2022/11/03
International Symposium on Clustering as a Window on the Hierarchical
Structure of Quantum Systems (CLUSHIQ2022)

Study of three nucleon force via
3
proton- He scattering
1. Introduction
2. Measurement of p-3He Scattering
3. Experimental Results
4. Future Plan
5. SummaryTokyo Institute of Technology,
Department of physics

Atomu WatanabeStudy of Nuclear Forces –from quark to universe–
Quark

Nucleon

Nucleus

Universe

Neutronneutronstar

ProtonQuark-gluon
interactions

Nucleon-nucleon
interactions

Many-nucleon interactions（Three nucleon forces）

Supernovae, neutronstar, etc…

Consistent understanding from quarks to the universe2

2 & 3 Nucleon Force
Theoretical Description of Nucleon-Nucleon (NN) Force1935

Meson exchange picture by H. Yukawa

Proc. Phys. Math. Soc. Jpn 17, 48.

1990’s Realistic NN potentials
 precisely reproduce 3000–4000 NN scattering data (𝜒𝜒 2 /datum~1)

Hideki Yukawa

Three-Nucleon Force (3NF)
First theoretical insight by Fujita & Miyazawa  2π-exchange 3NF

NProg. Theor. Phys. 17, 360 (1957).

 ∆-isobar excitation in the intermediate state.

N 3NFs play important roles in various nuclear properties(e.g., few-nucleon scattering, B.E. of light nuclei, and nuclear matter).

∆∆ : exited state of N

3NF is a key to understand nuclear phenomena
2π-exchange 3NF diagram3

Few-Nucleon Scattering
A good probe to study the dynamical aspects of 3NFs.

Momentum dependenceSpin & Iso-spin dependence✎Theory : Faddeev (-Yakubovsky) eq., etc…
DirectComparison

Rigorous numerical calc. for 3, 4N systemwith 2NF, 3NF inputs✎Exp. : Precise Data

Cross section, Spin observables (Ai, Cij, Kij)

We can extract fundamental information of Nuclear Forces !
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Where can we find 3NFs?
Nucleon-Deuteron Scattering

H. Witala et al., Phys. Rev. Lett. 81, 1183 (1998).

✎ H. Witala et al. predicted that 3NF effects are seenin the cross section minimum at around 100 MeV/nucleon.

@Higher energy@Low energy

Ein ~ 100 MeV/nucleon

Ein ~ 10 MeV/nucleon

5

3NF Study via d+p Elastic Scattering at 70–300 MeV/u

K. Sekiguchi et al., PRC 65, 034003 (2002).
2NF (AV18, CDB, Nijm I,II)
2NF + 3NF (TM’99)
Urbana IX + AV18 Differential Cross Section dσ/dΩ- 3NFs are clearly needed.

 Spin Observables (iT11, T20, T21, T22, Kijl’ )- The data are partially reproduced by including 3NFs.

Solid basis to explore the 3NF properties6T = 3/2 channel of 3NFs
 Important roles for Neutron-rich nuclei, Neutron matter, etc. ...
 Total isospin channel of 3NFs is limited to T = 1/2 for d + p.

3NF
2NF

S. C. Pieper et al., NPA 751, 516 (2005).

A. Akmal et al., PRC 58, 1804 (’98).

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3NF Study via p-3He Scattering
Measurement of p+3He system (Ep ≥ 65 MeV)

Observables✎ First Step from few to many nucleon systems✎ Approach to iso-spin dependence of 3NFs (T = 3/2 3NFs)✎ Theory in progress…

Cross section,
Analyzing powers,
Spin correlation coefficients.

up to 30 MeV

Ep = 5.54 MeV

2NF
2NF + 3NF

M. Viviani et al., PRL 111, 172302 (2013).

A. Deltuva and A. C. Fonseca, PRC 87, 054002 (2013).

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3
Measurements of proton- He Scattering
Ep = 65, 70, 100 MeV
Reported in “AW et al., Phys. Rev. C 103, 044001 (2021)” for 65, 70 MeV.
Paper of the measurement at 100 MeV has been accepted to PRC.
9Summary of Measurement for p+3He
Incident Energy
BeamObservables
Measured Angles (θc.m.)
FacilityExp. Course

70 MeV

65 MeV

65 MeV

100 MeVppol. ppol. ppol. p

Ay(3He)dσ/dΩ, Ay(p)Ay(p), Ay(3He), Cy,yAy(p), Ay(3He), Cy,y46°– 141°27°– 170°46°– 133°47°– 149°

CYRIC,
Tohoku Univ.

RCNP,
Osaka Univ.

RCNP,
Osaka Univ.

RCNP,
Osaka Univ.

