理研.08 少数体系アプローチの研究と今後の課題 Few-Body Approach and Future Problems ・ NN interaction is characterized by strong short-range repulsion and long-range tensor force ・ Accurate solution is possible for FBS ・ The interplay between BB interaction and dynamics of strongly interacting few-body quantum systems is revealed ・ The effect of three-body forces is one of current issues Y. Suzuki (Niigata) 1.Ab initio calculation in FBS 2.Towards more-particle systems 3.Continuum problems 4. Breakup reactions Present status and future direction on

理研.08 NN potential Even partial waves Odd partial waves

理研.08 Benchmark calculation for the ground state of 4 He FY CRCGV, SVM, HH (Variational) GFMC NCSM, EIHH (P-space effective int.) 1.1 Various accurate methods for bound states H.Kamada et al. PRC64 (2001) AV8’

理研.08 AV8’ Correlation functions for s-shell nuclei Triplet even Singlet even Y. Suzuki, W. Horiuchi, arXiv (2008)

理研.08 Correlation functions (continued) Triplet odd Coulomb

理研.08 Density Hiyama et al. PRC70 (2004) 1.2 First excited state of 4 He 3N+N cluster state Inelastic electron scatt. form factor

理研.08 ± Horiuchi,Ikeda: PTP 40(1968) Quartets: J: 1/2 + 1/2 + 0 = 0, 1 T: 1/2 + 1/2 = 0, 1 3N + N structure  Asymmetric clusters  Parity inverted state E.g. Ammonia molecule of NH 3 Inversion doublets: J: 1/2+ 1/2 + 1 = 0, 1, 2 Questions arising from 3N+N clusters with spins

理研.08 Quartets, Negative parity partners, and level spacing W.Horiuchi et al. PRC78 (2008) 1.3 Energy levels of 4 He

理研.08 Only has a peak near 3N surface, indicating a resonance Spectroscopic amplitude (SA) W.Horiuchi et al. PRC78 (2008)

理研.08 Width of 0 - : 0.61 MeV (Cal) 0.84 MeV (Exp) Negative parity partners Peak position Centrifugal barrier 3N+N cluster structure Inversion doublet

理研.08 ・ Binding energies ・ The ground state of 10 B (1+ or 3+) S.C.Pieper et al. PRC66 (2002) E.Caurier et al., PRC66 (2002) ・ Scattering observables Nd scattering 1.4 Three-body forces See Proceedings of FM 50 (2007)

理研.08 S.C.Pieper et al. Proc. of FM50 Effects of three-body forces: Correct spin-parity of 10 B ～ 20MeV contribution for 12 C

理研 sensitive to short-range and tensor correlations Momentum distribution Dueteron: D-wave fills the dip of S-wave Effects of short-range repulsion 6 He: nn (pp) pair 6 Li: np pair W. Horiuchi et al. PRC76 (2007) T. Suda et al. 6 He(p,dn) 4 He

理研.08 R. Schiavilla et al. PRL98 (2007) Ｑ =0 ： Back to back geometry pn (lines) pp (symbols)

理研.08 Dependence on Q R.B. Wiringa et al. PRC78 (2008) pn (lines) 4 pp (symbols) 1 Q=p 1 +p 2 q=(p 1 -p 2 )/2 R. Subedi et al. Science 320 (2008) Exp. for 12 C

理研.08 H.Nemura et al. PRL94 (2005) 1.6 Accurate calculations needed to explore YN and YY interactions in Hypernuclei Interactions are poorly known experimentally ΛN-ΣN coupling,

理研.08 ・ GFMC (A ～ 12) ・ NCSM, UMOA (P-space effective interaction) Intruder states (e.g. Excited 0+ states of 12 C and 16 O) Slow convergence ・ Transformation to milder interaction (indep. of P and Q) UCOM (Unitary transf., cluster exp.) Transcorrelated method (Similarity transf.) ・ Semi-microscopic model Assuming a core nucleus or a cluster ・ DFT 2 Extension to more-particle systems

