Exploring Three Nucleon Forces with NucleonDeuteron Scattering RIKEN

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

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

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.

To explore the laws of the nature, step in 1 → 2 → 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

To explore the laws of the nature, step in 1 → 2 → 3.

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

Are there three nucleon forces in Nuclei ? | | | Nucleus : a

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

Before Three Nucleon Force Two Nucleon Force (2 NF) 1935 Yukawa’s meson theory (2

Before Three Nucleon Force Two Nucleon Force (2 NF) 1935 Yukawa’s meson theory (2 NF) Theory : One Pion Exchange Model One Boson Exchange Model Heavier Meson Exchange e. g. r, w Experiment : Nucleon-Nucleon (NN) Scattering Data Set (ds/d. W and Spin Observables) Deuteron Properties 1990’s Realistic Modern NN Force CDBonn, AV 18, Nijmegen I, II, 93 reproduce 3500 exp. NN scattering data with high precision, c 2 1

Three Nucleon Force (3 NF) 1957 Fujita-Miyazawa 3 NF Prog. Theor. Phys. 17, 360

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

Where could we see 3 NF effects ? - I Ab Initio Calculations for

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

Where could we see 3 NF effects ? - II Equation of State for

Where could we see 3 NF effects ? - II Equation of State for Nuclear Matter • All NN potentials (AV 18, Nijmegen I, II, CD Bonn) provide larger saturation point of Nuclear Matter. • 3 NF - shift to the empirical saturation point - significant at higher density A. Akmal et al. , PRC 58, 1804(’ 98)

 • Understanding of 3 NF is one key element to describe nuclear phenomena.

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

How to Extract 3 NF Effects in Nucleon-Deuteron (Nd) scattering? Nd Scattering – three

How to Extract 3 NF Effects in Nucleon-Deuteron (Nd) scattering? Nd Scattering – three nucleon unbound system Direct Comparison between Theory and Experiment l Theory : Faddeev Calculations Rigorous Numerical Calculations of 3 N System l 2 NF Input 3 NF Input 2 NF & 3 NF Input • CDBonn • Argonne V 18 (AV 18) • Nijmegen I, II, 93 • Tucson-Melbourne • Urbana IX • Nucleon & D isobar by coupled channel • Chiral Effective Field Pot. Experiment : Precise Data l ds/d. W, Spin Observables (Aij, Kij, Cij) → Extract 3 NF effects

Where is the Hot Spot for 3 NF Effects in Nd scattering? Predictions by

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

Nd Scattering at Low Energies ( E ≤ 30 Me. V/A ) High precision data

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

Intermediate Energies (E = 100 ~ 200 Me. V/A)

Intermediate Energies (E = 100 ~ 200 Me. V/A)

Precise Measurement of dp scattering at RIKEN Accelerator Research Facility dp Elastic Scattering 1

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

RIKEN Accelerator Research Facility K 70 AVF cyclotron K 135 Ring cyclotron AVF +

RIKEN Accelerator Research Facility K 70 AVF cyclotron K 135 Ring cyclotron AVF + Ring cyclotrons pol. d beams 65 ~ 135 Me. V/A Beam Intensity : 200 pn. A Polarized Ion Source Spin symmetry axis of polarized d beams is freely controlled ! ØSpin axis is controlled by Spin Rotator prior to acceleration. Ø Single-turn extraction feature of RARF maintain the polarization amplitudes Beam polarizations : 60 -80% Wien Filter (Spin Rotator) Beam Line Polarimeter By d+p Elastic Scattering

Focal Plane Polarimeter DPOL Swinger and Magnetic Analyzer with Rotator and Twister Target (SMART)

Focal Plane Polarimeter DPOL Swinger and Magnetic Analyzer with Rotator and Twister Target (SMART) CH 2 / Liq. H 2 DPOL / EPOL

Determination of Absolute Values of the Cross Section 1. d + p at 135

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

dp Elastic Scattering Differential Cross Section

dp Elastic Scattering Differential Cross Section

K. Sekiguchi et al. PRC 65, 034003 (2002) Calculations by Bochum-Cracow Gr. 2 NF

K. Sekiguchi et al. PRC 65, 034003 (2002) Calculations by Bochum-Cracow Gr. 2 NF (CDBonn, AV 18, Nijmegen I, II) : Large discrepancy in Cross Section Minimum ( ~ 30%) 2 p-exchange 3 NFs (Tucson-Melbourne, Urbana IX) : Good Agreement

