What have we learned about three-nucleon forces at intermediate energies? Nasser Kalantar-Nayestanaki Kernfysisch Versneller Instituut, RuG Strong interactions: From methods to structures February 14,

3 A three-body force is a force that does not exist in a system of two objects but appears in a system of three objects (three-body system like in Euler's three-body problem) or more. In physics, an intuitive example of a three-body force is the case of charged, metallic spheres: the charge distribution at the surface of two spheres placed close to each other will be modified, and thus the total force felt by a third sphere cannot be described by the sum of the forces from the two other spheres taken individually. The fundamental strong interaction seems to exhibits such behaviours. In particle physics, the interactions between the three quarks that compose baryons can be described in a diquark model which is equivalent to the hypothesis of a three-body force. There is growing evidence in the field of nuclear physics that three-body forces exist among the nucleons inside atomic nuclei (three-nucleon force). Three-body forces and Wikipedia As an analogy, if we identify bodies with human beings and forces with emotions, jealousy is a good example of three-body force: it is not felt as long as only two persons are acting, but it can show up as soon as a third person enters into the scene. Retrieved from "

4 N-N Potentials Modern phenomenological NN potentials: Comparison with experimental np&pp database gives:  2 /data ~ 1 Comparison with experimental np&pp database gives:  2 /data ~ 1  Nijmegen I  Nijmegen II  Reid 93  CD-Bonn  Argonne V18  …  Nijmegen I  Nijmegen II  Reid 93  CD-Bonn  Argonne V18  …

5 Three-Body Forces in Nuclear Physics “...the replacement of field interactions by two- body action-at-a-distance potentials is a poor approximation in nuclear problems.”

6 Triton Binding Energy Model  2 /data 3 H B.E. [MeV] NIJM I NIJM II Reid Argonne V

7 Triton Binding Energy Model  2 /data 3 H B.E. [MeV] NIJM I NIJM II Reid Argonne V EXPERIMENT-8.48 Modern N-N potentials fail to describe triton B.E.

8 Beyond phenomenological N-N forces Phenomenological N-N forces fail to describe A>2 systems! How to resolve? Three-Nucleon Force! (3NF) Three-Nucleon Force! (3NF)

(+3NF) 9 Ab-initio calculations for light nuclei Courtesy S. Pieper, Argonne

10 Three-Body Forces in Nuclear Physics Ggggggg      parametrization of Fuijta-Miyazawa force + 2  rescattering + higher-order interactions  Added to 2N potential as correction  Tucson-Melbourne, Urbana IX, …

11 Effective-Field Theory Approach  Developed by Weinberg  Coupling of pions and nucleons in EFT  Predicts structure of 3NF  Self-consistent approach  Only works at energies below pion-mass scale

12 - Electromagnetic interaction on 3B systems - 3B (and more bodies?) Bound states - 3B Elastic scattering in large parts of phase space - 3B Break-up reaction in different kinematics - Many-body systems  Nuclear matter Study of Three-Body Force in Nuclear Physics Which reactions (and systems) to study? N + d  N + d N + d  N + N + N N + d  3 He( 3 H) +     + 3 He( 3 H)  N + d   + 3 He( 3 H)  N + N + N N + d  N + d N + d  N + N + N N + d  3 He( 3 H) +     + 3 He( 3 H)  N + d   + 3 He( 3 H)  N + N + N

13 Binding Energies in 3 H & 4 He

14 Total nd Cross sections High precision data from Los Alamos W.P. Abfalterer et al., PRL 81, 57 (1998) nd scattering np scattering Only 2NF  Effect of 3NF small  High-precision mandatory  In addition, look for sensitivity: exclusive channels other observables  Effect of 3NF small  High-precision mandatory  In addition, look for sensitivity: exclusive channels other observables

15 Nd elastic scattering cross sections H. Witala et al. PRL 81, 1183 (1998) E n lab = 12 MeV E n lab = 65 MeV E n lab = 140 MeV E n lab = 200 MeV 3NF only 2NF only Total

