Three-nucleon force effects in proton-deuteron scattering

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Three-nucleon force effects in proton-deuteron
scattering
FB19, Aug. 31 - Sep. 5, 2009 _at_ Bonn

• Souichi Ishikawa (Hosei University)

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1. Introduction
(2pE-3NF)

• The 2pE-3NF is successful in explaining 3N
  binding energy and N-d differential cross
  sections.
• On the other hand It is unsuccessful for some
  N-d polarization observables such as Ay(q),
  iT11(q), and T21(q). (see figure)
• Refs S. I. et al., PRC 67 (2003) 061001(R), PRC
  75 (2007) 061002(R)(1) Tensor component in the
  2pE-3NF is responsible for the undesirable effect
  on T21(q).(2) A phenomenological 3NF (Vphe) is
  introduced to remedy the disease.

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pd T21(q) _at_ 10 MeVEffects of 2pE-3NF and a
phenomenological 3NF
2pE-3NF
Vphe
pd T21 _at_ Ep10.0 MeV (Ed20.0 MeV) Exp. data M.
Sawada et al., PRC27 (1983) 1932.
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Phenomenological 3NF Vphe
S. I., PRC 75 (2007) 061002(R).
In this talk To show 3NF from the exchange
of pion and s-boson is a possible candidate to
Vphe.
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2. p-s three-nucleon force Vps

• 3NF model considered here
• - Pion produces scalar tensor forces-
  s-boson produces scalar force
• Exchange of p and s produces a tensor component,
  which is different from that of 2pE-3NF.

3NF from p-s Born diagram Ref J. Adam, Jr. et
al., PRC 69 (2004) 034008.
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General form of ps-3NF in Q-space
The parameter gs is chosen to reproduce the 3H
binding energy
ms (MeV) gs2/4p
Vps 500 9
OBEP (BONN) 584 10
Cutoff masses of the form factors Lp800
MeV, Ls1300 MeV
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3. Proton-deuteron calculations

• Calculations of proton-deuteron scattering are
  performed including the proton-proton long-range
  Coulomb force effects based on an integral
  equation approach to solve Coulomb-modified
  Faddeev equation in coordinate space.
• Refs. S. I., - Mod.
  Phys. Lett. A 70 (2009) 855 APFB08
  - arXiv 0908.3360
• Inputs-2NF Argonne V18 potential (AV18)-3NF
  Brazil 2pE-3NF (BR)-2N states Jmax 4-3N
  states J0,max 19/2

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4. Results

• T21(q)
• Polarization transfer coeffients d(p?,p?)d
  Kxx(q), Kyy(q), etc
• s(q) at forward angle

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Effects of Vps on T21(q) at 10 MeV
Similar effect as Vphe is obtained !
2pE-3NF
Vps
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Polarization transfer coefficients in d(p?,p?)d
reaction at 22.5MeV
Vphe gives wrong effect !
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Effects of Vps on polarization transfer
coefficients
Vps gives desirable effect !
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Effects of 3NFs on s(q) at Ep10MeV
At forward angles AV18(2p) Kyushu
data AV18(2p)(p,s) Koeln data
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5. SUMMARY

1. We studied effects of a 3NF from pion-sigma
   exchange mechanism (Vps) on some pd observables.
2. Vps may cancel a wrong behavior of the tensor
   components in 2pE-3NF, and as a result, works to
   explain the tensor analyzing power T21(q).
3. Vps also successfully explains the polarization
   transfer coefficients, Kxx(q) and Kyy(q).
4. Vps gives a large effect in Nd differential cross
   section at forward angles. (Precise data are
   required to check.)

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Energy dependence of T21(q90o)
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(No Transcript)
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References

• S. Ishikawa Spin-dependent three-nucleon force
  effects on nucleon-deuteron scattering Phys.
  Rev. C 75 (2007) 061002(R) (arXiv0705.1665)
• S. IshikawaCalculation of Proton-Deuteron
  Scattering with Coulomb Force EffectsMod. Phys.
  Lett. A 70 (2009) 855 APFB08
• S. IshikawaCoordinate space proton-deuteron
  scattering calculations including Coulomb force
  effectssubmitted for publication (arXiv
  0908.3360)

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General form of ps-3NF in R-space
1
p
s
3
2
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AppendixA formalism for proton-proton-neutron
system

• Coordinate space integral equation approach
  -Wave functions expanded by complete sets (plane
  wave or Coulomb wave) with respect to variable
  y-Sets of equations for the variable x
  (2-body equations)-Use of 2-body Coulomb wave
  functions
• Modification of Faddeev eq.T. Sasakawa and T.
  Sawada, Phys. Rev. C 20, 1954 (1979).
  Introducing an auxiliary potential

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Consider 1(p)2(p)3(n) system
Yes for finite x1bound state scattering (Elt
E3BB) No, when 3-body breakup occurs(Egt E3BB)
p-p Coulomb potential causes a singularity
in Faddeev equation
Introduction of an auxiliary potential uC(y1)
VC(x3) - uC(y1) 0 for a large x3 ?
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Modified Faddeev eq.
uC(y1) Distortion of spectator (proton)
R8fm
Cancellation of the long-range character in p-p
Coulomb force
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Phase shift parameters with AV18
5 MeV 2S1/2 4D1/2 h1/2
KVP (-41.8, 1.74) (-5.43, 0.004) (1.05, -0.03)
Ours (-41.8, 2.15) (-5.45, 0.000) (1.05, -0.04)
10 MeV 2S1/2 4D1/2 h1/2
KVP (-60.6, 11.7) (-7.30, 0.24) (1.01, 0.06)
Ours (-60.8, 11.9) (-7.34, 0.22) (1.01, 0.04)
KVP (Kohn variational principle) M. Viviani et
al., FBS 30, 39 (2001).
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Cancellation of the long-range character in p-p
Coulomb force