29
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

slide30

“ECM”

T-base

6He

S. Aoyama et al. PTP93 (1995)

“COSM”

V-base

Correlation of n-n

T-base is important

slide31

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

slide32

Even though angular momenta

In the basis set increase

Contributions of the sum of

p3/2 and p1/2 do not change

slide33

Details of poles and continua

p3/2

p1/2

Almost the same

Changes drastically!!

summary

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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