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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, 2011 1

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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, 2011. Three-body forces and Wikipedia. - PowerPoint PPT Presentation

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Page 1: What have we learned about three-nucleon forces at intermediate energies?

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, 2011

1

Page 2: What have we learned about three-nucleon forces at intermediate energies?
Page 3: What have we learned about three-nucleon forces at intermediate energies?

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 humanbeings and forces with emotions, jealousy is agood example of three-body force: it is not felt as long as only two persons are acting, but it canshow up as soon as a third person enters into the scene. Retrieved from "http://en.wikipedia.org/wiki/Three-body_force"

Page 4: What have we learned about three-nucleon forces at intermediate energies?

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N-N PotentialsModern phenomenological NN

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 …

Page 5: What have we learned about three-nucleon forces at intermediate energies?

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.”

“...the replacement of field interactions by two-body action-at-a-distance potentials is a poor approximation in nuclear problems.”

Page 6: What have we learned about three-nucleon forces at intermediate energies?

6

Triton Binding Energy

Model 2/data 3H B.E. [MeV]

NIJM I 1.03 7.72

NIJM II 1.03 7.62

Reid93 1.03 7.63

Argonne V18 1.09 7.62

Page 7: What have we learned about three-nucleon forces at intermediate energies?

7

Triton Binding Energy

Model 2/data 3H B.E. [MeV]

NIJM I 1.03 7.72

NIJM II 1.03 7.62

Reid93 1.03 7.63

Argonne V18 1.09 7.62

EXPERIMENT - 8.48

Modern N-N potentials fail to describe triton B.E. Modern N-N potentials fail to describe triton B.E.

Page 8: What have we learned about three-nucleon forces at intermediate energies?

8

Beyond phenomenological N-N forces

Phenomenological N-N forces fail to describe A>2 systems! How to resolve?

Phenomenological N-N forces fail to describe A>2 systems! How to resolve?

Three-Nucleon Force!

(3NF)

Three-Nucleon Force!

(3NF)

Page 9: What have we learned about three-nucleon forces at intermediate energies?

(+3NF)

9

Ab-initio calculations for light nucleiC

ourt

esy

S. P

iepe

r, A

rgon

ne

Page 10: What have we learned about three-nucleon forces at intermediate energies?

10

Three-Body Forces in Nuclear Physics

Ggggggg

parametrization of Fuijta-Miyazawa force + 2rescattering + higher-order interactions

Added to 2N potential as correction Tucson-Melbourne, Urbana IX, …

Page 11: What have we learned about three-nucleon forces at intermediate energies?

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

Page 12: What have we learned about three-nucleon forces at intermediate energies?

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 Forcein Nuclear Physics

• Which reactions (and systems) to study?

N + d N + dN + d N + N + NN + d 3He(3H) +

+ 3He(3H) N + d + 3He(3H) N + N + N

N + d N + dN + d N + N + NN + d 3He(3H) +

+ 3He(3H) N + d + 3He(3H) N + N + N

Page 13: What have we learned about three-nucleon forces at intermediate energies?

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

n + d →n + d &

n + d →n + n + p

Page 14: What have we learned about three-nucleon forces at intermediate energies?

15

Nd elastic scattering cross sections

H. Witala et al. PRL 81, 1183 (1998)

Enlab = 12 MeV

Enlab = 65 MeV

Enlab = 140 MeV

Enlab = 200 MeV

3NF only 2NF only

Total

p + d → p + d

Page 15: What have we learned about three-nucleon forces at intermediate energies?

16

The Ay puzzle at low energies

18 MeV

5 MeV 7 MeV 9 MeV

10 MeV 12 MeV 16 MeV

22.7 MeV 28 MeV

2NF

2+3NF

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 16: What have we learned about three-nucleon forces at intermediate energies?

17

The Ay puzzle at low energies

L. E. Marcucci et al., Phys. Rev. C80, 034003(2009)

rp + d → p + d

Page 17: What have we learned about three-nucleon forces at intermediate energies?

18

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 18: What have we learned about three-nucleon forces at intermediate energies?

19

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 19: What have we learned about three-nucleon forces at intermediate energies?

20

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 20: What have we learned about three-nucleon forces at intermediate energies?

21

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 21: What have we learned about three-nucleon forces at intermediate energies?

22

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 22: What have we learned about three-nucleon forces at intermediate energies?

23

pd elastic scattering cross sections

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

p + d → p + d

Page 23: What have we learned about three-nucleon forces at intermediate energies?

24

pd elastic scattering cross sections

(the

ory

–dat

a)/d

ata

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

Page 24: What have we learned about three-nucleon forces at intermediate energies?

25

pd elastic scattering cross sections

(the

ory

–dat

a)/d

ata

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

Page 25: What have we learned about three-nucleon forces at intermediate energies?