16 The A y puzzle at low energies 18 MeV 5 MeV7 MeV9 MeV 10 MeV12 MeV16 MeV 22.7 MeV28 MeV 2NF 2+3NF

17 The A y puzzle at low energies L. E. Marcucci et al., Phys. Rev. C80, (2009)

18 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

19 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

20 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

21 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

22 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

23 pd elastic scattering cross sections K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

24 pd elastic scattering cross sections (theory –data)/data K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

25 pd elastic scattering cross sections (theory –data)/data K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

26 pd elastic scattering cross sections Hanover Approach of dynamical delta (theory –data)/data K. Ermisch et al., PRC 68, (2003), PRC 71, (2005)

27 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

28 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

29 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

30 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

31 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

32 p+d vector analyzing powers Bieber et al., PRL84, 606 (2000) Ermisch et al., PRL86, 5862 (2001) PRC71, (2005)

33 p+d vector analyzing powers theory-data Ermisch et al., PRC71, (2005)

34 p+d vector analyzing powers theory-data Ermisch et al., PRC71, (2005)

35 p+d vector analyzing powers theory-data Hanover Approach of dynamical delta Ermisch et al., PRC71, (2005)

36 Effect of 3NF as a function of Energy

37 Effect of 3NF as a function of Energy  cm =140º PRC 78 (2008) (CDB+C+Δ) (CDB+C) Phys. Rev. C78, (2008)

38 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

39 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

40 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

41 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

42 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

43 Spin-Transfer Coefficients Hanover Approach of dynamical delta Phys. Rev. C75, (R) (2007)

44 Spin-Transfer Coefficients Phys. Rev. C75, (R) (2007)

45 5 dimensional phase space (  1,  2, E 1, E 2,  12 ) i.e. much larger than in the elastic channel (  ) 5 dimensional phase space (  1,  2, E 1, E 2,  12 ) i.e. much larger than in the elastic channel (  ) Allows detailed road-map for the study of nuclear forces Allows detailed road-map for the study of nuclear forces Requires a setup with large coverage Break-up channel

46 The break-up channel  2NF+3NF –  2NF  2NF+3NF  Bochum-Cracow Group (2NF=CDB, 3NF=TM’)

47 The new Polarimeter and the 4  detector

48 Break-up and the kinematical variable S

Break-up channel at 130 MeV S (MeV) Kistryn et al., PLB 641, 23 (2006)

50 Cross sections for break-up channel for E p =135 MeV Relativistic effects ! M. Eslami-Kalantari, et al.

51 Analyzing power for break-up channel for E p =135 MeV M. Eslami-Kalantari, et al.

52 E p = 190 MeV θ = 14º - 30º θ 1 =θ 2, small φ 12 E pp < 1 MeV (pp) ≈ 2 He I = 1/2, 3/2I = 1/2 H. Mardanpour et al., Phys. Lett. B687, 149 (2010) Analyzing power for break-up channel for E p =190 MeV

53 Global Analysis, Elastic channel, MeV/nucleon

54 Global Analysis, Elastic channel, MeV/nucleon Reports on Progress in Physics, in preparatoin

55 Global Analysis, Elastic channel, MeV/nucleon Reports on Progress in Physics, in preparatoin

56 Global Analysis, Elastic channel, MeV/nucleon Reports on Progress in Physics, in preparatoin

57 Global Analysis, Breakup Channel, MeV/nucl. Reports on Progress in Physics, in preparatoin

58 Global Analysis, Breakup Channel, MeV/nucl. Reports on Progress in Physics, in preparatoin

59 Limitations of effective field theories

60 Overview world database elastic & breakup  rich set of observables, allowing a multi-dim. study of 3NF  a sizable fraction has been measured accurately and systematically (RIKEN/RCNP/IUCF/KVI,Jülich)  rich set of observables, allowing a multi-dim. study of 3NF  a sizable fraction has been measured accurately and systematically (RIKEN/RCNP/IUCF/KVI,Jülich)

