P

1
3??????????????????????? 3?????
Kyushu Institute of Technology H.
KamadaRuhr-Universitaet Bochum
W.GlöckleJagiellonian University H. Witala, J.
Golak, R. SkibinskiBonn Universitaet E.
Epelbaum, Ulf-G. MeißnerForschungszentrum
Juelich A. Nogga University of Iowa W. N.
Polyzou
?????????????????? ????RCNP 2008?12?23?-25?
N
P

P
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Motivation
The nonrelativistic theoretical prediction of the
Nd scattering cross section beyond 200MeV/u is
getting to be poor even including the 3-body
force (FM type).What is missing?
3
Total cross section of the pd scattering
Data
Only 2NF
Phys. Rev. C 59, 3035 (1999)
4
Phys. Rev. C 59, 3035 (1999)
5
Faddeev three-body calculation for the
proton-deuteron elastic scattering with the
realistic NN potential and the three-nucleon
force
3
65
Differential Cross Section
ElabMeV
2NF only
190
135
3NF included
TM 3NF
Urbana IX 3NF
Sagara Discrepancy
Phys. Rev. C 63, 024007 (2001)
6
Phys. Rev. C 57, 2111 (1998)
7
Phys. Rev. C 57, 2111 (1998)
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??????

• Faddeev????????????
• ????????????????
• ????Wigner??

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Boosted Potential
Two-body Mass operator
Two-body Free Mass operator
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Boosted Potential
OUTPUT
???????
INPUT
Phys. Rev. C 66, 044010 (2002)
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Iteration Method
????????
Phys. Lett. B655, 119(2007) nucl-th/0703010
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Convergence to the iteration
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RESULTS?triton binding energy

• Lorenz Boost
• Wigner Rotation
• ?Scattering State
• ?Ay Puzzle

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?Triton binding energies
Rel.
Nonrel.
-6.97 -8.22 -7.58 -7.90 -7.68 -7.59
0.05 0.11 0.07 0.10 0.08 0.07
-7.02 -8.33 -7.65 -8.00 -7.76 -7.66
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?Wigner Rotation
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Partial wave decomposition
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k
qBoost direction
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Effect of Wigner Rotation 34ch Calculation with
CD-Bonn (np)
Nonrel. Relativistic (non-Wigner Rotation) Relativistic (Wigner Rotation)
-8.247 -8.1459MeV -8.1443MeV
Difference 2keV
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??????(1)

• ? 100keV???Triton???????????????
• ? Wigner???????2keV???

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????????
?
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Solid nonrelativistic Dashed Non- boosted
Dotted Approx. Dash-dotted Good approx.
Phys. Rev. C 71, 054001 (2005)
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Phys. Rev. C 71, 054001 (2005)
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Phys. Rev. C 71, 054001 (2005)
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??????(2)

• ????????????????????????????????
• ??????????????3??????(p??????EFT...)

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Ay????????

• Physical Review C 77, 034004 (2008)

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???????
?????? No-Wigner rotation
?????? with Wigner rotation
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??????(3)

• ???????(????)???????????????(???)???????10???????
  ????
• ??????????????3??????(?EFT...)

?
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Ay????????
??
??????
??!?
??? RSC KoikeHaidenbauer (1986)(with Paris pot.)
??? Argonne Kievsky(1999)
???? Bonn? Nijmegen L.Canton W.Schadow (2001)
????? ?EFT (E.Epelbaum)
(???) ? ???(2008)
3Pj
LS-3NF
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??????????3??

• LO????
• NLO????
• NNLO?3??????
• ????type, E-type, D-type
• NNNLO????
• ?????????????????????

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Few-nucleon forces in chiral EFT
2??
3??
4??
Q0
LO
(2)
NLO
Q2
(7)
N2LO
Q3
(0)
(2)
FM
D-
E-
N3LO
Q4
(15)
?
?
( )
?
( )
(0)
(0)
3??
4??
2??
()???????????LEC????????
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2
FM
a-term
b-term
d-term
D-
???
E-
Phys. Rev. C66, 064001 (2002).
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2006.11.17
??????? ???????
?
Fujita-Miyazawa, TM and Urbana
?
Canton-Schadow
?
Illinoi 3NF
???
T3/2???????????
?
Hueber

D-
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Fujita-Miyazawa 3NF b-term, d-term
Urbana 3NF
Tucson-Melbourne 3NF Brazil 3NF
a-term,(c-term)
Scalar Short range U0
p? exchange F(I?), Kroll-Ruderman term
Illinoi Model
Chiral perturbation Theoretical 3NF (NNNLO)
3p exchange

2p-1p term 2p exchange between all three
nucleons contact 1pexchange contact 2pexchnge

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NN, pN????????
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q?????0? 1? 2? 1?
a-term?NNLO b-term?NNLO c-term?NNLO d-term?NNLO
TM (c0)
c-term
a-term ????
D-term ????
Few Body Syst. 30 (2001) 121
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Triton????????
3NF-B
3NF-A
c??????2??????
Few Body Syst. 30 (2001) 121
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• N3LO(Idaho)N2LO(FMD-typeE-type)
• Triton, a????????????????2?? A??B? ?

Ep250MeV???????????????? ?????????
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?EFT Red lineN3LO, Dashed BlueN3LO 3NF-A(N2LO)
, Dash-Dotted BlackN3LO 3NF-B(N2LO)
250MeV
Ay(N)
(N3LOIdaho03)
Ay(N)
Realistic pot. Red lineCDBonn, Dashed
BlueCDBonn 3NF(TM99)
250MeV
PANIC08(Israel)
Data Hatanaka et al., PRC66,044002(2002) Maeda
et al., PRC76,014004(2007).
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??

• ??????????????250MeV?Sagara- discrepancy
  ???????????(N2LO)?D-type, E-type?3????????????????
  ?

N3LO?3??????????????????
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Canton-Schadow
International Symposium on New Facet of Three
Nucleon Force (Tokyo University, 29-30 Oct.
2007)
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Elastic nucleon-deuteron scattering observables
NLO
E3 MeV
NNLO
E10 MeV
E65 MeV
nd Coulomb-corrected pd data
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Polarization transfer coefficients in d(p, p)d
and d(p, d)p at Ep22.7 MeV
Coulomb-corrected pd data
H. Witala et al., PRC 73 (2006) 044004
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Breakup cross section in the reaction d(p, pp)n
at Ep16 MeV
part.
part.
?1 ?2 71.2º, f1 0º, f2 180º
?1 ?2 68.6º, f1 15º, f2 165º
part.
?1 ?2 51.5º, f1 0º, f2 180º
C. Düwecke et al., PRC 72 (2006) 044001