26

pd elastic scattering cross sections

Hanover Approach of dynamical delta

(the

ory

–dat

a)/d

ata

K. Ermisch et al.,

PRC 68, 054004 (2003),

PRC 71, 064004 (2005)

Page 26: What have we learned about three-nucleon forces at intermediate energies?

27

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 27: What have we learned about three-nucleon forces at intermediate energies?

28

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 28: What have we learned about three-nucleon forces at intermediate energies?

29

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 29: What have we learned about three-nucleon forces at intermediate energies?

30

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 30: What have we learned about three-nucleon forces at intermediate energies?

31

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 31: What have we learned about three-nucleon forces at intermediate energies?

32

p+d vector analyzing powers

Bieber et al.,

PRL84, 606 (2000)

Ermisch et al.,

PRL86, 5862 (2001)

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 32: What have we learned about three-nucleon forces at intermediate energies?

33

p+d vector analyzing powers

theo

ry-d

ata

Ermisch et al.,

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 33: What have we learned about three-nucleon forces at intermediate energies?

34

p+d vector analyzing powers

theo

ry-d

ata

Ermisch et al.,

PRC71, 064004 (2005)

rp + d → p + d

σ =σ0(1+ pAy cosϕ )

⇒ Ay =σ L −σ R

σ L +σ R

Page 34: What have we learned about three-nucleon forces at intermediate energies?

35

p+d vector analyzing powers

theo

ry-d

ata

Hanover Approach of dynamical delta

Ermisch et al.,

PRC71, 064004 (2005)

rp + d → p + d

Page 35: What have we learned about three-nucleon forces at intermediate energies?

36

Effect of 3NF as a function of Energy

rp + d → p + d

Page 36: What have we learned about three-nucleon forces at intermediate energies?

37

Effect of 3NF as a function of Energy

cm=140º

PRC 78 (2008) 014006

(CDB+C+Δ)

(CDB+C)

rp + d → p + d

Phys. Rev. C78, 014006 (2008)

Page 37: What have we learned about three-nucleon forces at intermediate energies?

38

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 38: What have we learned about three-nucleon forces at intermediate energies?

39

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 39: What have we learned about three-nucleon forces at intermediate energies?

40

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 40: What have we learned about three-nucleon forces at intermediate energies?

41

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 41: What have we learned about three-nucleon forces at intermediate energies?

42

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 42: What have we learned about three-nucleon forces at intermediate energies?

43

Spin-Transfer Coefficients

Hanover Approach of dynamical delta

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 43: What have we learned about three-nucleon forces at intermediate energies?

44

Spin-Transfer Coefficients

rd + p →

r p + d@180MeV

σ =σ0(1+3

2pz Ay +

1

2pzz Ayy )

pyσ = σ 0(Py' +3

2pzKy

y ' +1

2pzzKyy

y ')

Phys. Rev. C75, 041001 (R) (2007)

Page 44: What have we learned about three-nucleon forces at intermediate energies?

45

5 dimensional phase space (1, 2, E1, E2, 12) i.e. much larger than in the elastic channel ()5 dimensional phase space (1, 2, E1, E2, 12) i.e. much larger than in the elastic channel ()

Allows detailed road-map for the study of nuclear forcesAllows detailed road-map for the study of nuclear forces

Requires a setup with large coverageRequires a setup with large coverage

Break-up channelBreak-up channel

rp + d → p + p + n

Page 45: What have we learned about three-nucleon forces at intermediate energies?

46

The break-up channel

σ2NF+3NF – σ2NF

σ2NF+3NF σ=

Bochum-Cracow Group(2NF=CDB, 3NF=TM’)

p + d → p + p + n

Page 46: What have we learned about three-nucleon forces at intermediate energies?

47

The new Polarimeter and the 4 detector

Page 47: What have we learned about three-nucleon forces at intermediate energies?

48

Break-up and the kinematical variable S

rp + d → p + p + n

Page 48: What have we learned about three-nucleon forces at intermediate energies?

p + d → p + p + nBreak-up channel at 130 MeV

S (MeV)

Kistryn et al.,PLB 641, 23 (2006)

Page 49: What have we learned about three-nucleon forces at intermediate energies?

50

Cross sections for break-up channel for Ep=135 MeV

Relativisticeffects !

M. Eslami-Kalantari, et al.

rp + d → p + p + n

Page 50: What have we learned about three-nucleon forces at intermediate energies?

51

Analyzing power for break-up channel for Ep=135 MeV

M. Eslami-Kalantari, et al.

rp + d → p + p + n

Page 51: What have we learned about three-nucleon forces at intermediate energies?

52

Ep = 190 MeV

θ = 14º - 30º

θ1=θ2, small φ12

Epp < 1 MeV(pp) ≈ 2He

I = 1/2, 3/2 I = 1/2

H. Mardanpour et al.,Phys. Lett. B687, 149 (2010)

Analyzing power for break-up channel for Ep=190 MeV

rp + d → p + p + n

2H(r p ,2 He)n

2H(r p ,2 H) p

Page 52: What have we learned about three-nucleon forces at intermediate energies?

