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Exploring Three Nucleon Forces with Nucleon-Deuteron Scattering

Exploring Three Nucleon Forces with Nucleon-Deuteron Scattering. RIKEN Nishina Center Kimiko Sekiguchi. The Tao produced One, One produced Two, Two produced Three, and Three produced All things.

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Exploring Three Nucleon Forces with Nucleon-Deuteron Scattering

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  1. Exploring Three Nucleon Forces with Nucleon-Deuteron Scattering RIKEN Nishina Center Kimiko Sekiguchi

  2. The Tao produced One, One produced Two, Two produced Three, and Three produced All things. “Tao-te Ching“by Lao Zi in B.C. 400 To explore the laws of the nature, step in 1 → 2 → 3 .

  3. To explore the laws of the nature, step in 1 → 2 → 3 . Earth-Moon-Satellite Gravitational Interactions • Two Body Interactions : Gravity • Three Body Interactions by the polarizations of the ocean water of the earth by the moon’s gravity

  4. To explore the laws of the nature, step in 1 → 2 → 3 . Triplets of Atoms Van der Waals Type Three Body Force • Two Body Interactions : Gravity • Three Body Interactions Effects of the polarizations of the electron density distribution

  5. Nucleus : a compact system of nucleons Nuclear Force : Strong Interactions Effects of Three Nucleon Forces – Where and How to attack- ? Are there three nucleon forces in Nuclei ?

  6. Before Three Nucleon Force Two Nucleon Force (2NF) 1935 Yukawa’s meson theory (2NF) • Theory : • One Pion Exchange Model • One Boson Exchange Model • Heavier Meson Exchange • e.g. r, w • Experiment : • Nucleon-Nucleon (NN) • Scattering Data Set • (ds/dW and Spin Observables) • Deuteron Properties 1990’s Realistic Modern NN Force CDBonn, AV18, Nijmegen I,II,93 reproduce 3500 exp. NN scattering data with high precision, c2 1

  7. N N N Three Nucleon Force (3NF) 1957 Fujita-Miyazawa 3NF Prog. Theor. Phys. 17, 360 (1957) • 2p-exchange 3NF : • - Main Ingredients : • D-isobar excitations in the intermediate D: excited state of nucleon • Tucson-Melbourne (TM) • Urbana IX • Brazil, Texas etc…

  8. Where could we see 3NF effects ? - I - Ab Initio Calculations for Light Nuclei (A<10) • Green’s Function Monte Carlo • Ab Initio No-Core Shell Model etc.. • 2NFs provide less binding energies • 3NF : well reproduce the data • - 3H, 3He, 4He • by 2p-exchange 3NF (UR) • - p-shell nuclei • by 2p-exchange • + 3p-ring with D-isobar • 3NF Effects in B.E. • 10 – 25 % • attractive S.C. Pieper PRC 64,014001(2001)

  9. Where could we see 3NF effects ? - II - Equation of State for Nuclear Matter • All NN potentials • (AV18, Nijmegen I,II, CD Bonn) • provide larger saturation point • of Nuclear Matter. • 3NF • - shift to the empirical • saturation point • - significant at higher density A. Akmal et al., PRC 58, 1804(’98)

  10. Understanding of 3NF is one key element to describe • nuclear phenomena. • How to constrain the properties of 3NF ? Nucleon-Deuteron Scattering is a good probe to study the dynamical aspects of 3NFs. • Momentum dependence • Spin dependence • Iso-spin dependence : only T=1/2

  11. How to Extract 3NF Effects in Nucleon-Deuteron (Nd) scattering? Nd Scattering – three nucleon unbound system - Direct Comparison between Theory and Experiment • Theory : Faddeev Calculations Rigorous Numerical Calculations of 3N System • Experiment : Precise Data • ds/dW, Spin Observables (Aij, Kij, Cij) • → Extract 3NF effects • 2NF Input • CDBonn • Argonne V18 (AV18) • Nijmegen I, II, 93 • 3NF Input • Tucson-Melbourne • Urbana IX • Nucleon & D isobar • by coupled channel • 2NF & 3NF Input • Chiral Effective Field Pot.

  12. Where is the Hot Spot for 3NF Effects in Nd scattering? Predictions by H. Witala et al. (1998) Cross Section minimum for Nd elastic scattering at Intermediate Energies (E/A~100 MeV) Nd scattering Low Energy Intermediate Energy NN NN 3NF Forward Backward 3NF 3NF q =0 ～ 4 fm-1

  13. Nd Scatteringat Low Energies ( E ≤ 30 MeV/A ) • High precision data are explained • by Faddeev calculations based on 2NF. • No signatures of 3NF. • Exp. Data from • Kyushu, TUNL, Cologne etc.. W. Glöckle et al., Phys. Rep. 274, 107 (1996).

