Status of three-nucleon force study by nucleon- deuteron system August 22, 2006 FB18, Santos, Brazil 1. Introduction 2. dp elastic measurements by NUCLOTRON at DUBNA 3. How far we understand 3NF effects? 4. How data are reliable ? 5. Facilities 6. Summary H. Sakai Department of Physics The University of Tokyo
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Status of three-nucleon force study by nucleon-deuteron system August 22, 2006 FB18, Santos, Brazil 1.Introduction 2.dp elastic measurements by NUCLOTRON.
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Status of three-nucleon force study by nucleon-deuteron system
Status of three-nucleon force study by nucleon-deuteron system
August 22, 2006FB18, Santos, Brazil
1. Introduction
2. dp elastic measurements by NUCLOTRON at DUBNA
3. How far we understand 3NF effects?
4. How data are reliable ?
5. Facilities
6. Summary
H. Sakai
Department of Physics
The University of Tokyo
1. Introduction
How 3NF are established
by experiments?
How to study 3NF?
2BS
3BS
2NF
3NF
3NF is much smaller than 2NF.
→ 3NF effects are easily masked by 2NF effects.
1 Equations of motion for 3BS must be solved exactly. →Faddeev eq.
2 Realistic modern 2NF must be established. x2 1 for 4,000 data points.
CD Bonn AV18
Nijmegen I/II Main differences are off-shell properties.3 2πexchange 3NF (Fujita-Miyazawa)
TM99 Urbana IX (U9)
New development in theory
1 PT
2 Relativistic effects
3 Coulomb effects
Why Nd measurements at intermediate energies?
•H.Witała et al., PRL 81(1998) 1183.
→ Go to higher energies for Nd elastic scatt.
and look at X-sec. minimum region.
Typical mom. transfer: 1.5--3 fm-1 for Nd scatt. at intermediate energies.
D-state of deuteron mainly contributes in the reaction.
At intermediate energy, this may correspond to x-sec. min.
internal mom. dist. of deuteron
Reactions for Nd system
Observables (Nd-sys.)
d/d
AP (Ay, iT11, T20, T21, T22) VLS, (VLS)2, VT, D-state
Organizers: Organizers: H. Sakai (UT) (chair)H. Sakai (UT) (chair) K. Hatanaka (RCNP)K. Hatanaka (RCNP) H. Okamura (RCNP)H. Okamura (RCNP) K. Sagara (Kyushu)K. Sagara (Kyushu) Y. Suzuki(Nigata)Y. Suzuki(Nigata) Y. Akaishi (Nihon/RIKEN)Y. Akaishi (Nihon/RIKEN) T. Motobayashi(RIKEN)T. Motobayashi(RIKEN) K. Sekiguchi (RIKEN) (secretary)K. Sekiguchi (RIKEN) (secretary)Topics to be covered :Topics to be covered :
- Few Nucleon Systems and Three Nucleon Force- Few Nucleon Systems and Three Nucleon Force - Chiral Effective Field Theory- Chiral Effective Field Theory - Three Nucleon Force Effects in Nuclear Structure- Three Nucleon Force Effects in Nuclear Structure - Three Nucleon Forces in Hyper Nuclei- Three Nucleon Forces in Hyper Nuclei
International Symposium onInternational Symposium on
New Facet of Three Nucleon ForceNew Facet of Three Nucleon Force~ ~ 50 years of Fujita-Miyazawa Three Nucleon Force50 years of Fujita-Miyazawa Three Nucleon Force ~~
October 29(Mon.) - 31(Wed.), 2007October 29(Mon.) - 31(Wed.), 2007Koshiba Hall, University of TokyoKoshiba Hall, University of Tokyo
End
Thank you for your attention.
Four nucleon system is interesting.
2BS
3BS
2NF
3NF
4BS 4NF
2NF 3NF 4NF
1
3 1
6 4 1
─ 4BS is a good tool to study 3NF effects.
─ stressed by Fonseca.
─ solve Faddeev-Yakubovsky eq. exactly.
─ 4NF effects?
─ First of all, establish 3NF.
─ But look for where?
VNN 20 MeV/pair
V3NF 1 MeV/triplet
V4NF 0.1 MeV/quartet
by J.L. Friar, FBS 22(1997)161.
Results(1) Differential Cross Sections
Faddeev calc (by Prof. H. Kamada) : NN only
(CD-Bonn, AV18, Nijmegen-I,II,93) : NN with TM-3NF : AV18+UrbanaIX-3NF : CD-Bonn+TM’-3NF
Calculations even including 3NF still underestimate the data at cm = 110 – 180 deg.
CC calc (by Honnover group) : CD-Bonn : CD-Bonn+-3NF
Relativistic effects
Hamiltonian of 3N system (total momentum = 0) Relativistic energy
Relativistic NN potential ( in CM system of particle i, j)
Lorentz boosted NN potential into CM system of 3N (Fully relativistic)
Approximations of Vij
• pij <<1• Dependence of k and k’
ji
ijVHH2
10
i
i mmH ])p[( 2/1220
2
2
2
2
41)
21(
)q(
1
,)q'(
1)q'q,(
)q(
1)'kk,(
m
q
m
q
h
hv
hv NR
ijij
22
2/1222/122
2)k(
,]p)k([p])k([
mk
vV
ij
ijijijijijij
ijij
ijij vm
vV2
2
8
p
2222
2
k'
1
k
1
8
p
mv
mvV ij
ijijij
Relativistic prediction
Relativistic kinematical correction
(calc. by Prof. H. Witala) relativistic energy relativistic NN potential
(green line; not fully relativistic) Lorentz boost to 3N c.m. syst
em
(red & pink line) Fully relativistic calculations im
prove the fit to the data only at cm > 160 deg but improvements are not enough. Relativistic 3NF Dirac eq.
Non-Rel.
Rel. NN potential
Lorentz boosted potential
Approx. 1 Approx. 2
There still remains 50% discrepancy!.
X-sec. ratios at 250 MeV & 95 MeV
σ(p+d) /σ(n+d)σ(p+d) /σ(n+d) at at 250250 MeV MeV σ(d+p)/σ(n+d)σ(d+p)/σ(n+d)