FB181 Dynamics of Macroscopic and Microscopic Three-Body Systems 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 3-nucleon ： N: (0s)3 quark cluster Pauli principle, nonlocality, energy-dependence Y. Suzuki (Niigata) Collaborators: Y. Fujiwara (Kyoto), H. Matsumura (Niigata), M. Orabi (Niigata)

FB182 Unexplored Three-body System Pauli constraint acts only between core-n Giant two-neutron halo S-wave dominance W.Horiuchi and Y.S. PRC, in press Reaction cross sections A~ 60 Borromean, n-dripline SVM on CG

FB183 x 1 =x 2 =x x ＝ 5 fm θ=17 ○ Two-neutron Correlation Function 22 C

FB C 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)

FB185 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

FB186

7 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)

FB188 Energy of 12 C from 3αThreshold BFW potential Expt. HOFS Tursunov,Baye,Descouvemont. NPA723(2003) Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press

FB189 energy-dependent, nonlocal potential Intercluster potential (RGM) Note ： A B B

FB1810 (self-consistency) Fujiwara et al., Prog.Theor.Phys.107(2002) Use of 2-cluster RGM kernel A B C

FB1811 Summary of 3α Calculations Interaction States eliminated ground state energy (MeV) BFW Bound states of the potential BFW HOWF αRGM HOWF -9.6 Kernel NN potential (HOWF) (microscopic) Expt Matsumura,Orabi,Suzuki,Fujiwara, NPA, in press Fujiwara et al., Few-Body Systems 34(2004),PRC70(2004)

FB1812 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

FB1813 np Phase Shifts (S,P,D)

FB1814 Deuteron properties np effective range parameters Prediction with Quark Model Potential Isospin basis, NoCSB

FB1815 Triton Binding Energy vs Deuteron D-state Probability MeV MeV 8.48 MeV PRC66(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 dependence except CD-Bonn (34 ch)

FB1816 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

FB1817 3α-system Triton--system Local pot. BFW Realistic Force Nonlocal pot. 2αRGM NNRGM Kernel (fss2, … )

FB1818 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

FB1819 model parameters model parameters

FB1820 Decomposition of triton energy:

FB1821

FB1822

FB1823 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

FB1824 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

FB1825 αα Phase Shifts Redundant states: 0s, 1s, 0d

FB1826 np Phase Shifts

FB1827 Hypertriton (pnΛ) Potential B Λ (keV) P Σ (%) fss FSS Exp. 130(50) Nogga,Kamada,Glockle,PRL88(2002) Miyagawa,Kamada,Glockle,Stoks,PRC51(1995) 1 S 0 / 3 S 1 ΛN interaction PRC70(2004)

FB1828 NN and YN total cross sections (fss2) recent KEK exp’t Y. Kondo et al. Nucl. Phys. A676 (2000) 371

FB1829

FB1830 αα RGM Phase Shifts

FB1831

FB1832 Triton Binding Energy vs Deuteron D-state Probability MeV MeV 8.48 MeV PRC66(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 dependence except CD-Bonn (34 ch)