6He及び6LiにおけるN

少数体系アプローチの研究と今後の課題
Few-Body Approach and Future Problems
Y. Suzuki (Niigata)
・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
Present status and future direction on
1.
2.
3.
4.
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Ab initio calculation in FBS
Towards more-particle systems
Continuum problems
Breakup reactions
NN potential
Even partial waves
Odd partial waves
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1.1 Various accurate methods for bound states
Benchmark calculation for the ground state of 4He
FY
CRCGV, SVM, HH (Variational)
GFMC
NCSM, EIHH (P-space effective int.)
AV8’
H.Kamada et al. PRC64 (2001)
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Correlation functions
for s-shell nuclei
Triplet even
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AV8’
Singlet even
Y. Suzuki, W. Horiuchi, arXiv (2008)
Correlation functions (continued)
Triplet odd
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Coulomb
1.2 First excited state of 4He
Density
Inelastic electron
scatt. form factor
3N+N cluster state
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Hiyama et al. PRC70 (2004)
Questions arising from 3N+N clusters with spins
3N + N structure  J: 1/2 + 1/2 + 0 = 0, 1
T: 1/2 + 1/2 = 0, 1
Quartets:
Asymmetric clusters  Parity inverted state
E.g. Ammonia molecule of NH3
Inversion doublets:
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±
J: 1/2+ 1/2 + 1 = 0, 1, 2
Horiuchi,Ikeda: PTP 40(1968)
1.3 Energy levels of 4He
Quartets,
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Negative parity partners,
0-0 and 0-1 level spacing
W.Horiuchi et al. PRC78 (2008)
Spectroscopic amplitude (SA)
Only 02+0 has a peak near 3N surface, indicating a resonance
W.Horiuchi et al. PRC78 (2008)
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Negative parity partners
Peak position
Centrifugal barrier
Width of 0- : 0.61 MeV (Cal)
0.84 MeV (Exp)
3N+N cluster structure
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Inversion doublet
1.4 Three-body forces
See Proceedings of FM 50 (2007)
・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
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Effects of three-body forces: Correct spin-parity of 10B
～ 20MeV contribution for 12C
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S.C.Pieper et al. Proc. of FM50
1.5 Momentum distribution
--- sensitive to short-range and tensor correlations---
Dueteron: D-wave fills the dip of S-wave
Effects of short-range repulsion
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6He:
nn (pp) pair
6Li: np pair
W. Horiuchi et al. PRC76 (2007)
T. Suda et al. 6He(p,dn)4He
Ｑ=0： Back to back geometry
R. Schiavilla et al. PRL98 (2007)
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pn (lines)
pp (symbols)
Dependence on Q
Q=p1+p2
q=(p1-p2)/2
pn (lines)
pp (symbols)
R.B. Wiringa et al. PRC78 (2008)
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R. Subedi et al. Science 320 (2008) Exp. for 12C
4
1
1.6 Accurate calculations needed to explore
YN and YY interactions in Hypernuclei
Interactions are poorly known experimentally
ΛN-ΣN coupling,
H.Nemura et al. PRL94 (2005)
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2 Extension to more-particle systems
・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
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2.1 GFMC
GFMC propagation requires huge storage of memory
12C(A=12) ～3×1012 (3兆）
～ 3A-1 2A 2A
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S.C.Pieper et al. PRC66 (2002)
2.2 NCSM
Convergence for intruder states is slow
Huge 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
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02
P. Maris et al. arXiv (2008)
2.3 Transcorrelated Method
E-indep. effective interaction eliminating short-range repulsion
Separation of short-range repulsion
Choosing f(r) to eliminate W
HTC is indep. of P and Q, non-Hermitean.
Energy minimization is not applicable.
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Y.Suzuki et al. PTP113 (2005)
2.4 Semi-microscopic model
Assuming clusters
Phenomenological interaction is used
Pauli-forbidden states
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E.Hiyama et al. PRC74 (2006)
Ambiguity in cluster potentials
---RGM formalism---
Energy-indep. nonlocal potential
12C=3αmodel
Dep. of E on
phase-equivalent
α-α potentials
Different off-shell
behavior
Exp.
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-7.27
0.38 MeV
Y. Suzuki et al. PLB659 (2008)
2.5 Density Functional Theory
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P. Hohenberg, W. Kohn, PR136 (1964)
W. Kohn, L.J. Sham, PR140 (1965)
Is the DFT justifiable for nuclei?
Critical difference between electron gasses and nuclei
Self-bound system with no external (s.p.) potential
Correlation functions are basic variables
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Y. Suzuki, W. Horiuchi, arXiv (2008)
3.1 Application of discretized states
to continuum problems
・Strength function
CSM, LITM
・Scattering phase shifts
Effects of three-body forces
in α+n scattering phase shifts
K.M. Nollett et al. PRL99 (2007)
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3.2 Complex Scaling Method
4He+n+n
model for 6He
T.Myo et al. PRC63 (2001)
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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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4He
photo-absorption cross section
Proc. of FM 50
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S.Quaglioni et al. PLB652 (2007)
3.4 Scattering phase shift
---correcting spectroscopic amplitude with Green’s function (SAGF)---
α+n scattering
effective force
(central+LS)
R-matrix (lines)
SAGF (symbols)
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Study with realistic interactions is in progress
4.1 Breakup reactions of halo nuclei
Breakup effects of fragile nucleus
Elastic scattering of 6He on 12C
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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Breakup effects are taken into account by
Glauber- and Eikonal-model calculations
VMC wave function for 6He
40 MeV/nucleon
Folding
Eikonal approx.:
N-12C optical potential
Full
Glauber model:
3α microscopic cluster
model w.f. for 12C
NN profile function
B. Abu-Ibrahim et al. NPA 728 (2003)
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
Coulomb-corrected eikonal model
J. Margueron et al. NPA703 (2002): P. Capel et al. PRC78 (2008)
6He
breakup on 208Pb at 240 MeV/A
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 (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

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