Exploring Three Nucleon Forces
with Nucleon-Deuteron Scattering
RIKEN Nishina Center
Kimiko Sekiguchi
The Tao produced One,
One produced Two,
Two produced Three, and
Three produced All things.
“Tao-te Ching“ by Lao Zi in B.C. 400
To explore the laws of the nature, step in 1 → 2 → 3 .
To explore the laws of the nature, step in 1 → 2 → 3 .
Earth-Moon-Satellite Gravitational
Interactions

Two Body Interactions : Gravity

Three Body Interactions
by the polarizations of the ocean
water of the earth by the moon’s
gravity
To explore the laws of the nature, step in 1 → 2 → 3 .
Triplets of Atoms
Van der Waals Type Three Body Force

Two Body Interactions : Gravity

Three Body Interactions
Effects of the polarizations of the
electron density distribution
Are there three nucleon forces
in Nuclei ?



Nucleus : a compact system of nucleons
Nuclear Force : Strong Interactions
Effects of Three Nucleon Forces
– Where and How to attack- ?
Before Three Nucleon Force
Two Nucleon Force (2NF)
1935 Yukawa’s meson theory (2NF)
Theory :
One Pion Exchange Model
One Boson Exchange Model
Heavier Meson Exchange
e.g. r, w
Experiment :
Nucleon-Nucleon (NN)
Scattering Data Set
(ds/dW and Spin Observables)
Deuteron Properties
1990’s Realistic Modern NN Force
CDBonn, AV18, Nijmegen I,II,93
reproduce 3500 exp. NN scattering data
with high precision, c2  1
Three Nucleon Force (3NF)
1957 Fujita-Miyazawa 3NF
Prog. Theor. Phys. 17, 360 (1957)
N
2p-exchange 3NF :
- Main Ingredients :
D-isobar excitations in the intermediate
N
N
D : excited state of nucleon
Tucson-Melbourne (TM)
Urbana IX
Brazil, Texas etc…
m Δ c 2  1232 MeV


3
3
π
J , T   , 
2 2


Where could we see 3NF effects ? - I Ab Initio Calculations for Light Nuclei (A<10)
Green’s Function Monte Carlo
 Ab Initio No-Core Shell Model etc..

2NFs provide less binding energies
3NF : well reproduce the data
- 3H, 3He, 4He
by 2p-exchange 3NF (UR)
- p-shell nuclei
by 2p-exchange
+ 3p-ring with D-isobar
3NF Effects in B.E.
10 – 25 %
attractive
S.C. Pieper PRC 64,014001(2001)
Where could we see 3NF effects ? - II Equation of State for Nuclear Matter
•All NN potentials
(AV18, Nijmegen I,II, CD Bonn)
provide larger saturation point
of Nuclear Matter.
•3NF
- shift to the empirical
saturation point
- significant at higher density
A. Akmal et al., PRC 58, 1804(’98)
• Understanding of 3NF is one key element to describe
nuclear phenomena.
• How to constrain the properties of 3NF ?
Nucleon-Deuteron Scattering is a good probe
to study the dynamical aspects of 3NFs.
 Momentum dependence
 Spin dependence
 Iso-spin dependence : only T=1/2
How to Extract 3NF Effects in
Nucleon-Deuteron (Nd) scattering?
Nd Scattering – three nucleon unbound system Direct Comparison between Theory and Experiment
 Theory : Faddeev Calculations
Rigorous Numerical Calculations of 3N System

2NF Input
3NF Input
2NF & 3NF Input
• CDBonn
• Argonne V18 (AV18)
• Nijmegen I, II, 93
• Tucson-Melbourne
• Urbana IX
• Nucleon & D isobar
by coupled channel
• Chiral Effective Field Pot.
Experiment : Precise Data

