Yukie Maeda（前田幸重） Univ. of Miyazaki（宮崎大学） Effects of three-nucleon force and the experimental study via the few-nucleon systems Yukie Maeda（前田幸重） Univ. of Miyazaki（宮崎大学） The 9th Japan-China Joint Nuclear Physics Symposium (JCNP 2015) Osaka University, Nov 10 2015

Outline History Experimental study by few-nucleon systems Three-body problem Three-nucleon force (3NF) effects in the nuclear physics Experimental study by few-nucleon systems nucleon – deuteron (N+d) elastic scattering proton – deuteron (pd) breakup reaction 4 body system (tetra neutron & p-3He) New theoretical study Summary

Lao zi (老子) said in “Tao-te Ching (道德经)”; The Tao produced One; One produced Two; Two produced Three; Three produced All things. [Chapter 42]

One produced Two [Nucleon – Nucleon potentials] One pion exchange Yukawa (1935) Phenomenological NN potential (1990 - ) CDBonn, AV18, Nijmegen I, II, 93 The c2/datum ~ 1 for the fit of about 4500 np & pp scattering data Cross sections, Spin observables @ E < 350 MeV Next : Two produced Three ? Many body interactions are needed ? S. Aoki et al. PTEP 2012 (2012) 01A105

It will be found that the use of two-body interactions is an excellent approximation for electronic motions in atomic systems, but a relatively poor one for the heavy particles in nuclei. The three-body effect is very small in pure s-state. If there is a considerable amount of p- and higher states in triton, the three-body force becomes important.

Two pion exchange 3NF 2p-exch. + D-isobar Tucson-Melbourne (TM) Fujita-Miyazawa (1957) Tucson-Melbourne (TM) Urbana-IX (UIX) a,b,c,d ; determined by pN scattering data <- FM type A, U0 ; determined by fitting B.E.(3H) & nuclear matter density

Two produced Three [Binding Energy of 3H] Faddeev calculations based on phenomenological NN pot. under bind about 0.5 – 1 MeV -> explained by introducing 3NF ! parameter of 3NF is determined to reproduce B.E. of 3NS. Next : Three produced All things ? Many body systems require 3NF ?

Three produced All things ? [Neutron drip line] T. Otsuka et al., Phys. Rev. Lett. 105 (2010) 032501. Drip line of oxygen is near from the stability line (oxygen anomaly) 3NF provides repulsive interactions between valence neutrons.

Three produced All things ? [Neutron Star] S. Gandolfi et al., PRC 85 (2012) 032801. NASA Many data about M ~ 1.4 Msolar Recent accurate data of M = 2 Msolar Short-range term of 3NF plays a key role in the high-density EOS. Mass-to-radii correlation is sensitive to the detail of 3NF.

Three produced All things ? [3N scattering states] 3NF is essential for the nuclear physics. Phenomenological NN ; c2/datum ~ 1 for the fit of 4500 data !! 3NF potentials ; should be studied comprehensively. Experiments of the nucleon-deuteron (Nd) scattering at the intermediate energy region Cross sections & spin observables at various energies Comparison with the Faddeev calculations p+d & n+d elastic pd breakup pd capture

By Courtesy of K. Sekiguchi (Tohoku Univ.)

By Courtesy of K. Sekiguchi (Tohoku Univ.)

NN NN+TM’ AV18+UR

pd inclusive/exclusive breakup meas. @ RCNP Neutron TOF N0 p LAS p Grand Raiden inclusive D(p,p’) & exclusive D(p,2p) @250MeV n p inclusive D(p,n)@170MeV

D(p,p)pn & D(p,n)pp inclusive breakup FSI FSI FSI D(p,p)pn @ 250MeV S. Kuroita et al. (Kyushu Univ.)　 D(p,n)pp @ 170MeV Y.M. et al.

d(p,p1p2) exclusive breakup reaction @ 250MeV q1= (qn=) 40 deg, q2~ 67 deg, Y.M. et al. q1=15 deg, E1~150 MeV, S. Kuroita et al. Discrepancies are large at small q2 (small En) Data around FSI region is well reproduced

Summary of Nd scattering (isospin T=1/2) Nd scatterings are good probe for the study of 3NF Dynamics of 3NF (Energy & Spin dependence) Some data is well reproduced by NN + 3NF Cross sections & Ay of elastic scattering @ E < 150 MeV Exclusive breakup reactions in FSI kinematical configurations Some data is not reproduced by NN + 3NF Elastic & breakup scattering @ higher energy region Tensor spin observables of elastic scattering What is missing ? Relativistic effects, Coulomb force Higher order (3p-ring etc) 3NF, heavier meson (r, s) exchange 3NF Isospin T = 3/2 components NEXT topic

3NF of T=3/2 components in the Light Nuclei J. Carlson et al., Rev. Mod. Phys. 87 (2015) 1067. Illinois-7 (IL7) ; parameters are determined by fitting of g.s. & excited states of light nuclei Strong isospin dependence How we can get almost direct information of T = 3/2 3NF components by 3 or 4 body systems?