理研 GFMC S.C.Pieper et al. PRC66 (2002) GFMC propagation requires huge storage of memory ～ 3 A-1 2 A 2 A 12 C(A=12) ～ 3×10 12 (3 兆）

理研 NCSM Convergence for intruder states is slow Huge size of memory is required 12 C N max =8 M=0 states in m-scheme Basis dimension 594,496,743 (6 億） No. of nonzero matrix elements for 2B potentials 539,731,979,351 (5400 億） P. Maris et al. arXiv (2008)

理研 Transcorrelated Method E-indep. effective interaction eliminating short-range repulsion Separation of short-range repulsion Choosing f(r) to eliminate W H TC is indep. of P and Q, non-Hermitean. Energy minimization is not applicable. Y.Suzuki et al. PTP113 (2005)

理研.08 E.Hiyama et al. PRC74 (2006) Assuming clusters Phenomenological interaction is used Pauli-forbidden states 2.4 Semi-microscopic model

理研.08 Ambiguity in cluster potentials Y. Suzuki et al. PLB659 (2008) Energy-indep. nonlocal potential Exp MeV 12 C=3αmodel Dep. of E on phase-equivalent α-α potentials Different off-shell behavior ---RGM formalism---

理研 Density Functional Theory P. Hohenberg, W. Kohn, PR136 (1964) W. Kohn, L.J. Sham, PR140 (1965)

理研.08 Critical difference between electron gasses and nuclei Self-bound system with no external (s.p.) potential Is the DFT justifiable for nuclei? Y. Suzuki, W. Horiuchi, arXiv (2008) Correlation functions are basic variables

理研.08 ・ Strength function CSM, LITM ・ Scattering phase shifts 3.1 Application of discretized states to continuum problems K.M. Nollett et al. PRL99 (2007) Effects of three-body forces in α+n scattering phase shifts

理研 Complex Scaling Method T.Myo et al. PRC63 (2001) 4 He+n+n model for 6 He

理研 Lorentz Integral Transform method Invert Lorentz integral transform to obtain R or σ V.D.Efros et al. PLB338 (1994)

理研.08 4 He photo-absorption cross section Proc. of FM 50 S.Quaglioni et al. PLB652 (2007)

理研 Scattering phase shift α+n scattering effective force (central+LS) R-matrix (lines) SAGF (symbols) ---correcting spectroscopic amplitude with Green’s function (SAGF)--- Study with realistic interactions is in progress

理研 Breakup reactions of halo nuclei Elastic scattering of 6 He on 12 C Breakup effects of fragile nucleus α+ n + n three-body model for 6 He Continuum-discretized states Coupled-channel calculation (cdcc) T. Matsumoto et al. PRC70 (2004)

VMC wave function for 6 He Glauber model: 3α microscopic cluster model w.f. for 12 C NN profile function Eikonal approx.: N- 12 C optical potential Folding Full 40 MeV/nucleon B. Abu-Ibrahim et al. NPA 728 (2003) Breakup effects are taken into account by Glauber- and Eikonal-model calculations

Description of the elastic breakup reaction of two-neutron halo nucleus Challenging four-body problem including continuum final states ・ How to solve ・ Final-state interaction ・ Extraction of E1 strength function or effects of other multipoles 6 He breakup on 208 Pb at 240 MeV/A Coulomb-corrected eikonal model J. Margueron et al. NPA703 (2002): P. Capel et al. PRC78 (2008) D. Baye et al. submitted T. Aumann et al. PRC59 (1999)

Hoping for 1. Fundamental and Breakthrough Works 2. Center for Discussions and Facilities 3. Positions for Young Promising Physicists Example: α ＋ α S-wave scattering phase shifts with realistic potentials ～ 4000 (N α ) 2 times Time(α+n) Time(α+n)=0.1 day on a PC N α =10 at least 40,000 days on a single processor Demand for a number of parallel processors