Experimental Study of Three Nucleon Experimental Study of Three Nucleon Forces via Few Nucleon SystemForces via Few Nucleon System

RIKENRIKEN

Kimiko SekiguchiKimiko Sekiguchi

Three Nucleon Force (3NF)

1957 Fujita-Miyazawa 3NF Model1957 Fujita-Miyazawa 3NF Model

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

Three nucleon force (3NF) has been predictedas a concept of the meson theory.

1934 Yukawa’s meson theory(2NF)1934 Yukawa’s meson theory(2NF)

1950’s N scattering experiment (1232) was discovered.

3NF is relatively weak compared to 2NF. Hard to approach and find evidence

for 3NF experimentally.

3NF is relatively weak compared to 2NF. Hard to approach and find evidence

for 3NF experimentally.

2- Exchange 3NF Model Tucson-Melbourne (TM) Urbana IX Brazil Texas Ruhr Pot.

Pieper et al. Phys. Rev. C 64, 014001(2001)

First Indication of 3NF in 3H (A=3 Nuclei) Exp. v.s. Faddeev calc.Exp. v.s. Faddeev calc. B.E. (Exp.)B.E. (Exp.) －－ B.E.(Faddev Calc.) B.E.(Faddev Calc.) = 0.5 – 1 MeV= 0.5 – 1 MeV

A few methods are applied to descriptions of A>4 Nuclei

Green’s Function Monte Carlo Green’s Function Monte Carlo Ab InitioAb Initio No-Core Shell Model No-Core Shell Model

　 etc…well reproduce B.E. of light nucleiwell reproduce B.E. of light nuclei

3NF Effects in Nuclei3NF Effects in Nuclei

Better understanding of 3NF is one key element to describe Nuclear Better understanding of 3NF is one key element to describe Nuclear Structure.Structure. How to constrain the properties of 3NF ?How to constrain the properties of 3NF ?To study dynamical aspects of 3NF, Spin and Momentum To study dynamical aspects of 3NF, Spin and Momentum

dependences,dependences,Few Nucleon (3N,4N) Scattering is attractive.Few Nucleon (3N,4N) Scattering is attractive.

To study dynamical aspects of 3NF, Spin and Momentum To study dynamical aspects of 3NF, Spin and Momentum dependences,dependences,

Few Nucleon (3N,4N) Scattering is attractive.Few Nucleon (3N,4N) Scattering is attractive.

GFMC

Comparing the Faddeev Calculations based on 2NF (e.g. CDBonn, AV18, Nijm I, II)

Cross Section forCross Section for d-p d-p Elastic Scattering Elastic Scattering at Intermediate Energiesat Intermediate Energies

Nd elastic scattering at intermediate energies (E/A ～ 100 MeV ） is a good probe to study 3NFs.

Nd elastic scattering at intermediate energies (E/A ～ 100 MeV ） is a good probe to study 3NFs.

- Discrepancy in the Cross Section Minimum → 3NF Effect!

K. Sekiguchi et al.Phys. Rev. C 65, 034003 (2002)

d-pd-p

N-d Elastic Scattering Data at 70-400 MeV/Aon the Market

Data mainly came from Data mainly came from RIKEN, RCNP, KVI, IUCF .RIKEN, RCNP, KVI, IUCF .

N-d Elastic Scattering Data at 70-400 MeV/Aon the Market

)(,,,, ' py

yxzxxyy

dy APAAAA

RIKEN

d-p Elastic Measurement at 70,100, and 135 MeV/A

Observables :

'''' ,,, yxz

yyy

yxx

yy KKKK– d to p polarization transfer

RIKEN Accelerator Research Facility (RARF)Spin symmetry axis of polarized d beams is freely controlled.

Polarized Ion Sourcevector & tensor d

Beam Line PolarimeterBy d+p Elastic Scattering

E ×B Spin Rotator

Spin axis is controlled by Spin Rotator prior to acceleration.

Single-turn extraction feature of RARF maintain the polarization amplitudes Beam polarizations : 60-80%

Spin axis is controlled by Spin Rotator prior to acceleration.

