1. Status of three-nucleon force study by nucleon-deuteron system August 22, 2006 FB18, Santos, Brazil 1.Introduction 2.dp elastic measurements by NUCLOTRON at DUBNA 3.How far we understand 3NF effects? 4.How data are reliable ? 5.Facilities 6.Summary H. Sakai Department of Physics The University of Tokyo

2. 1. Introduction How 3NF are established by experiments?

3.  How to study 3NF? 2BS 3BS 2NF 3NF  3NF is much smaller than 2NF. →3NF effects are easily masked by 2NF effects. 1 Equations of motion for 3BS must be solved exactly. →Faddeev eq. 2 Realistic modern 2NF must be established. x 2  1 for 4,000 data points. CD Bonn AV18 Nijmegen I/II Main differences are off-shell properties. 3 2πexchange 3NF (Fujita-Miyazawa) TM99 Urbana IX (U9)  New development in theory 1  PT 2 Relativistic effects 3 Coulomb effects

4.  Why Nd measurements at intermediate energies? H.Witała et al., PRL 81(1998) 1183. →Go to higher energies for Nd elastic scatt. and look at X-sec. minimum region. Typical mom. transfer: 1.5--3 fm -1 for Nd scatt. at intermediate energies.  D-state of deuteron mainly contributes in the reaction. At intermediate energy, this may correspond to x-sec. min. internal mom. dist. of deuteron

5.  Reactions for Nd system  Observables (Nd-sys.) d  /d  AP (A y, iT 11, T 20, T 21, T 22 ) V LS, (V LS ) 2, V T, D-state PT (K i j, K ij k ) V  (spin-spin int.) SC (C i,j, C i,jk, C ij,k ) V  q(fm-1)@135 MeV 1 elastic scattering 0--2.4--3.4 (0º--90º--180º) 2 breakup (FSI, QFS, Space star) 0--3 3 capture2.5--3.5 (0º--180º), MEC

6. Cross section/AP meas. pd nd n p n d p d p/d p  difficulties of measurements p/d p d L R PT characteristic Cross section : absolute quantity systematic errors Pol. Obs. : relative quantity normalize to pp scatt. normalize to np scatt. tiny yield (difficult exp.) Pol. transfer meas. polarimeter calibration small yield (difficult exp.)

7.  Present achievement of experiments @ intermediate energies

8.  Recent tendency of experiments @ intermediate energies 1 higher bombarding energies R3-17 Tamii et al. pd-392 MeV 2 nd data become available R3-16 Maeda et al. nd-250 MeV 3 breakup 2πcoverage, PT R2- Kystrin et al. dp-130 MeV (cancelled) R3-15 Mardanpour et al. dp-190 MeV 2πcoverage R3-25 Sekiguchi et al. dp-270 MeV PT 4 radiative capture R3-18 Messchendorp et al. dp-190 MeV  -coinc. R3-24 Tameshige et al. dp-137 MeV 5 four-nucleon system R3-20 Miki et al. dd-270 MeV DFSI Please come to “Experimental Few-Body session”, Room 3, Friday (Aug. 25) RIKEN exp. DUBNA exp.

9. 2 dp elastic measurements by NUCLOTRON at DUBNA

10. Nuclotron at JINR, Dubna superconducting synchrotron (E/A < 6 GeV) Nuclear structure Medium effects on particle production Modification of nuclear matter Hypernuclei and  nuclei Nucleon structure  d-p elastic scattering measurement at NUCLOTRON Internal Target Station 30-pairs plastic scintillation counters target:CH2(10  m) Measurements at 270 MeV, 880 MeV and 2 GeV by Uesaka/Ladygin et al.

11. A y ~  0.3 ; moderately large A yy ; large only at  cm  0 deg insufficient statistics due to small beam intensity → strong beam with new ion source CIPIOS  d-p Analyzing powers at 880 MeV Beam Intensity < 2-3 x10 7 /spill Polarizations (p Z, p ZZ )=(+1/3,+1),(+1/3,-1), (0,0) measured values: (preliminary) p Z p ZZ mode 1 -0.207 ± 0.044 0.879 ± 0.116 mode 2 -0.176 ± 0.035 -0.421 ± 0.093 Results Suda et al. R3-17 Tamii pd-392 MeV

12. 3 How far we understand 3NF effects? Success and failure

13.  Success & failure 1 d  /d , vector AP(A y ), PT(K ij k ) (T p  135 MeV)  very successful 2 tensor AP, PT, SC  some successful, some not. confusing, chaotic! 3 d  /d  (T p >200 MeV)  large discrepancy in backward angles (nucleon-exchange process) due to 3NF? / relativity? / ?

14.  Success 1 d  /d , vector AP(A y ), PT(K ij k ) (T p  135 MeV)  very successful Sekiguchi et al. NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+ △ Coulomb

15.  Failure? 2 iT 11, T ij, PT  some successful, some not. confusing, chaotic! Sekiguchi et al. NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+ △

16.  Failure? 3 d  /d  ? (T p >200 MeV) R3-17 Maeda nd elastic scattering measurements at E n =250MeV Calc. even including 3NF still underestimate the data by 50% ! nucleon-exchange process ? Relativistic calc. by Witala improve the fit only at θcm > 160 deg. but not enough. Doleschall approx. by Kamada Screened Coulomb by Deltuva Coulomb effects ? (too large !)