  14. Intermediate Energies(E = 100 ~ 200 MeV/A)

  15. Precise Measurement of dp scatteringat RIKEN Accelerator Research Facility dp Elastic Scattering 1 Differential Cross Section and All Deuteron Analyzing Powers (Ay , Ayy , Axx , Axz) at 70, 100, 135 MeV/A - Whole Angular Range : q c.m. = 10°－180° 2． Deuteron to ProtonPolarization Transfer Coefficients at 135 MeV/A - Double Scattering Experiment : Measurement of Polarizations of Recoil Protons - Angular range :qc.m. = 90°－180° - Strong sensitivities to Three Nucleon Force dp Breakup Reactions - Extension from Elastic to Breakup - Limited kinematical configurations : sensitive to 3NF - First measurement of Polarization Transfer Coefficient

  16. RIKEN Accelerator Research Facility Spin symmetry axis of polarized d beams is freely controlled ! • Spin axis is controlled by Spin Rotator prior to acceleration. • Single-turn extraction feature of RARF maintain the polarization amplitudes Beam polarizations : 60-80% K70 AVF cyclotron K135 Ring cyclotron AVF + Ring cyclotrons pol. d beams 65 ～135 MeV/A Beam Intensity : 200 pnA Polarized Ion Source Wien Filter (Spin Rotator) Beam Line Polarimeter By d+p Elastic Scattering

  17. Swinger and Magnetic Analyzer with Rotator and Twister (SMART) Focal Plane Polarimeter DPOL Target CH2 / Liq.H2 DPOL / EPOL SMART: Swinger and Magnetic Analyzer with Rotator and Twister

  18. Determination of Absolute Values of the Cross Section 1. d + p at 135 MeV/A (70 MeV/A) beam d H2+ 2. measure p + p 135 MeV (70MeV) 3.Direct Comparison with NN phase-shift solution(SAID) pp scattering at 135 MeV Ratio = ds/dW(exp) / ds/dW (calc.) Same Exp. Setup • Target CH2 • Faraday Cup • Detection System

  19. dp Elastic ScatteringDifferential Cross Section

  20. K. Sekiguchi et al. PRC 65,034003 (2002) Calculations by Bochum-Cracow Gr. 2NF (CDBonn, AV18, Nijmegen I,II) : Large discrepancy in Cross Section Minimum ( ~ 30%) 2p-exchange 3NFs (Tucson-Melbourne, Urbana IX) : Good Agreement

  21. Calculations by Hannover-Lisbon Gr. Coulomb Coupled channel approach with Nucleon&D-isobar : Good Agreement. Disagreement at very forward angles : Coulomb effects. A. Deltuva et al., PRC 68, 024005 (2003) A. Deltuva et al., PRC 71, 054005 (2005)

  22. Relativistic Treatment- would be significant at higher energies Are there any other effects than 2p-exchange 3NF? Calculations with Lorentz boosted NN potentials by Bochum-Cracow Gr. Kamada et al. PRC66,044010(2002) Relativistic effects are visible at backward angles, but small. Discrepancy in the Cross Section Minimum for dp Elastic Scattering comes from 2p-exchange 3NF. K. Sekiguchi et al., PRL95, 162301 (’05)

  23. dp Elastic ScatteringSpin Observables Analyzing Powers & Polarization Transfer Coefficients

  24. K. Sekiguchi. et al. PRC 65, 034003(2002) Analyzing Power 2NF (CDBonn, AV18, Nijmegen I,II) : Large discrepancy in Cross Section Minimum 3NF (Tucson-Melbourne, Urbana IX, D-isobar) : Vector Analyzing Power Ayp : Good Agreement Tensor Analyzing Power Ayy : No superiority

  25. K. Sekiguchi. et al. PRC 70, 014001(2004) Polarization Transfer 3NF : Kxxy’–Kyyy’ : Good Agreement Kyy’: Direction : O.K. Magnitude : not enough Spin Observables (Aij, Kij) : Not always explained by 2p-exchange 3NF ⇒ Defects of spin dependent parts of 3NF

  26. New Approach other than Meson Exchange Picture - Chiral Effective Field Theory - 3NF 4NF 2NF • Interactions : • p + Nucleon • + contact terms • (heavier mesons...) • Nuclear forces (2NF, 3NF, … ) • and currents are derived • in a consistent way. • - Hierarchy of Nuclear Forces : • 2NF > 3NF > 4NF • The first 3NF appears in NNLO.

