What have we learned about three-nucleon forces at intermediate energies?
description
Transcript of 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
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"
4
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 …
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.”
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
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.
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)
(+3NF)
9
Ab-initio calculations for light nucleiC
ourt
esy
S. P
iepe
r, A
rgon
ne
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, …
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 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
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
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
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
17
The Ay puzzle at low energies
L. E. Marcucci et al., Phys. Rev. C80, 034003(2009)
€
rp + d → p + d
18
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
19
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
20
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
21
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
22
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
23
pd elastic scattering cross sections
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
€
p + d → p + d
24
pd elastic scattering cross sections
(the
ory
–dat
a)/d
ata
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
25
pd elastic scattering cross sections
(the
ory
–dat
a)/d
ata
K. Ermisch et al.,
PRC 68, 054004 (2003),
PRC 71, 064004 (2005)
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)
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
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
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
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
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
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
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
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
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
36
Effect of 3NF as a function of Energy
€
rp + d → p + d
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)
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)
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)
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)
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)
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)
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)
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)
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
46
The break-up channel
σ2NF+3NF – σ2NF
σ2NF+3NF σ=
Bochum-Cracow Group(2NF=CDB, 3NF=TM’)
€
p + d → p + p + n
47
The new Polarimeter and the 4 detector
48
Break-up and the kinematical variable S
€
rp + d → p + p + n
€
p + d → p + p + nBreak-up channel at 130 MeV
S (MeV)
Kistryn et al.,PLB 641, 23 (2006)
50
Cross sections for break-up channel for Ep=135 MeV
Relativisticeffects !
M. Eslami-Kalantari, et al.
€
rp + d → p + p + n
51
Analyzing power for break-up channel for Ep=135 MeV
M. Eslami-Kalantari, et al.
€
rp + d → p + p + n
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
53
Global Analysis, Elastic channel, 50-250 MeV/nucleon
54
Global Analysis, Elastic channel, 50-250 MeV/nucleon
€
rp + d → p + d
Reports on Progress in
Physics,in
preparatoin
55
Global Analysis, Elastic channel, 50-250 MeV/nucleon
€
rp + d → p + d
Reports on Progress in
Physics,in
preparatoin
56
Global Analysis, Elastic channel, 50-250 MeV/nucleon
€
rp + d → p + d
Reports on Progress in
Physics,in
preparatoin
57
Global Analysis, Breakup Channel, 65-190 MeV/nucl.
€
rp + d → p + p + n
Reports on Progress in
Physics,in
preparatoin
58
Global Analysis, Breakup Channel, 65-190 MeV/nucl.
€
rp + d → p + p + n
Reports on Progress in
Physics,in
preparatoin
59
Limitations of effective field theories
€
rp + d → p + d
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
€
rp + He → p + He
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
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
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
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
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)
67
Spin-Transfer Coefficients
68
More Analyzing powers (from RIKEN)K. Sekiguchi et al., PRC, 65, 034003 (2002)
69
The break-up channel
€
p + d → p + p + n
70
The break-up channel
€
p + d → p + p + n
71
The break-up channel
€
p + d → p + p + n
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!
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
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
75
Vector and tensor analyzing powersin d+p->3He+ @ KVI
Calc. Hanover group
Data:A. Mehmandoost nucl-ex/0501012; PLB 617, 18 (2005)
76
pd radiative capture anomaly
KVI and (preliminary) RCNP data are inconsistent!
KVI and (preliminary) RCNP data are inconsistent!