6He??6Li????N-N??????

1
?????????????????? 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

• Ab initio calculation in FBS
• Towards more-particle systems
• Continuum problems
• 4. Breakup reactions

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NN potential
Even partial waves
Odd partial waves
3
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
Singlet even
AV8
Y. Suzuki, W. Horiuchi, arXiv (2008)
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Correlation functions (continued)
Triplet odd
Coulomb
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Density
1.2 First excited state of 4He
Inelastic electron scatt. form factor
3NN cluster state
Hiyama et al. PRC70 (2004)
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Questions arising from 3NN clusters with spins
Asymmetric clusters ? Parity inverted state
E.g. Ammonia molecule of NH3
Horiuchi,Ikeda PTP 40(1968)
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1.3 Energy levels of 4He
W.Horiuchi et al. PRC78 (2008)
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Spectroscopic amplitude (SA)
Only 020 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
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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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S.C.Pieper et al. Proc. of FM50
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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
6He nn (pp) pair 6Li np pair
W. Horiuchi et al. PRC76 (2007) T. Suda et al.
6He(p,dn)4He
??.08
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pn (lines) pp (symbols)
Q0 Back to back geometry
R. Schiavilla et al. PRL98 (2007)
??.08
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Dependence on Q
Qp1p2 q(p1-p2)/2
pn (lines) 4 pp (symbols) 1
R.B. Wiringa et al. PRC78 (2008)
R. Subedi et al. Science 320 (2008) Exp. for 12C
??.08
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1.6 Accurate calculations needed to explore
YN and YY interactions in Hypernuclei
Interactions are poorly known experimentally
?N-SN coupling,
H.Nemura et al. PRL94 (2005)
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2 Extension to more-particle systems
GFMC (A12) 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
3A-1 2A 2A 12C(A12) 31012 (3?)
S.C.Pieper et al. PRC66 (2002)
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2.2 NCSM
Convergence for intruder states is slow Huge size
of memory is required
12C Nmax8 M0 states in m-scheme
Basis dimension 594,496,743 (6?) No. of
nonzero matrix elements for 2B potentials
539,731,979,351
(5400?)
01
02
P. Maris et al. arXiv (2008)
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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.
Y.Suzuki et al. PTP113 (2005)
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2.4 Semi-microscopic model
Assuming clusters Phenomenological interaction
is used Pauli-forbidden states
E.Hiyama et al. PRC74 (2006)
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Ambiguity in cluster potentials
---RGM formalism---
Energy-indep. nonlocal potential
12C3amodel Dep. of E on phase-equivalent a-a
potentials Different off-shell behavior
Y. Suzuki et al. PLB659 (2008)
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2.5 Density Functional Theory
P. Hohenberg, W. Kohn, PR136 (1964) W. Kohn, L.J.
Sham, PR140 (1965)
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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
Y. Suzuki, W. Horiuchi, arXiv (2008)
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3.1 Application of discretized states
to continuum problems
Strength function CSM, LITM
Scattering phase shifts
Effects of three-body forces in an scattering
phase shifts
K.M. Nollett et al. PRL99 (2007)
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3.2 Complex Scaling Method
4Henn 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 s
V.D.Efros et al. PLB338 (1994)
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4He photo-absorption cross section
Proc. of FM 50
S.Quaglioni et al. PLB652 (2007)
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3.4 Scattering phase shift
---correcting spectroscopic amplitude with
Greens function (SAGF)---
an scattering effective force (centralLS)
R-matrix (lines) SAGF (symbols)
Study with realistic interactions is in progress
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4.1 Breakup reactions of halo nuclei
Breakup effects of fragile nucleus
Elastic scattering of 6He on 12C
a 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
B. Abu-Ibrahim et al. NPA 728 (2003)
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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
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 aa S-wave scattering phase shifts
with realistic potentials 4000 (Na)2 times
Time(an) Time(an)0.1 day on a PC
Na10 at least 40,000 days on a single
processor Demand for a number of
parallel processors