ds/dW, Spin Observables (Aij, Kij, Cij)
→ Extract 3NF effects
Where is the Hot Spot for 3NF Effects
in Nd scattering?
Predictions by H. Witala et al. (1998)
Cross Section minimum for Nd elastic scattering
at Intermediate Energies (E/A~100 MeV)
Nd scattering
Low Energy
Intermediate Energy
NN
3NF
NN
3NF
Forward Backward
3NF
q =0 ～ 4 fm-1
Nd Scattering at Low Energies ( E ≤ 30 MeV/A )
High precision data are explained
by Faddeev calculations based on 2NF.
No signatures of 3NF.
Exp. Data from
Kyushu, TUNL, Cologne etc..
W. Glöckle et al., Phys. Rep. 274, 107 (1996).
Intermediate Energies
(E = 100 ~ 200 MeV/A)
Precise Measurement of dp scattering
at RIKEN Accelerator Research Facility
dp Elastic Scattering
1
Differential Cross Section and All Deuteron Analyzing Powers
(Ay , Ayy , Axx , Axz) at 70, 100, 135 MeV/A
- Whole Angular Range : q c.m. = 10°－180°
2． Deuteron to Proton Polarization Transfer Coefficients at 135 MeV/A
- Double Scattering Experiment : Measurement of Polarizations of Recoil Protons
- Angular range : q c.m. = 90°－180°
- Strong sensitivities to Three Nucleon Force
dp Breakup Reactions
- Extension from Elastic to Breakup
- Limited kinematical configurations : sensitive to 3NF
- First measurement of Polarization Transfer Coefficient
RIKEN Accelerator Research Facility
K70 AVF cyclotron
K135 Ring cyclotron
AVF + Ring cyclotrons
pol. d beams 65 ～135 MeV/A
Beam Intensity : 200 pnA
Polarized Ion Source
Spin symmetry axis of polarized d
beams is freely controlled !
Spin axis is controlled by Spin Rotator
prior to acceleration.
 Single-turn extraction feature of RARF
maintain the polarization amplitudes
Beam polarizations : 60-80%
Wien Filter
(Spin Rotator)
Beam Line Polarimeter
By d+p Elastic Scattering
Focal Plane Polarimeter
DPOL
Swinger and Magnetic Analyzer with Rotator
and Twister
Target
(SMART)
CH2 / Liq.H2
DPOL / EPOL