61 How about four-body systems? Kievsky et al., private communication

62 How about four-body systems? θ d =25º, θ p =20º E d = 130 MeV θ = 15º - 30º, Ф 12 = 140º - 180º A. Ramazani-Moghaddam-Arani et al., PRC 83, (2011) Three-body break-up channel Elastic dd

63 Summary Three-body hadronic reactions are the most promising tool for the study of 3BF effects. A large body of data has been gathered for cross sections and spin observables for elastic and break-up reactions at intermediate energies at KVI, RIKEN, RCNP, IUCF and Jülich. The Coulomb effect is now well under control. All data together show unambiguously the effect of 3NF. There are, however, still discrepancies indicating that the exact nature of 3NF is not yet known. Relativisitc corrections are now underway but expected to be small. Four-body systems underway both exp. and theoretically.

64 Acknowledgements H.R. Amir Ahmadi, A.M. van den Berg, R. Bieber, K. Ermisch, M. Elsami-Kalantari, M.N. Harakeh, H. Huisman, M. Kis, H. Mardanpour, A. Mehmandoost, J.G. Messchendorp, M. Mahjour-Shafiei, A. Ramazani, E. Van Garderen, M. Volkerts, S.Y. van der Werf, H. Woertche + Cracow Experimental Group (O. Biegun, K. Bodek, St. Kistryn, A. Micherdzinska, E. Stephan, J. Zejma and W. Zipper) + Theoretical support from Bochum-Cracow (Gloeckle, Golak, Kamada, Kuros-Zolnierczuk, Skibinski and Witala) Hanover-Lisbonne (Sauer, Deltuva and Fonseca) Epelbaum, Nogga

65 Overview world database pd->pd  rich set of spin observables, allowing a multi-dim. study of 3NF  a sizable fraction has been measured accurately and systematically (RIKEN/RCNP/IUCF/KVI)  still much to explore!  rich set of spin observables, allowing a multi-dim. study of 3NF  a sizable fraction has been measured accurately and systematically (RIKEN/RCNP/IUCF/KVI)  still much to explore!

66 Spin-transfer Coefficients K y x’x’ - K y y’y’ K x x’y’ K z x’y’ K x y’z’ K z y’z’ K y z’z’ E lab =10 MeV E lab =22.7 MeV K z x’ (d) K y y’ (d) K x x’ (d)

67 Spin-Transfer Coefficients

68 More Analyzing powers (from RIKEN) K. Sekiguchi et al., PRC, 65, (2002)

69 The break-up channel

70 The break-up channel

71 The break-up channel

72 Nucleon-deuteron Radiative Capture Why study Nd radiative capture? 1)Initial (pd) and final state ( 3 He) show 3NF effects-> radiative capture should also! 2)High-momentum component of 3 He w.f. 3)Sensitive to electro-magnetic currents!

73 Study of three-body systems at KVI “Tensor anomaly” in pd-radiative capture o IUCF, PRC35, 37(87)  RCNP (Preliminary) Bochum-Cracow  Faddeev calculation  Potentials: AV18 (NN) +UIX (3NF)  E.M. current operator: non-rel single nucleon + many-body currents in  and  exchange (explicit) p+d  3 He+ 100 MeV/nucleon A y (d)A y (N) A yy A xx

74 o IUCF, PRC35, 37(87)  RCNP (Preliminary) A y (d)A y (N) A yy A xx Hanover  Coupled channel  Potentials: CD Bonn+ (NN) +virtual   E.M. current operator: Siegert form of the current operator + expl. MEC contrs. not accounted for by SGE “Tensor Anomaly” “Tensor anomaly” in pd-radiative capture p+d  3 He+ 100 MeV/nucleon

75 Vector and tensor analyzing powers in d+p-> 3 He+ KVI Calc. Hanover group Data: A. Mehmandoost nucl-ex/ ; PLB 617, 18 (2005)

76 pd radiative capture anomaly KVI and (preliminary) RCNP data are inconsistent!