Tetra-neutron (4n) Search By Courtesy of K. Kisamori (RIKEN) Tetra-neutron (4n) Search SHARAQ06 Collaboration S. Shimoura, K. Kisamori 1 CNS, The University of Tokyo K. Kisamori2, S. Shimoura, H. Miya2, S. Michimasa, S. Ota, T. Fujii, S. Go, S. Kawase, M. Kobayashi, Y. Kubota2, C. S. Lee2, Y. Sasamoto, M. Takaki, L. Tang, H. Tokieda, K. Yako, R. Yokoayama 2 RIKEN Nishina Center H. Baba, M. Dozono, N. Fukuda, N. Inabe, D. Kameda, T. Kubo, M. Kurata-Nishimura, H. Sakai, M. Sasano, H. Sato, Y. Shimizu, H. Suzuki, H. Takeda, S. Takeuchi, T. Uesaka, Y. Yanagisawa 3 Kyoto University T. Kawabata, T. Baba, M. Tsumura 4 RCNP Osaka University E. Ideguchi, K. Miki, A. Tamii 5 CYRIC, Tohoku University M. Itho 6 Tokyo Institute of Technology Y. Kondo 7 University of Miyazaki Y. Maeda 8 the University of Tokyo T. Nishi 9 NSCL, Michigan State University S. Noji, A. Stolz, 10 Kyushu University S. Sakaguchi2 11 IPN Orsay D. Beaumel, M. Assie, F. Hammache 12 National Institute of Radiological Sciences H. Matsubara part of collaborators

Design of the Experiment By Courtesy of K. Kisamori (RIKEN) Design of the Experiment Reaction : 4He(8He,8Be)4n Reaction with unstable beam → 4n system with small momentum transfer. (almost recoil less condition) 4n 8He 8Be 4He Compensate Q=-30.9 MeV Q=+27.7 MeV target system projectile Missing-mass spectroscopy SHARAQ spectrometer → high resolution: ~ 1 MeV 2α detection at 200 MuV/u → good signal-to-noise ratio

Experimental Setup Primary Beam from Cyclotron (13.7 MHz) Dispersive Focal Plane ・MWDC (Multi-Wire Drift Chamber) momentum tagging for 8He beam production target F6 F3 High Resolution Beam Line ・plastic scintillator ・micro hodoscope start point of ion optics ・plastics scintillator ・MWDCs target position liq. He target 120 mg/cm2 φ=30 mm FH9 8He beam α liq. He target x S2 focal plane S0 S0 SHARAQ spectrometer S2 ・plastic scintillator ・CRDCs (Cathode Readout Drift Chamber) two α tracking Final Focal Plane

preliminary Result Missing-mass Spectrum of 4n By Courtesy of K. Kisamori (RIKEN) Result preliminary Missing-mass Spectrum of 4n energy resolution: 1.2 MeV uncertainty of calibration: ± 1.3 MeV background: 2.3±1.0 events → almost background free Candidate of the resonant state clear strength with 4.9σ significance level E4n = 0.83 ± 0.65 (stat.) ± 1.25 (syst.) MeV upper limit of Γ = 2.6 MeV (FWHM) cross section : 3.8 nb (int. up of θCM < 5.4 degree) +2.9 -1.8

By Courtesy of K. Sekiguchi (Tohoku Univ.)

Chiral Effective Field Theory (CFT) E. Epelbaum, Few-Body Syst. (2013) 54 Chiral EFT provides a systematic approach to nuclear forces which relies on the symmetries of QCD. 3NF naturally appear at N2LO. Recently NN & 3NF at N3LO are constructed.

Faithful to Phase shift at asymptotic region By Courtesy of T. Doi (RIKEN) 3NF from Lattice QCD NBS wave function  Potential Unified Contraction Algorithm (UCA) Systematically reduce the huge computational cost Faithful to Phase shift at asymptotic region by 2N calc S.Aoki et al. (HAL Coll.), PRD88(2013)014036 Doi-Endres CPC184(2013)117 (Wick) (color/spinor) x ~ 1000 for A=2  A=3 ~ 100-1000 in our calc Speed up by UCA Speed up factor:

short-range repulsive 3NF ! By Courtesy of T. Doi (RIKEN) Numerical Results Triton channel mp=0.76-1.1GeV (mN=1.6-2.1GeV) T.D. et al. (HAL QCD Coll.) PTP127(2012)723 + t-dep method updates etc. short-range repulsive 3NF ! Preliminary (cutoff artifact) In progress/Prospects Other geometries Nf=2 clover (CP-PACS), 1/a=1.27GeV, L=2.5fm Lighter mass w/ K-computer 3BF w/ hyperon (YNN/YYN/YYY)

2-baryon forces (NN/YN/YY) at (almost) physical point By Courtesy of T. Doi (RIKEN) Breaking News 2-baryon forces (NN/YN/YY) at (almost) physical point NN Tensor Force in 3S1-3D1 Clearly visible w/ physical mass ! Calc on K-computer in progress to improve S/N (& take larger t) Preliminary 10PFlops [HPCI Field5 Project 1]

Summary 3NF effect is one of the essential building blocks of the study of nuclear physics. Highly precise Nd scattering data have been measured and allowed us to test the detail of 3NF models. -> Energy & spin dependencies are not good enough yet. Theoretical progress in developing new 3NF potentials is highly expected. More experimental studies are also expected. -> Massive & precise scattering data for parameter fittings -> New experiments for the study of 3NF (T=3/2) by using new experimental technique.