  27. Comparing the data with predictions based on cEFT pot. Calc. based on cEFT pot. (NNLO) is only available below 100 MeV/A. Reasonable agreement for all the measured data d-p at 70 MeV/A Calc. with cEFT Pot. (NNLO) by E. Epelbaum et al.

  28. Nd Elastic Scattering Data at Intermediate Energies ~1998 1998 ~ • Rich data set • ds/dW & many spin observables • from RIKEN, RCNP,KVI,IUCF • Many data exit at 135 MeV/A RIKEN provided the first precise data set of ds/dW , Aij, Kij for dp Elastic Scattering at Intermediate Energies, especially 135 MeV/A. RIKEN

  29. 2nd Stepdp Breakup Reactions

  30. Nd Breakup Reactions 1st Step : Nd Elastic Scattering at Intermediate Energies 2nd Step : Nd Breakup Reactions at Intermediate Energies - Leading Channel at Intermediate Energies nd total cross section sbr > sel e.g. sbr ~ 2.5 sel at 135MeV/A - Rich Phase-Spaces - a large amount of kinematical configurations - Selectivity

  31. dp In-PlaneBreakup Reaction at 135 MeV/A Which is better, Tucson-Melbourne or Urbana IX ? • Observables : • d to p Polarization Transfer Coefficients : Kyyy’ • Analyzing Powers :Ayd, Ayy, Axx, Axz • Kinematical Condition • (q1,q2) = (28 – 32 deg, 31deg) • f12 = 180° • Near Final State Interaction Kyyy’ Ayd Axx 3NF : partly success, partly not. Kyyy’ shows superiority of Urbana IX.

  32. Summary • Three Nucleon Forces (3NF) • play essential roles to explain fundamental properties of nuclear phenomena, e.g. binding energies of light nulcei, EOS of nuclear matter. • Nd Scatteing • is a good probe to study the dynamical aspects of 3NF • - Momentum & Spin dependence - . For iso-spin, T=1/2 only. Precise data of dp scattering at intermediate energies (E ~ 100MeV/A, q = 2~3.5 fm-1) : ds/dW and many spin observables Achievements of rigorous numerical three-nucleon Faddeev calculations based on 2NF+2p-exchange 3NF below p-threshold energies Direct comparison between Experiment and Theory Cross Section for dp Elastic Scattering : - Magnitudes of 3NF is O.K. - First Clear Signatures of 3NF Effects in 3N scattering Spin Observables for dp Elastic Scattering & Breakup Reactions - not always explained by 2p-exchange 3NF - require further study of detailed properties of 3NF

  33. New developments of theory – in progress - Chiral Effective Field Theory Approach Treatment of Relativistic Effect Treatment of Coulomb Meson Exchange Picture – further ingredients of 3NF - r-r and p-r exchange 3NF

  34. Perspective of 3NF Study Nd Scattering provide Fundamental Data/Theory of 3NF Momentum dependence Higher Energies Full treatment of dp Breakup Reactions Spin dependence RIBF/RCNP T=1/2 Iso-spin dependence Neutron-rich Nuclei Hypernuclei Iso-spin dependence of 3NF Strangeness From NNN to YNN & YYN RIBF JPARC

  35. Acknowledgments : SMART Gr. Collaboration School of Science, University of Tokyo H. Sakai, K. Yako, S. Sakoda, H. Kato, M. Hatano, T. Saito, N. Uchigashima, H. Kuboki, M. Sasano, Y. Takahashi CNS, University of Tokyo T. Uesaka, T. Kawabata, S. Sakaguchi, Y. Sasamoto RIKEN N. Sakamoto, T. Ohnishi RCNP, Osaka H. Okamaura, A.Tamii, K. Suda TITech Y. Satou KVI N. Kalantar-Nayestanaki K. Ermisch Kyushu University T. Wakasa, Y. Maeda Saitama University J. Nishikawa, K. Itoh

  36. Theoretical Supports from Ruhr-Universität, Bochum W. Glöckle Jagellonian University H. Witała, J. Golak Kyushu Institute of Technology H. Kamada Forshungszentrum of Jülich A. Nogga Hannover University P.U. Sauer, S. Nemoto Lisbon University A. Deltuva, A. C. Fonseca University of Bonn / Forshungszentrum of Jülich E. Epelbaum, Ulf-G. Meißner Thanks for delivering excellent beams : Accelerator staff of RIKEN Nishina Center and RCNP.

  37. Thank you very much !

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