Effects of three-nucleon force
and the experimental study
via the few-nucleon systems
Yukie Maeda（前田幸重）
Univ. of Miyazaki（宮崎大学）
The 9th Japan-China Joint Nuclear Physics Symposium (JCNP 2015)
Osaka University, Nov 10 2015
Outline
• History
– Three-body problem
– Three-nucleon force (3NF) effects in the nuclear physics
• Experimental study by few-nucleon systems
– nucleon – deuteron (N+d) elastic scattering
– proton – deuteron (pd) breakup reaction
– 4 body system (tetra neutron & p-3He)
• New theoretical study
• Summary
Lao zi (老子) said in “Tao-te Ching (道德经)”;
The Tao produced One;
One produced Two;
Two produced Three;
Three produced All things.
[Chapter 42]
One produced Two [Nucleon – Nucleon potentials]
• One pion exchange
– Yukawa (1935)
•
Phenomenological NN potential (1990 - )
– CDBonn, AV18, Nijmegen I, II, 93
– The c2/datum ~ 1 for the fit of
about 4500 np & pp scattering
data
– Cross sections, Spin observables
@ E < 350 MeV
S. Aoki et al. PTEP 2012 (2012) 01A105
It will be found that the use of two-body interactions is an excellent approximation for
electronic motions in atomic systems, but a relatively poor one for the heavy particles
in nuclei.
The three-body effect is very small in pure s-state. If there is a considerable
amount of p- and higher states in triton, the three-body force becomes
important.
Two pion exchange 3NF
• 2p-exch. + D-isobar
– Fujita-Miyazawa (1957)
• Tucson-Melbourne (TM)
a,b,c,d ; determined by pN scattering data
• Urbana-IX (UIX)
<- FM type
A, U0 ; determined by fitting B.E.(3H) & nuclear matter density
Two produced Three [Binding Energy of 3H]
• Faddeev calculations
– based on phenomenological NN pot.
– under bind about 0.5 – 1 MeV -> explained by introducing 3NF !
– parameter of 3NF is determined to reproduce B.E. of 3NS.
2  mp2
Fp NN (q )  2
πNN form factor
  q2
 : cut  off parameter
2
2
Three produced All things ? [Neutron drip line]
T. Otsuka et al., Phys. Rev. Lett. 105 (2010) 032501.
• Drip line of oxygen is near from the
stability line (oxygen anomaly)
3NF provides repulsive interactions
between valence neutrons.
Three produced All things ? [Neutron Star]
S. Gandolfi et al., PRC 85 (2012) 032801.
NASA
• Many data about M ~ 1.4 Msolar
• Recent accurate data of M = 2 Msolar
Short-range term of 3NF plays a key role in
the high-density EOS.
Mass-to-radii correlation is sensitive to the
detail of 3NF.
Three produced All things ? [3N scattering states]
• 3NF is essential for the nuclear physics.
– Phenomenological NN ; c2/datum ~ 1 for the fit of 4500 data !!
– 3NF potentials ; should be studied comprehensively.
• Experiments of the nucleon-deuteron (Nd) scattering at the
intermediate energy region
– Cross sections & spin observables at various energies
– Comparison with the Faddeev calculations
p+d & n+d elastic
pd breakup
pd capture
By Courtesy of K. Sekiguchi (Tohoku Univ.)
By Courtesy of K. Sekiguchi (Tohoku Univ.)
NN
NN+TM’
AV18+UR
pd inclusive/exclusive breakup meas. @ RCNP
Neutron TOF
p
LAS
p
Grand
Raiden
inclusive D(p,p’) & exclusive D(p,2p) @250MeV
n
p
inclusive D(p,n)@170MeV
N0
D(p,p)pn & D(p,n)pp inclusive breakup
D(p,p)pn
@ 250MeV
S. Kuroita et al.
(Kyushu Univ.)
D(p,n)pp
@ 170MeV
Y.M. et al.
FSI
FSI
FSI
d(p,p1p2) exclusive breakup reaction @ 250MeV
q1=15 deg, E1~150 MeV, S. Kuroita et al.
q1= (qn=) 40 deg,
q2~ 67 deg, Y.M. et al.
Discrepancies are large at small q2 (small En)
Data around FSI region
is well reproduced
Summary of Nd scattering (isospin T=1/2)
• Nd scatterings are good probe for the study of 3NF
– Dynamics of 3NF (Energy & Spin dependence)
– Some data is well reproduced by NN + 3NF
• Cross sections & Ay of elastic scattering @ E < 150 MeV
• Exclusive breakup reactions in FSI kinematical configurations
– Some data is not reproduced by NN + 3NF
• Elastic & breakup scattering @ higher energy region
• Tensor spin observables of elastic scattering
– What is missing ?
• Relativistic effects, Coulomb force
• Higher order (3p-ring etc) 3NF, heavier meson (r, s) exchange 3NF
• Isospin T = 3/2 components
NEXT topic
3NF of T=3/2 components in the Light Nuclei
J. Carlson et al., Rev. Mod. Phys. 87 (2015) 1067.
Illinois-7 (IL7) ; parameters are
determined by fitting of g.s. & excited
states of light nuclei
Strong isospin dependence
How we can get almost direct
information of T = 3/2 3NF
components by 3 or 4 body
systems?
By Courtesy of K. Kisamori (RIKEN)
Tetra-neutron (4n) Search
SHARAQ06 Collaboration
S. Shimoura, K. Kisamori
1 CNS,
The University of Tokyo
K. Kisamori2, S. Shimoura, H. Miya2,
S. Michimasa, S. Ota, T. Fujii, S. Go,
S. Kawase, M. Kobayashi, Y. Kubota2,
C. S. Lee2, Y. Sasamoto, M. Takaki,
L. Tang, H. Tokieda, K. Yako,
R. Yokoayama
2 RIKEN
Nishina Center
H. Baba, M. Dozono, N. Fukuda,
N. Inabe, D. Kameda, T. Kubo,
M. Kurata-Nishimura, H. Sakai,
M. Sasano, H. Sato, Y. Shimizu,
H. Suzuki, H. Takeda, S. Takeuchi,
T. Uesaka, Y. Yanagisawa
3 Kyoto
University
T. Kawabata, T. Baba, M. Tsumura
4 RCNP
5 CYRIC,
10 Kyushu
11 IPN
Institute of Technology
Y. Kondo
7 University
of Miyazaki
University
S. Sakaguchi2
Tohoku University
M. Itho
Michigan State University
S. Noji, A. Stolz,
Osaka University
E. Ideguchi, K. Miki, A. Tamii
6 Tokyo
9 NSCL,
Orsay
D. Beaumel, M. Assie, F. Hammache
Institute of Radiological Sciences
H. Matsubara
12 National
Y. Maeda
8 the
University of Tokyo
T. Nishi
part of collaborators
20
By Courtesy of K. Kisamori (RIKEN)
Design of the Experiment
Reaction : 4He(8He,8Be)4n

