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

2. Three Nucleon Force (3NF) 1957 Fujita-Miyazawa 3NF Model Prog. Theor. Phys. 17, 360 (1957) Prog. Theor. Phys. 17, 360 (1957) Three nucleon force (3NF) has been predicted as a concept of the meson theory. 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.

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

4. Comparing the Faddeev Calculations based on 2NF (e.g. CDBonn, AV18, Nijm I, II) Cross Section for d-p Elastic Scattering at 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-p

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

6. N-d Elastic Scattering Data at 70-400 MeV/A on 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. Polarized Ion Source vector & tensor d Beam Line Polarimeter By 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%

8. Focal Plane Polarimeter DPOL RIKEN Magnetic Spectrograph SMART

9. SMART: Swinger and Magnetic Analyzer with Rotator and Twister Swinger Focal Plane Target CH 2 / Liq.H 2

10. 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 ( )  -isobar Excitations NN Interactions : CDBonn Comparison of the Data with the Faddeev Calculations

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 d  /d  : good agreement  3NFs are clearly needed. Spin Observables : TM99/ Urbana IX does better job for A y p & T 20  Requirement of chiral symmetry Vector Pol. (A y p & iT 11 ) : good agreement Tensor Pol. ( T 20, T 21, T 22 ) : T 20 & T 21 : moderate agreement T 22 : Chaotic Defects of 3NF Higher order pol. (pol. transfer) : moderate agreement Directions are O.K, but sizes are not enough for K y y’ & K xz y’. When the 2  -exchange 3NFs are included …

14. What are we missing? 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  and  exchange 3NF many  -contributions with  -rings  e.g. 3π-rings with  -isobar excitations (Illinois Model) - Link to QCD - Nuclear forces (2NF, 3NF, … ) and currents are derived in a consistent way. and currents are derived in a consistent way.

15. Three Nucleon Force Study via Few Nucleon Scattering at RIBF with pol d. beams up to near  threshold energy E/A ≤ 350 MeV (E d ≤ 700 MeV) E/A ≤ 350 MeV (E d ≤ 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 pol. d beams at RIBF : E/A = 250 – 440 MeV

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

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

18. Finally A new microscope “Few-N Scattering-at-intermediate- energies” has been set for exploring 3NFs. The 1 st 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