d
Determination of Absolute Values
of the Cross Section
1. d + p
at 135 MeV/A (70 MeV/A)
beam d  H2+
2. measure p + p 135 MeV (70MeV)
Same Exp. Setup
• Target CH2
• Faraday Cup
• Detection System
3. Direct Comparison with
NN phase-shift solution(SAID)
pp scattering at 135 MeV
Ratio = ds/dW(exp) / ds/dW (calc.)
dp Elastic Scattering
Differential Cross Section
K. Sekiguchi et al. PRC 65,034003 (2002)
Calculations by Bochum-Cracow Gr.
2NF (CDBonn, AV18, Nijmegen I,II)
: Large discrepancy in Cross Section Minimum ( ~ 30%)
2p-exchange 3NFs (Tucson-Melbourne, Urbana IX) : Good Agreement
Calculations by Hannover-Lisbon Gr.
Coulomb
Coupled channel approach with Nucleon&D-isobar : Good Agreement.
Disagreement at very forward angles : Coulomb effects.
A. Deltuva et al., PRC 68, 024005 (2003)
A. Deltuva et al., PRC 71, 054005 (2005)
Are there any other effects than 2p-exchange 3NF?
Relativistic Treatment
- would be significant at higher energies
Calculations with Lorentz boosted
NN potentials by Bochum-Cracow Gr.
Kamada et al. PRC66,044010(2002)
Relativistic effects are visible
at backward angles, but small.
Discrepancy in the Cross Section
Minimum for dp Elastic Scattering
comes from 2p-exchange 3NF.
K. Sekiguchi et al., PRL95, 162301 (’05)
dp Elastic Scattering
Spin Observables
Analyzing Powers & Polarization Transfer Coefficients
Analyzing Power
K. Sekiguchi. et al. PRC 65, 034003(2002)
2NF (CDBonn, AV18, Nijmegen I,II) :
Large discrepancy
in Cross Section Minimum
3NF (Tucson-Melbourne, Urbana IX, D-isobar) :
Vector Analyzing Power Ayp
: Good Agreement
Tensor Analyzing Power Ayy
: No superiority
Polarization Transfer
K. Sekiguchi. et al. PRC 70, 014001(2004)
3NF :
Kxxy’–Kyyy’ : Good Agreement
Kyy’ : Direction : O.K.
Magnitude : not enough
Spin Observables (Aij, Kij) :
Not always explained by 2p-exchange 3NF
⇒ Defects of spin dependent parts of 3NF
New Approach other than Meson Exchange Picture
- Chiral Effective Field Theory - Interactions :
p + Nucleon
+ contact terms
(heavier mesons...)
- Nuclear forces (2NF, 3NF, … )
and currents are derived
in a consistent way.
- Hierarchy of Nuclear Forces :
2NF > 3NF > 4NF
The first 3NF appears in NNLO.
2NF
3NF
4NF
Comparing the data with predictions based on cEFT pot.
Calc. based on cEFT pot. (NNLO) is only available below 100 MeV/A.
Reasonable agreement for all the measured data
d-p at 70 MeV/A
Calc. with cEFT Pot.
(NNLO)
by E. Epelbaum et al.
Nd Elastic Scattering Data at Intermediate Energies
~1998
1998 ~
• Rich
data set
ds/dW & many spin observables
from RIKEN, RCNP,KVI,IUCF
• Many data exit at 135 MeV/A
RIKEN
RIKEN provided
the first precise data set of
ds/d W , Aij, Kij
for dp Elastic Scattering
at Intermediate Energies,
especially 135 MeV/A.
2nd Step
dp Breakup Reactions
Nd Breakup Reactions
1st Step : Nd Elastic Scattering
at Intermediate Energies
2nd Step : Nd Breakup Reactions
at Intermediate Energies
- Leading Channel at Intermediate Energies
nd total cross section
sbr > sel
e.g. sbr ~ 2.5 sel at 135MeV/A
- Rich Phase-Spaces
- a large amount of kinematical configurations
- Selectivity
dp In-Plane Breakup Reaction at 135 MeV/A
Which is better, Tucson-Melbourne or Urbana IX ?
Kinematical Condition
(q1,q2) = (28 – 32 deg, 31deg)
f12 = 180°
Near Final State Interaction
Observables :
d to p Polarization Transfer Coefficients : Kyyy’
Analyzing Powers : Ayd, Ayy, Axx, Axz
Kyyy’
Ayd
Axx
3NF : partly success, partly not.
Kyyy’ shows superiority of Urbana IX.
Summary
Three Nucleon Forces (3NF)
play essential roles to explain fundamental properties of nuclear
phenomena, e.g. binding energies of light nulcei, EOS of nuclear matter.
Nd Scatteing
is a good probe to study the dynamical aspects of 3NF
- Momentum & Spin dependence - . For iso-spin, T=1/2 only.
Precise data of dp scattering at intermediate energies
(E ~ 100MeV/A, q = 2~3.5 fm-1) : ds/dW and many spin observables
Achievements of rigorous numerical three-nucleon Faddeev calculations
based on 2NF+2p-exchange 3NF below p-threshold energies
Direct comparison between Experiment and Theory
Cross Section for dp Elastic Scattering :
- Magnitudes of 3NF is O.K.
- First Clear Signatures of 3NF Effects in 3N scattering
Spin Observables for dp Elastic Scattering & Breakup Reactions
- not always explained by 2p-exchange 3NF
- require further study of detailed properties of 3NF
New developments of theory – in progress Chiral Effective Field Theory Approach
Treatment of Relativistic Effect
Treatment of Coulomb
Meson Exchange Picture – further ingredients of 3NF
- r-r and p-r exchange 3NF
Perspective of 3NF Study
Momentum
dependence
Spin
dependence
Nd Scattering
provide Fundamental Data/Theory of 3NF
Higher Energies
Full treatment of dp Breakup Reactions
T=1/2
RIBF/RCNP
Iso-spin
dependence
Hypernuclei
Strangeness
From NNN
to YNN & YYN
JPARC
Neutron-rich
Nuclei
Iso-spin dependence of 3NF
RIBF
Acknowledgments : SMART Gr. Collaboration
School of Science, University of Tokyo
H. Sakai, K. Yako, S. Sakoda, H. Kato, M. Hatano, T. Saito, N. Uchigashima,
H. Kuboki, M. Sasano, Y. Takahashi
CNS, University of Tokyo
T. Uesaka, T. Kawabata, S. Sakaguchi, Y. Sasamoto
RIKEN
N. Sakamoto, T. Ohnishi
RCNP, Osaka
H. Okamaura, A.Tamii,
K. Suda
TITech
Y. Satou
KVI
N. Kalantar-Nayestanaki
K. Ermisch
Kyushu University
T. Wakasa, Y. Maeda
Saitama University
J. Nishikawa, K. Itoh
Theoretical Supports from
Ruhr-Universität, Bochum
W. Glöckle
Jagellonian University
H. Witała, J. Golak
Kyushu Institute of Technology
H. Kamada
Forshungszentrum of Jülich
A. Nogga
Hannover University
P.U. Sauer, S. Nemoto
Lisbon University
A. Deltuva, A. C. Fonseca
University of Bonn / Forshungszentrum of Jülich
E. Epelbaum, Ulf-G. Meißner
Thanks for delivering excellent beams :
Accelerator staff of RIKEN Nishina Center and RCNP.
Thank you very much !