17. 4 How data are reliable ? Inconsistency between data sets

18.  Consistency between data sets 1 d  /d  (T p =135 MeV) pd-elastic scatt.  RIKEN vs. KVI 2 A xx,A yy (T d =200 MeV) dp-radiative capture  RCNP vs. KVI Different group data-sets are consistent? 3NF effects are at most 30% effect.

19.  Consistency among data sets 1 d  /d  (T p =135 MeV) pd-elastic scatt.  RIKEN vs. KVI ○ N. Sakamoto, PL B367 (1996)60. ● H. Sakai, PRL 84(2000)5288. ● K. Sekiguchi, PR C65(2002)34003. ▲ K. Ermisch, PR C68(2003)51001. ○ K. Sekiguchi, PRL 95(2005)162301. How do you judge? NN only NN+3NF(TM99) AV18+3NF(U9) CDBonn+ △

20.  Consistency among data sets 2 A xx, A yy (T d =200 MeV) dp-radiative capture  RCNP vs. KVI d+p  3 He+  @ 200 MeV/A No anomaly observed In KVI data!!  Sagara, Preliminary — Hanover (virt.  ) Deltuva, PRC67, 034001(03) — Bochum/Cracow (MEC) Skibinski, PRC67, 054001(03) — Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03)  KVI, PL B Mehmandoost/van Garderen A yy A xx

21. A yy AxxAxx d+p  3 He+  @ 270 MeV/A at RIKEN One of the last experiment at SMART. by Suzuki et al.by Sekiguchi et al. Another confusion ! 270 MeV 200 MeV

22. 5 Facilities

23.  Facilities 1.Phase out from nuclear physics experiment IUCF (2002) pol-p, d TSL (2005) n-fac. RIKEN (2005) pol-d KVI (2007) pol-p,d (soon) 2.Active RCNP pol-p(<400 MeV), pol-d(<200 MeV), n-fac. LANL n-fac. NUCLOTRON pol-d(<6 GeV) COSY pol-p, pol-d iThemba(NAC) p,d 3.Coming RIKEN RIBF pol-d(400-880 MeV)

24. Beam Line Polarimeter dp elastic/breakup Measurement Polarized Ion Source vector & tensor pol. d  RIKEN RIBF Polarized d (400-880 MeV) available in 2008(?) SMART Pol. d (140-270 MeV) Contact person: Dr. K. Sekiguchi SMART spectrometer Most of the 3NF studies were performed by using the magnetic spectrometer SMART!

25.  Facilities 1.Phase out for nuclear physics experiment IUCF (1998) pol-p, d TSL (2005) n-fac. RIKEN (2005) pol-d KVI (2007) pol-p,d (soon) 2.Active RCNP pol-p(<400 MeV), pol-d(<200 MeV), n-fac. NUCLOTRON pol-d(<6 GeV) COSY pol-p(<1GeV), pol-d(?) iThemba(NAC) p(<200 MeV), d(<80 MeV) LANL n-fac.(<800 MeV) 3.Coming RIKEN RIBF pol-d(400-880 MeV)  Theory Without exact calc., nothing can be conclusive! Key to the few-body study!

26. 6 Summary

27.  Summary ─ Tendency of 3NF study. 1.Higher energies  DUBNA exp. 2.nd measurement 3.Breakup 4.Readiative capture ─3NF are successful? (comparison to theories) 1. d  /d , Ay T p  135 MeV good fits 2. T p >200 MeV fail, 50% off. small rel. effects.  (nd)/  (pd) Coulomb ? 3. Tensor AP, PT confusing, chaotic!

28. dp-breakup measurement at 270 MeV at RIKEN R3-25 Sekiguchi another confusion ! ? vector APtensor AP tensor-to-vector PT  1 =27° - 35°,  2 =31 °,  12 ＝ 180 °

29.  Summary ─Tendency of 3NF study. 1.Higher energies  DUBNA exp. 2.nd measurement 3.Breakup 4.Readiative capture ─How present 3NF are successful. (comparison to theories) 1. d  /d , Ay T p  135 MeV good fits 2. T p >200 MeV fail, 50% off. small rel. effects.  (nd)/  (pd) Coulomb ? 3. Tensor AP, PT confusing, chaotic! ─Consistencies between data sets 1. d  /d  at T p =135 MeV 2. Radiative capture ─Facilities How far we understand 3NF, that is the question.

