1. Experimental Study of Three Nucleon Forces via Few Nucleon System RIKEN Kimiko Sekiguchi

2. Three Nucleon Force (3NF) 1934 Yukawa’s meson theory(2NF) 1957 Fujita-Miyazawa 3NF Model Prog. Theor. Phys. 17, 360 (1957) Three nucleon force (3NF) has been predicted as a concept of the meson theory. • 3NF is relatively weak compared to 2NF. • Hard to approach and find evidence • for 3NF experimentally. • 1950’s pN scattering experiment • D (1232) was discovered. • 2-p Exchange 3NF Model • Tucson-Melbourne (TM) • Urbana IX • Brazil • Texas • Ruhr Pot.

3. 3NF Effects in Nuclei • First Indication of 3NF in 3H (A=3 Nuclei) • Exp. v.s. Faddeev calc. • B.E. (Exp.)－B.E.(Faddev Calc.) = 0.5 – 1 MeV • A few methods are applied to descriptions of A>4 Nuclei • Green’s Function Monte Carlo • Ab Initio No-Core Shell Model etc… well reproduce B.E. of light nuclei GFMC Pieper et al. Phys. Rev. C 64, 014001(2001) • Better understanding of 3NF is one key element to describe Nuclear Structure. • How to constrain the properties of 3NF ? To study dynamical aspects of 3NF, Spin and Momentum dependences, Few Nucleon (3N,4N) Scattering is attractive.

4. Cross Section for d-p Elastic Scattering at Intermediate Energies d-p • Comparing the Faddeev Calculations based on 2NF (e.g. CDBonn, AV18, Nijm I, II) • Discrepancy in the Cross Section • Minimum → 3NF Effect! Nd elastic scattering at intermediate energies (E/A～100 MeV） is a good probe to study 3NFs. K. Sekiguchi et al. Phys. Rev. C 65, 034003 (2002)

5. N-d Elastic Scattering Data at 70-400 MeV/Aon the Market Data mainly came from RIKEN, RCNP, KVI, IUCF .

6. N-d Elastic Scattering Data at 70-400 MeV/Aon the Market RIKEN d-p Elastic Measurement at 70,100, and 135 MeV/A Observables : – d to p polarization transfer

7. RIKEN Accelerator Research Facility (RARF) Spin symmetry axis of polarized d beams is freely controlled. E×B Spin Rotator Beam Line Polarimeter By d+p Elastic Scattering Polarized Ion Source vector & tensor d Spin axis is controlled by Spin Rotator prior to acceleration. Single-turn extraction feature of RARF maintain the polarization amplitudes Beam polarizations : 60-80%

8. RIKEN Magnetic Spectrograph SMART Focal Plane Polarimeter DPOL

9. Swinger Target CH2 / Liq.H2 Focal Plane SMART: Swinger and Magnetic Analyzer with Rotator and Twister

10. Comparison of the Data with the Faddeev Calculations List of the Calculations By Bochum-Cracow-KIT Group • NN Forces Only • NN Interactions : CDBonn, AV18, Nijmegen I, II, & 93 • NN + Tucson Melbourne (TM) 3NF • NN Interactions : CDBonn, AV18, Nijmegen I, II, & 93 • NN + TM99 3NF- closer to chiral symmetry • NN Interactions : CDBonn, AV18, Nijimegen I,II • NN + Urbana IX 3NF • NN Interactions : AV18 By Hannover Group • NN with ( ) & w/o ( ) D-isobar Excitations • NN Interactions : CDBonn

13. Summary of Comparison : Results for d-p Elastic Scattering at 70-135MeV/A • Discrepancies between the data and the calculations based on 2NF only • Angular range : Clearly seen in the Cross Section Minimum • Energy dependence : Large as an Energy Increases • When the 2p-exchange 3NFs are included … • d/d: good agreement • 3NFs are clearly needed. • Spin Observables : • TM99/ Urbana IX does better job for Ayp & T20 •  Requirement of chiral symmetry • Vector Pol. (Ayp & iT11) : good agreement • Tensor Pol. ( T20 , T21 , T22 ): • T20& T21: moderate agreement • T22 : ChaoticDefects of 3NF • Higher order pol. (pol. transfer) : moderate agreement • Directions are O.K, but sizes are not enough for Kyy’ & Kxzy’.

14. What are we missing? • r-r and p-r exchange 3NF • many D-contributions with p-rings • e.g. 3π-rings with D-isobar excitations • (Illinois Model) • Further ingredients of 3NF • Treatment of Relativistic Effect • New Nuclear Potential • Chiral Effective Field Theory etc… • Systematic Exp. Study of Few-Nucleon (3N-, 4N-) Scattering • Spin Observables • Energy Dependence • Solid Base to Test Theory • - Link to QCD • Nuclear forces (2NF, 3NF, … ) • and currents are derived in a consistent way.

15. Three Nucleon Force Study via Few Nucleon Scattering at RIBF with pol d. beams pol. d beams at RIBF : E/A = 250 – 440 MeV up to near p threshold energy E/A≤ 350 MeV (Ed≤ 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 3NF

16. PIS-AVF-RRC-SRC – then,Where? Polarized Ion Source vector & tensor pol. d Beam Line Polarimeter dp elastic/breakup Measurement SAMURAI dp elastic & radiative capture Measurement

17. N-d Elastic Scattering Data at 70-400 MeV/Aon the Market at RIBF at RARF

18. Finally • A 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.

19. Experiments were carried out under the collaboration of RIKEN K. Sekiguchi, N. Sakamoto, T. Ohnishi University of Tokyo H. 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 University H. Okamura, A.Tamii, Tokyo Institute of Technology Y. Satou Kyushu University T. Wakasa KVI N. Kalantar, K. Ermisch Saitama University J. Nishikawa, K. Itoh