Calculations by Hannover-Lisbon Gr. Coulomb Coupled channel approach with Nucleon&D-isobar : Good Agreement. Disagreement

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)

Are there any other effects than 2 p-exchange 3 NF? Relativistic Treatment - would

Are there any other effects than 2 p-exchange 3 NF? Relativistic Treatment - would be significant at higher energies Calculations with Lorentz boosted NN potentials by Bochum-Cracow Gr. Kamada et al. PRC 66, 044010(2002) Relativistic effects are visible at backward angles, but small. Discrepancy in the Cross Section Minimum for dp Elastic Scattering comes from 2 p-exchange 3 NF. K. Sekiguchi et al. , PRL 95, 162301 (’ 05)

dp Elastic Scattering Spin Observables Analyzing Powers & Polarization Transfer Coefficients

dp Elastic Scattering Spin Observables Analyzing Powers & Polarization Transfer Coefficients

Analyzing Power K. Sekiguchi. et al. PRC 65, 034003(2002) 2 NF (CDBonn, AV 18,

Analyzing Power K. Sekiguchi. et al. PRC 65, 034003(2002) 2 NF (CDBonn, AV 18, Nijmegen I, II) : Large discrepancy in Cross Section Minimum 3 NF (Tucson-Melbourne, Urbana IX, D-isobar) : Vector Analyzing Power Ayp : Good Agreement Tensor Analyzing Power Ayy : No superiority

Polarization Transfer 3 NF : Kxxy’–Kyyy’ : Good Agreement Kyy’ : Direction : O.

Polarization Transfer 3 NF : Kxxy’–Kyyy’ : Good Agreement Kyy’ : Direction : O. K. Magnitude : not enough K. Sekiguchi. et al. PRC 70, 014001(2004)

New Approach other than Meson Exchange Picture - Chiral Effective Field Theory - Interactions

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

Comparing the data with predictions based on c. EFT pot. Calc. based on c.

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

Nd Elastic Scattering Data at Intermediate Energies ~ 1998 • Rich data set ds/d.

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

2 nd Step dp Breakup Reactions

2 nd Step dp Breakup Reactions

Nd Breakup Reactions 1 st Step : Nd Elastic Scattering at Intermediate Energies 2

Nd Breakup Reactions 1 st Step : Nd Elastic Scattering at Intermediate Energies 2 nd 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 135 Me. V/A - Rich Phase-Spaces - a large amount of kinematical configurations - Selectivity

dp In-Plane Breakup Reaction at 135 Me. V/A Which is better, Tucson-Melbourne or Urbana

dp In-Plane Breakup Reaction at 135 Me. V/A Which is better, Tucson-Melbourne or Urbana IX ? Kinematical Condition (q 1, q 2) = (28 – 32 deg, 31 deg) f 12 = 180° Near Final State Interaction Observables : d to p Polarization Transfer Coefficients : Kyyy’ Analyzing Powers : Ayd, Ayy, Axx, Axz Kyyy’ A yd Axx 3 NF : partly success, partly not. Kyyy’ shows superiority of Urbana IX.

Summary Three Nucleon Forces (3 NF) play essential roles to explain fundamental properties of

Summary Three Nucleon Forces (3 NF) 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 3 NF - Momentum & Spin dependence -. For iso-spin, T=1/2 only. Precise data of dp scattering at intermediate energies (E ~ 100 Me. V/A, q = 2~3. 5 fm-1) : ds/d. W and many spin observables Achievements of rigorous numerical three-nucleon Faddeev calculations based on 2 NF+2 p-exchange 3 NF below p-threshold energies Direct comparison between Experiment and Theory Cross Section for dp Elastic Scattering : - Magnitudes of 3 NF is O. K. - First Clear Signatures of 3 NF Effects in 3 N scattering Spin Observables for dp Elastic Scattering & Breakup Reactions - not always explained by 2 p-exchange 3 NF - require further study of detailed properties of 3 NF

New developments of theory – in progress Chiral Effective Field Theory Approach Treatment of

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

Perspective of 3 NF Study Momentum dependence Spin dependence Nd Scattering provide Fundamental Data/Theory

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

Acknowledgments : SMART Gr. Collaboration School of Science, University of Tokyo H. Sakai, K.

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

Theoretical Supports from Ruhr-Universität, Bochum W. Glöckle Jagellonian University H. Witała, J. Golak Kyushu

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.

Thank you very much !

Thank you very much !