Single-turn extraction feature of RARF maintain the polarization amplitudes Beam polarizations : 60-80%

Focal Plane PolarimeterDPOL

RIKEN Magnetic Spectrograph SMART

SMART: Swinger and Magnetic Analyzer with Rotator and Twister

d

Swinger

Focal Plane

TargetCH2 / Liq.H2

List of the CalculationsBy Bochum-Cracow-KIT Group

NN Forces OnlyNN Interactions : CDBonn, AV18, Nijmegen I, II, & 93

NN + Tucson Melbourne (TM) 3NFNN Interactions : CDBonn, AV18, Nijmegen I, II, & 93

NN + TM99 3NF 　　　　 - closer to chiral symmetryNN Interactions : CDBonn, AV18, Nijimegen I,II

NN + Urbana IX 3NFNN Interactions : AV18

By Hannover Group NN with ( ) & w/o ( ) -isobar Excitations

NN Interactions : CDBonn

Comparison of the Data with the Faddeev Calculations

Summary of Comparison : Results for d-p Elastic Scattering at 70-135MeV/A

Discrepancies between the data and the calculations based on 2NF Discrepancies between the data and the calculations based on 2NF onlyonly Angular range : Clearly seen in the Cross Section Minimum

Energy dependence : Large as an Energy Increases

d/d : good agreement 3NFs are clearly needed.

Spin Observables : TM99/ Urbana IX does better job for Ay

p & T20 Requirement of chiral symmetry

Vector Pol. (Ayp & iT11 ) : good agreement

Tensor Pol. ( T20 , T21 , T22 ) : T20 & T21 : moderate agreement T22 : Chaotic Defects of 3NF

Higher order pol. (pol. transfer) : moderate agreementDirections are O.K, but sizes are not enough for Ky

y’ & Kxzy’.

When the When the 22-exchange 3NFs-exchange 3NFs are included … are included …

What are we missing?What are we missing?

Further ingredients of 3NF

Treatment of Relativistic EffectNew Nuclear Potential

Chiral Effective Field Theory etc…

Systematic Exp. Study of Few-Nucleon (3N-, 4N-) ScatteringSystematic Exp. Study of Few-Nucleon (3N-, 4N-) ScatteringSpin ObservablesSpin ObservablesEnergy DependenceEnergy DependenceSolid Base to Test TheorySolid Base to Test Theory

and exchange 3NF many -contributions with -rings

e.g. 3π-rings with -isobar excitations　　 (Illinois Model)

- Link to QCD - Link to QCD - Nuclear forces (2NF, 3NF, … ) Nuclear forces (2NF, 3NF, … ) and currents are derived in a consistent way.and currents are derived in a consistent way.

Three Nucleon Force Study Three Nucleon Force Study viavia Few Nucleon Scattering at RIBF with pol d. beams Few Nucleon Scattering at RIBF with pol d. beams

up to near up to near threshold energy threshold energy

E/AE/A ≤ ≤ 350 MeV (350 MeV (EEdd ≤ 700 MeV≤ 700 MeV))

- 3NF effects are most strongly enhanced.- Max. energy where the state of the art Faddeev calc. based on NN forces are applicable. Nail down the spin parts of 3NFNail down the spin parts of 3NF

pol. pol. dd beams at RIBF : beams at RIBF : E/AE/A = 250 – 440 MeV = 250 – 440 MeV

Beam Line Polarimeter

dp elastic/breakup Measurement

SAMURAIdp elastic & radiative capture Measurement

PIS-AVF-RRC-SRC – then,PIS-AVF-RRC-SRC – then, Where?Where?

Polarized Ion Sourcevector & tensor pol. d

N-dN-d Elastic Scattering Data at 70-400 Elastic Scattering Data at 70-400 MeV/AMeV/Aon the Marketon the Market

at RIBFat RIBFat RARFat RARF

FinallyA new microscope “Few-N Scattering-at-intermediate-energies” has been set for exploring 3NFs.The 1st step is the Nd elastic scattering.Cross section shows the clear signature of 3NFs.

Spin observables have started showing their ability but not fully yet.

Future Key Elements : - Precise Data Set for Few Nucleon Scattering

- Chiral Effective Field Theory- Relativistic Effect- Further Ingredients of 3NF based on meson-exchange picture

The new microscope will lead us to clear understanding of 3NFs but also allow us to step into a further process.

Experiments were carried out under the collaboration of

RIKENK. Sekiguchi, N. Sakamoto, T. Ohnishi

University of TokyoH. Sakai, T. Uesaka, K. Yako, T. Kawabata, K. Suda, S. Sakoda,

Y. Maeda, H. Kato, M. Hatano, T. Saito, N. Uchigashima, H. Kuboki,M. Sasano, S. Satoshi, Y. Sasamoyoto, Y. Takahashi

RCNP, Osaka UniversityH. Okamura, A.Tamii,

Tokyo Institute of TechnologyY. Satou

Kyushu UniversityT. Wakasa

KVIN. Kalantar, K. ErmischSaitama UniversityJ. Nishikawa, K. Itoh