30.  Collaborators Jagiellonian Univ. H. Witala, J. Golak KIT H. Kamada Bochum W. Glockle Honnove P.U. Sauerr Lisbon A. Deltuva University of Tokyo RCNP RIKEN Kyushu University TITech Saitama University This talk is helped by K. Sekiguchi (RIKEN) Y. Meda (U. Tokyo) K. Suda (U. Tokyo) J. Messchendorp (KVI) Experiments Theory

31. Announcements.

32. The 23rd International Nuclear Physics Conference with a special session in commemoration of the centennial of the birth of Prof. Hideki Yukawa June 3(Sun)-8(Fri), 2007 Tokyo International Forum, Tokyo hosted by KEK, RIKEN, RCNP, JAEA, JWE and Yukawa Memorial Foundation sponsored by IUPAP, The Science Council of Japan, The Physical Society of Japan The Organizing Committee chaired by Shoji Nagamiya (KEK) homepage: http://www.inpc2007.jp for pre-registration email: inpc07reg@convention.co.jp

33. Organizers: H. Sakai (UT) (chair) H. Sakai (UT) (chair) K. Hatanaka (RCNP) K. Hatanaka (RCNP) H. Okamura (RCNP) H. Okamura (RCNP) K. Sagara (Kyushu) K. Sagara (Kyushu) Y. Suzuki(Nigata) Y. Suzuki(Nigata) Y. Akaishi (Nihon/RIKEN) Y. Akaishi (Nihon/RIKEN) T. Motobayashi(RIKEN) T. Motobayashi(RIKEN) K. Sekiguchi (RIKEN) (secretary) K. Sekiguchi (RIKEN) (secretary) Topics to be covered : - Few Nucleon Systems and Three Nucleon Force - Few Nucleon Systems and Three Nucleon Force - Chiral Effective Field Theory - Chiral Effective Field Theory - Three Nucleon Force Effects in Nuclear Structure - Three Nucleon Force Effects in Nuclear Structure - Three Nucleon Forces in Hyper Nuclei - Three Nucleon Forces in Hyper Nuclei International Symposium on New Facet of Three Nucleon Force ～ 50 years of Fujita-Miyazawa Three Nucleon Force ～ October 29(Mon.) - 31(Wed.), 2007 Koshiba Hall, University of Tokyo

34. End Thank you for your attention.

35.  Four nucleon system is interesting. 2BS 3BS 2NF 3NF 4BS4NF 2NF 3NF 4NF 1 3 1 6 4 1 ─ 4BS is a good tool to study 3NF effects. ─ stressed by Fonseca. ─ solve Faddeev-Yakubovsky eq. exactly. ─ 4NF effects? ─ First of all, establish 3NF. ─ But look for where?  V NN   20 MeV/pair  V 3NF   1 MeV/triplet  V 4NF   0.1 MeV/quartet by J.L. Friar, FBS 22(1997)161.

36. Results(1) Differential Cross Sections Faddeev calc (by Prof. H. Kamada) : NN only (CD-Bonn, AV18, Nijmegen-I,II,93) : NN with TM-3NF : AV18+UrbanaIX-3NF : CD-Bonn+TM’-3NF Calculations even including 3NF still underestimate the data at  cm = 110 – 180 deg. CC calc (by Honnover group) : CD-Bonn : CD-Bonn+  -3NF

37. Relativistic effects Hamiltonian of 3N system (total momentum = 0) Relativistic energy Relativistic NN potential ( in CM system of particle i, j) Lorentz boosted NN potential into CM system of 3N (Fully relativistic) Approximations of V ij p ij <<1 Dependence of k and k’

38. Relativistic prediction Relativistic kinematical correction (calc. by Prof. H. Witala) relativistic energy relativistic NN potential (green line; not fully relativistic) Lorentz boost to 3N c.m. system (red & pink line) Fully relativistic calculations improve the fit to the data only at  cm > 160 deg but improvements are not enough. Relativistic 3NF Dirac eq. Non-Rel. Rel. NN potential Lorentz boosted potential Approx. １ Approx. ２ There still remains 50% discrepancy!.

39. X-sec. ratios at 250 MeV & 95 MeV σ(p+d) /σ(n+d) at 250 MeV σ(d+p)/σ(n+d) at 95 MeV / nucleon Coulomb effects ? (too large !) <4% level by Sauer & Deltuva.

40. o IUCF, PRC35, 37(87)  Sagara, Preliminary — Hanover (virt.  ) Deltuva, PRC67, 034001(03) — Bochum/Cracow (MEC) Skibinski, PRC67, 054001(03) — Bochum/Cracow (Sieg.) Skibinski, PRC67, 054001(03) p+d  3 He+  @ 90 MeV/A No anomaly observed in preliminary KVI data!!  KVI, Preliminary Mehmandoost/van Garderen dddd A y (d)A y (N) A yy A xx

41. present data AV18 AV18+URBIX ● - - - ―

42. A yy present data AV18 AV18+URBIX ● - - - ―

43. A xx present data KVI data AV18 AV18+URBIX ● - - - ―

44. A yy present data KVI data AV18 AV18+URBIX ● - - - ―

45. A xx ~ A yy in pd capture KVI RCNP A ｘｘ AｙｙAｙｙ AｙｙAｙｙ Axx Ayy & Axx measured Only A yy measured