53

Global Analysis, Elastic channel, 50-250 MeV/nucleon

Page 53: What have we learned about three-nucleon forces at intermediate energies?

54

Global Analysis, Elastic channel, 50-250 MeV/nucleon

rp + d → p + d

Reports on Progress in

Physics,in

preparatoin

Page 54: What have we learned about three-nucleon forces at intermediate energies?

55

Global Analysis, Elastic channel, 50-250 MeV/nucleon

rp + d → p + d

Reports on Progress in

Physics,in

preparatoin

Page 55: What have we learned about three-nucleon forces at intermediate energies?

56

Global Analysis, Elastic channel, 50-250 MeV/nucleon

rp + d → p + d

Reports on Progress in

Physics,in

preparatoin

Page 56: What have we learned about three-nucleon forces at intermediate energies?

57

Global Analysis, Breakup Channel, 65-190 MeV/nucl.

rp + d → p + p + n

Reports on Progress in

Physics,in

preparatoin

Page 57: What have we learned about three-nucleon forces at intermediate energies?

58

Global Analysis, Breakup Channel, 65-190 MeV/nucl.

rp + d → p + p + n

Reports on Progress in

Physics,in

preparatoin

Page 58: What have we learned about three-nucleon forces at intermediate energies?

59

Limitations of effective field theories

rp + d → p + d

Page 59: What have we learned about three-nucleon forces at intermediate energies?

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)

Page 60: What have we learned about three-nucleon forces at intermediate energies?

61

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

rp + He → p + He

Page 61: What have we learned about three-nucleon forces at intermediate energies?

62

How about four-body systems?

θd=25º, θp=20º

Ed = 130 MeV

θ = 15º - 30º, Ф12 = 140º - 180º

A. Ramazani-Moghaddam-Arani et al.,PRC 83, 024002 (2011)

Three-body break-up channel

Elastic dd

Page 62: What have we learned about three-nucleon forces at intermediate energies?

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.

Page 63: What have we learned about three-nucleon forces at intermediate energies?

64

AcknowledgementsH.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

Page 64: What have we learned about three-nucleon forces at intermediate energies?

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!

Page 65: What have we learned about three-nucleon forces at intermediate energies?

66

Spin-transfer Coefficients

Kyx’x’ - Ky

y’y’

Kxx’y’ Kz

x’y’

Kxy’z’

Kzy’z’ Ky

z’z’

Elab =

10 MeV

Elab =

10 MeV

Elab =

22.7 MeV

Kzx’(d)

Kzx’(d)

Kyy’(d)

Kyy’(d)

Kxx’(d)

Kxx’(d)

Page 66: What have we learned about three-nucleon forces at intermediate energies?

67

Spin-Transfer Coefficients

Page 67: What have we learned about three-nucleon forces at intermediate energies?

68

More Analyzing powers (from RIKEN)K. Sekiguchi et al., PRC, 65, 034003 (2002)

Page 68: What have we learned about three-nucleon forces at intermediate energies?

69

The break-up channel

p + d → p + p + n

Page 69: What have we learned about three-nucleon forces at intermediate energies?

70

The break-up channel

p + d → p + p + n

Page 70: What have we learned about three-nucleon forces at intermediate energies?

71

The break-up channel

p + d → p + p + n

Page 71: What have we learned about three-nucleon forces at intermediate energies?

72

Nucleon-deuteron Radiative CaptureNucleon-deuteron Radiative Capture

Why study Nd radiative capture?Why study Nd radiative capture?

1) Initial (pd) and final state (3He) show 3NF effects-> radiative capture should also!

2) High-momentum component of 3He w.f.3)3) Sensitive to electro-magnetic Sensitive to electro-magnetic

currents!currents!

Page 72: What have we learned about three-nucleon forces at intermediate energies?

73Study 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+d3He+ @ 100 MeV/nucleon

Ay(d) Ay(N)

Ayy Axx

Page 73: What have we learned about three-nucleon forces at intermediate energies?

74

o IUCF, PRC35, 37(87)

RCNP (Preliminary)

Ay(d) Ay(N)

Ayy Axx

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 capturep+d3He+ @ 100

MeV/nucleon

Page 74: What have we learned about three-nucleon forces at intermediate energies?

75

Vector and tensor analyzing powersin d+p->3He+ @ KVI

Calc. Hanover group

Data:A. Mehmandoost nucl-ex/0501012; PLB 617, 18 (2005)

Page 75: What have we learned about three-nucleon forces at intermediate energies?

76

pd radiative capture anomaly

KVI and (preliminary) RCNP data are inconsistent!

KVI and (preliminary) RCNP data are inconsistent!