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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 FBS2. Towards more-particle systems3. Continuum problems4. Breakup reactions
Present status and future direction on
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理研 .08
NN potential
Even partial waves
Odd partial waves
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理研 .08
Benchmark calculation for the ground state of 4He 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’
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理研 .08 AV8’
Correlation functions for s-shell nuclei
Triplet even
Singlet even
Y. Suzuki, W. Horiuchi, arXiv (2008)
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理研 .08
Correlation functions (continued)
Triplet odd
Coulomb
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理研 .08
Density
Hiyama et al. PRC70 (2004)
1.2 First excited state of 4He
3N+N cluster state
Inelastic electron scatt. form factor
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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 NH3
Inversion doublets: J: 1/2+ 1/2 + 1 = 0, 1, 2
Questions arising from 3N+N clusters with spins
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理研 .08
Quartets, Negative parity partners, 0-0 and 0-1 level spacing
W.Horiuchi et al. PRC78 (2008)
1.3 Energy levels of 4He
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理研 .08
Only 02+0 has a peak near 3N surface, indicating a resonance
Spectroscopic amplitude (SA)
W.Horiuchi et al. PRC78 (2008)
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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
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理研 .08
・ Binding energies・ The ground state of 10B (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)
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理研 .08 S.C.Pieper et al. Proc. of FM50
Effects of three-body forces: Correct spin-parity of 10B~ 20MeV contribution for 12C
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理研 .08
--- sensitive to short-range and tensor correlations--- 1.5 Momentum distribution
Dueteron: D-wave fills the dip of S-wave Effects of short-range repulsion
6He: nn (pp) pair 6Li: np pair
W. Horiuchi et al. PRC76 (2007) T. Suda et al. 6He(p,dn)4He
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理研 .08R. Schiavilla et al. PRL98 (2007)
Q =0 : Back to back geometry pn (lines) pp (symbols)
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理研 .08
Dependence on Q
R.B. Wiringa et al. PRC78 (2008)
pn (lines) 4 pp (symbols) 1
Q=p1+p2
q=(p1-p2)/2
R. Subedi et al. Science 320 (2008) Exp. for 12C
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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,
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理研 .08
・ GFMC (A ~ 12)
・ NCSM, UMOA (P-space effective interaction) Intruder states (e.g. Excited 0+ states of 12C and 16O) 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
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理研 .08
2.1 GFMC
S.C.Pieper et al. PRC66 (2002)
GFMC propagation requires huge storage of memory ~ 3A-1 2A 2A 12C(A=12) ~ 3×1012 (3 兆)
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理研 .08
2.2 NCSM
Convergence for intruder states is slowHuge size of memory is required
12C Nmax=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)
01 02
P. Maris et al. arXiv (2008)
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理研 .08
2.3 Transcorrelated Method
E-indep. effective interaction eliminating short-range repulsion
Separation of short-range repulsionChoosing f(r) to eliminate W
HTC is indep. of P and Q, non-Hermitean.Energy minimization is not applicable.
Y.Suzuki et al. PTP113 (2005)
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理研 .08E.Hiyama et al. PRC74 (2006)
Assuming clusters Phenomenological interaction is used Pauli-forbidden states
2.4 Semi-microscopic model
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理研 .08
Ambiguity in cluster potentials
Y. Suzuki et al. PLB659 (2008)
Energy-indep. nonlocal potential
Exp. -7.27 0.38 MeV
12C=3αmodel
Dep. of E on phase-equivalent α-α potentials
Different off-shell behavior
---RGM formalism---
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理研 .08
2.5 Density Functional Theory
P. Hohenberg, W. Kohn, PR136 (1964)W. Kohn, L.J. Sham, PR140 (1965)
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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
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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
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理研 .08
3.2 Complex Scaling Method
T.Myo et al. PRC63 (2001)
4He+n+n model for 6He
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理研 .08
3.3 Lorentz Integral Transform method
Invert Lorentz integral transform to obtain R or σ
V.D.Efros et al. PLB338 (1994)
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理研 .08
4He photo-absorption cross section
Proc. of FM 50
S.Quaglioni et al. PLB652 (2007)
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理研 .08
3.4 Scattering phase shift
α+n scatteringeffective force(central+LS)
R-matrix (lines)SAGF (symbols)
---correcting spectroscopic amplitude with Green’s function (SAGF)---
Study with realistic interactions is in progress
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理研 .08
4.1 Breakup reactions of halo nuclei
Elastic scattering of 6He on 12C
Breakup effects of fragile nucleus
α+ n + n three-body model for 6He
Continuum-discretized states Coupled-channel calculation (cdcc)
T. Matsumoto et al. PRC70 (2004)
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VMC wave function for 6He
Glauber model: 3α microscopic cluster model w.f. for 12CNN profile function
Eikonal approx.: N-12C 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
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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
6He breakup on 208Pb 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)
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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 (Nα)2 times Time(α+n) Time(α+n)=0.1 day on a PC Nα=10 at least 40,000 days on a single processor Demand for a number of parallel processors