•
Reaction with unstable beam
→ 4n system with small momentum transfer.
(almost recoil less condition)
Missing-mass spectroscopy

•
•
SHARAQ spectrometer
→ high resolution: ~ 1 MeV
2α detection at 200 MuV/u
→ good signal-to-noise ratio
21
4n
Q=-30.9 MeV
8He
Q=+27.7 MeV
Compensate
4He
target system
8Be
projectile
Experimental Setup
Primary Beam
from Cyclotron
(13.7 MHz)
Dispersive Focal Plane
production
target
・MWDC (Multi-Wire Drift Chamber)
momentum tagging for 8He beam
F6
F3
High Resolution
Beam Line
・plastic scintillator
・micro hodoscope
start point of ion optics
liq. He target
120 mg/cm2
φ=30 mm
FH9
・plastics scintillator
・MWDCs
target position
S0
SHARAQ
spectrometer
liq. He target
S2 focal plane
α
8He
S0
α
beam
S2
Final Focal Plane
x
22
・plastic scintillator
・CRDCs
(Cathode Readout Drift Chamber)
two α tracking
By Courtesy of K. Kisamori (RIKEN)
Result
Missing-mass Spectrum of 4n

✦
energy resolution: 1.2 MeV
uncertainty of calibration: ± 1.3 MeV
✦
background: 2.3±1.0 events
✦
→ almost background free
preliminary

✦
✦
✦
✦
Candidate of the resonant state
clear strength with 4.9σ significance level
E4n = 0.83 ± 0.65 (stat.) ± 1.25 (syst.) MeV
upper limit of Γ = 2.6 MeV (FWHM)
+2.9 nb
cross section : 3.8
-1.8
(int. up of θCM < 5.4 degree)
23
By Courtesy of K. Sekiguchi (Tohoku Univ.)
Chiral Effective Field Theory (CFT)
E. Epelbaum, Few-Body Syst. (2013) 54
Chiral EFT provides a systematic approach to nuclear forces
which relies on the symmetries of QCD.
• 3NF naturally appear at N2LO.
• Recently NN & 3NF at N3LO are constructed.
By Courtesy of T. Doi (RIKEN)
3NF from Lattice QCD
• NBS wave function  Potential
Faithful to Phase shift at asymptotic region
by 2N calc
S.Aoki et al. (HAL Coll.), PRD88(2013)014036
• Unified Contraction Algorithm (UCA)
Doi-Endres CPC184(2013)117
– Systematically reduce the huge computational cost
(Wick)
(color/spinor)
x ~ 1000 for A=2  A=3
~ 100-1000 in our calc
Speed up by UCA
Speed up factor:
By Courtesy of T. Doi (RIKEN)
Numerical Results
mp=0.76-1.1GeV (mN=1.6-2.1GeV)
Triton channel
T.D. et al. (HAL QCD Coll.) PTP127(2012)723
+ t-dep method updates etc.
short-range
repulsive 3NF !
(cutoff artifact)
Preliminary
In progress/Prospects
Other geometries
Nf=2 clover (CP-PACS),
1/a=1.27GeV, L=2.5fm
Lighter mass w/ K-computer
3BF w/ hyperon (YNN/YYN/YYY)
By Courtesy of T. Doi (RIKEN)
2-baryon forces (NN/YN/YY)
at (almost) physical point
NN Tensor Force in 3S1-3D1
Clearly visible
w/ physical mass !
Preliminary
Calc on K-computer
in progress to improve S/N
(& take larger t)
10PFlops
[HPCI Field5 Project 1]
Summary
• 3NF effect is one of the essential building blocks of the study
of nuclear physics.
• Highly precise Nd scattering data have been measured and
allowed us to test the detail of 3NF models.
-> Energy & spin dependencies are not good enough yet.
• Theoretical progress in developing new 3NF potentials is
highly expected.
• More experimental studies are also expected.
-> Massive & precise scattering data for parameter fittings
-> New experiments for the study of 3NF (T=3/2) by using
new experimental technique.