41 course

WS course

ENN course

ENN courseGrand Raiden & LAS

CYRIC (AVF cyclotron)

RCNP

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Measurement of Differential Cross Section
RCNP, WS courseθlab = 41°

θlab = 20°– 165°

Target : 3He gas(1 atm, room temp.)
Pol. p beam
Exp. setup

θlab = 75°
Grand Raiden & LAS

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Experimental Setup with Pol. 3He Target
Top view
Target glass cell

to F.C.

@CYRIC, RCNP

Right Detectors

ΔE-E detectors(pla.+NaI(Tl) scinti.)
θlab = 35°– 135°

p beamPol. 3He Target
Method: AH-SEOP
Target cell: GE180 glass
Typical pol.: ~40%

150 mmBeamTarget part

Detectors
Left Detectors

Pumping part- 3He gas ： 3 atm, ~2 mg/cm2- N2 gas ： ~ 0.1 atm- A small amount of Rb, K

Target glass cell

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Experimental Results for p+3He*Calculations : A. Deltuva, private communications

65 MeVAy(p)65 MeV

Ay(3He)70 MeVCy,y100 MeV
AV18, CD-Bonn : Realistic NN potential
INOY04 : reproducing 3H, 3He B.E. w/o 3NFs
SMS : Chiral EFT (2NF, N4LO+)
CD-Bonn+∆ : including ∆-isobar dof*Coulomb force is omitted.

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Experimental Results for p+3He*Calculations : A. Deltuva, private communications

65 MeV

100 MeV

AV18, CD-Bonn : Realistic NN potential
INOY04 : reproducing 3H, 3He B.E. w/o 3NFs
SMS : Chiral EFT (2NF, N4LO+)
CD-Bonn+∆ : including ∆-isobar dof*Coulomb force is omitted.

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Conclusions
From comparison between the data and calculations...
 Clear discrepancies are found at dσ/dΩ minimum.
 larger than d-p scattering ∆-isobar effects do NOT always remedy that situation.
 Spin correlation coefficient Cy,y shows sizable effectsof ∆-isobar.

p-3He elastic scattering at intermediate energies
An excellent tool to explore the 3NFs which could not be accessible in 3N scattering.
Further study in view of analysis of scattering amplitude is in progress...

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Future Plan for 3NF Study
Determination of χEFT 3NFs from d-p elastic scattering
Experiment:
Measurement of spin correlation coefficientsfor d+p

Theory:Chiral Effective Field Theory (EFT)

pol. d-pol. p Elastic Scattering @RIBF

CDCE

13 LECs16

Measurement of Spin Correlation Coefficients for d+p
Experimental Setup

Polarized p Target

Polarized d Beam

Large Acceptance Detector(MWDCx4 + Solid detectors)

Electromagnet
Polarized Ion Source
beam axis

 High polarization: 60–80%
 Spin axis is freely controlled.

Beam test will be performed at HIMAC next month. 17

Summary
Study of 3NFs for p-3He elastic scattering at intermediate energies (E/A ≥ 65 MeV)
✎ First step from few-nucleons to many body
✎ Approach to total iso-spin T = 3/2 channel of 3NFs

Measurement of p-3He elastic scattering for 65, 70 and 100 MeV @CYRIC, RCNP
✎ Precise data of dσ/dΩ, Ay(p), A0y(3He), Cy,y
✎ Comparison the data with the predictions based on NN potential
 Calculation (with ∆-dof.) do NOT reproduce the data Different properties from d-p scattering system Cy,y shows sizable ∆-isobar effects

Future Pland-p scattering : Complete set of spin correlation coefficients
 Determination of 3NFs based on χEFT from d-p scattering data18

Collaborators
 Tokyo Institute of Technology
A. Watanabe, K. Sekiguchi

 Tohoku University
S. Nakai, Y. Wada, T. Akieda, D. Etoh, M. Inoue, Y. Inoue,K. Kawahara, H. Kon, K. Miki, T. Mukai, D. Sakai, S. Shibuya,
Y. Shiokawa, T. Taguchi, H. Umetsu, Y. Utsuki, M. Watanabe CYRIC, Tohoku University
M. Itoh National Institute of Radiological Science KEK
T. Ino Kyushu University
S. Goto, Y. Hirai, D. Inomoto,
H. Kasahara, S. Mitsumoto,
H. Oshiro, T. Wakasa

 Hosei University
S. Ishikawa

 Vilnius University
A. Deltuva

 RIKEN Nishina Center
H. Sakai, T. Uesaka

T. Wakui RCNP, Osaka University
K. Hatanaka, H. Kanda, H. J. Ong, D. T. Tran University of Miyazaki
Y. Maeda, K. Nonaka

 RAP, RIKEN
Y. Ikeda, Y. Otake, A. Taketani, Y. Wakabayashi

Thank you for your attention.

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