dynamics of macroscopic and microscopic three-body systems
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FB18 1
Dynamics of Macroscopic and Microscopic Three-Body Systems
Outline
Three-body systems of composite particles (clusters)Macroscopic = Use of fewer degrees of freedom 20C+n+n : 20C: shell-model inert core 3α : α: (0s)4 nucleon cluster 3-nucleon : N: (0s)3 quark clusterPauli principle, nonlocality, energy-dependence
Y. Suzuki (Niigata)
Collaborators: Y. Fujiwara (Kyoto), H. Matsumura (Niigata), M. Orabi (Niigata)
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Unexplored Three-body System
Pauli constraint acts only between core-n
Giant two-neutron haloS-wave dominance
W.Horiuchi and Y.S. PRC, in press
Reaction cross sections
A~ 60
Borromean, n-dripline
SVM on CG
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12C as 3α System
Ali-Bodmer potential: shallow, L-dependent, no bound states Buck-Friedrich-Wheatley potential: deep, L-independent, redundant states 0s, 1s, 0d bound states
These 2αpotentials produce poor results for 3α and 4α systems
Supersymmetric transform
ααlocal potential in macroscopic approach
D.Baye, PRL58(1987)
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Solution with Removal of Redundant States
Orthogonalizing pseudo potential
Allowed states
(for any pairwise redundant states)
Kukulin and Pomerantsev, Ann. Phys. 111 (1978)
Solution is to be found in allowed state space
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Comparison of 3α Allowed States
Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press
important in shell model
0+
Q=30
Ns=174
(NA=129,
NF=43)
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Energy of 12C from 3αThreshold
BFW potential
Expt.
HOFS
Tursunov,Baye,Descouvemont. NPA723(2003)Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press
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(self-consistency)
Fujiwara et al., Prog.Theor.Phys.107(2002)
Use of 2-cluster RGM kernel
A B
C
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Summary of 3α Calculations
Interaction States eliminated ground state energy (MeV)
BFW Bound states of -0.22 the potential BFW HOWF -19.3
2αRGM HOWF -9.6 Kernel NN potential (HOWF) -11.3 (microscopic) Expt. -7.27
Matsumura,Orabi,Suzuki,Fujiwara, NPA, in pressFujiwara et al., Few-Body Systems 34(2004),PRC70(2004)
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Meson Theory Short-Ranged Interaction Compositeness of Baryons (0s)3 quark cluster Baryon-Baryon Interaction with SU(6) quark model OGEP+EMEP at quark level FSS: Pseudo Scalar, Scalar PRC54 (1996) fss2: Pseudo Scalar, Scalar, Vector PRC65 (2002)
Application to Triton and Hypertriton PRC66 (2002), PRC70 (2004)
Fujiwara,Suzuki,Nakamoto, PPNP, in press
Three-Nucleon System with Quark-Model Potential
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Deuteron properties
np effective range parameters
Prediction with Quark Model Potential Isospin basis, NoCSB
T
t
t
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Triton Binding Energy vs Deuteron D-state Probability
8.519 MeV
8.394 MeV
8.48 MeVPRC66(2002)
Salamanca PRC65(2002)7 . 72 MeV (5ch ) PD=4 . 85% Takeuchi et al. NPA508(1990) 8 . 01 MeV (5ch) PD =5 . 58%
no charge dependenceexcept CD-Bonn
(34 ch)
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Two-nucleon system; Tensor force and Central force are counterbalanced Tensor force more (less) attractive (D-state probability larger (weaker)) Central force less (more) attractive More-nucleon system; Effects of Tensor force are reduced D-state probability larger (Central force less attractive) Weaker binding
Role of Tensor force in many-nucleon system
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3α-system Triton--system
Local pot. BFW Realistic ForceNonlocal pot. 2αRGM NNRGM Kernel (fss2, …)
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Summary
1. Macroscopic three-body systems with clusters are useful, with the following reservations 2. A significant difference appears in 3αsystem depending on the choice of redundant states (Pauli principle effects) Its reason is now clear. 3. The quark model potential gives larger binding for triton in spite of large D-state probability (energy-dependent, nonlocal potential)
Use of 2-cluster RGM kernels in three-cluster system is appealing, though further study remains to clarify roles of off-shell property, E-dependence, etc
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Three-body problems: advantage: accurate solutions for bound states possible Faddeev, Variational (CBF,SVM,…) interest: interplay between interaction and structure
Three-body systems with composite particles (clusters) micoscopic macroscopic mapping interaction between clusters role of Pauli principle
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Three-body System
Pauli constraint acts only between core-n
Giant two-neutron halo
Density of n-n relative motion
W.Horiuchi and Y.S. PRC, in press
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Hypertriton (pnΛ)
Potential BΛ(keV) PΣ(%)
fss2 289 0.805 FSS 878 1.361
Exp. 130(50)
Nogga,Kamada,Glockle,PRL88(2002)
Miyagawa,Kamada,Glockle,Stoks,PRC51(1995)
1S0/3S1 ΛN interaction
PRC70(2004)
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NN and YN total cross sections(fss2)
recent KEK exp’t Y. Kondo et al. Nucl. Phys. A676 (2000) 371
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