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Dynamics of Macroscopic and Microscopic Three-Body Systems

Dynamics of Macroscopic and Microscopic Three-Body Systems. Y. Suzuki (Niigata). Outline. Three-body systems of composite particles (clusters) Macroscopic = Use of fewer degrees of freedom 20 C+n+n ： 　 20 C: shell-model inert core 3α ： 　　　　 α: (0s)4 nucleon cluster

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Dynamics of Macroscopic and Microscopic Three-Body Systems

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  1. Dynamics of Macroscopic and Microscopic Three-Body Systems Y. Suzuki (Niigata) 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 cluster Pauli principle, nonlocality, energy-dependence Collaborators: Y. Fujiwara (Kyoto), H. Matsumura (Niigata), M. Orabi (Niigata)

  2. Unexplored Three-body System W.Horiuchi and Y.S. PRC, in press Borromean, n-dripline SVM on CG Pauli constraint acts only between core-n Reaction cross sections Giant two-neutron halo S-wave dominance A~ 60

  3. Two-neutron Correlation Function 22C x＝5 fm θ=17○ x1=x2=x

  4. 12C as 3α System ααlocal potential in macroscopic approach Ali-Bodmer potential: shallow, L-dependent, no bound states Buck-Friedrich-Wheatley potential: deep, L-independent, redundant states 0s, 1s, 0d bound states Supersymmetric transform D.Baye, PRL58(1987) These 2αpotentials produce poor results for 3α and 4α systems

  5. Solution with Removal of Redundant States (for any pairwise redundant states) Orthogonalizing pseudo potential Kukulin and Pomerantsev, Ann. Phys. 111 (1978) Allowed states Solution is to be found in allowed state space

  6. Comparison of 3αAllowed States 0+ Q=30 Ns=174 (NA=129, NF=43) important in shell model Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press

  7. Expt. HOFS Energy of 12C from 3αThreshold BFW potential Tursunov,Baye,Descouvemont. NPA723(2003) Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press

  8. Note： Intercluster potential (RGM) A B B energy-dependent, nonlocal potential

  9. Fujiwara et al., Prog.Theor.Phys.107(2002) Use of 2-cluster RGM kernel (self-consistency) A B C

  10. 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 press Fujiwara et al., Few-Body Systems 34(2004),PRC70(2004)

  11. Three-Nucleon System with Quark-Model Potential 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

  12. np Phase Shifts (S,P,D)

  13. Prediction with Quark Model Potential Isospin basis, NoCSB Deuteron properties np effective range parameters

  14. 8.519 MeV 8.48 MeV 8.394 MeV Triton Binding Energy vs Deuteron D-state Probability no charge dependence except CD-Bonn PRC66(2002) (34 ch) Ｓａｌａｍａｎｃａ PRC65(2002) ７.７２ ＭｅＶ （５ｃｈ) ＰＤ＝４.８５％　 Ｔａｋｅｕｃｈｉ et al. NPA508(1990) ８.０１ MeV （５ｃｈ） PD＝５.５８％

  15. Role of Tensor force in many-nucleon system 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

  16. 3α-system Triton--system Local pot.BFW Realistic Force Nonlocal pot. 2αRGM NNRGM Kernel (fss2, …)

  17. 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

  18. model parameters

  19. Decomposition of triton energy:

  20. 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 macroscopicmapping interaction between clusters role of Pauli principle

  21. Three-body System W.Horiuchi and Y.S. PRC, in press Pauli constraint acts only between core-n Density of n-n relative motion Giant two-neutron halo

  22. ααPhase Shifts Redundant states: 0s, 1s, 0d

  23. np Phase Shifts

  24. Hypertriton (pnΛ) 1S0/3S1 ΛN interaction Potential BΛ(keV) PΣ(%) fss2 289 0.805 FSS 878 1.361 Exp. 130(50) PRC70(2004) Miyagawa,Kamada,Glockle,Stoks,PRC51(1995) Nogga,Kamada,Glockle,PRL88(2002)

  25. NNandYNtotal cross sections (fss2) recent KEK exp’t Y. Kondo et al. Nucl. Phys. A676 (2000) 371

  26. αα RGM Phase Shifts

  27. 8.519 MeV 8.48 MeV 8.394 MeV Triton Binding Energy vs Deuteron D-state Probability no charge dependence except CD-Bonn PRC66(2002) (34 ch) Ｓａｌａｍａｎｃａ PRC65(2002) ７.７２ ＭｅＶ （５ｃｈ) ＰＤ＝４.８５％　 Ｔａｋｅｕｃｈｉ et al. NPA508(1990) ８.０１ MeV （５ｃｈ） PD＝５.５８％

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