1. Rimantas LAZAUSKAS, IPHC Strasbourg, France
Some aspects of two and three nucleon interactions in few-nucleon systems
Rimantas LAZAUSKAS, IPHC Strasbourg, France

2. Few nucleon systems are ideal to test nuclear interaction…
Properties of heavy and medium nuclei vary smoothly
Individuality of single nucleons is lost
Light nuclei keep their pecularities
Nucleons still behave as «individuals»
Diverse nuclear densities
Neutron/proton richest structures
One can still trace NN interaction effects
Can be treated using exact QM formalism

3. Status of exact QM calculations
First principles:
NN interaction
Complete description:
Bound states, scattering, EM reactions
No-adjustments!!
Machinery:
Bound states A12 : Green function Monte-Carlo (GFMC)1, No-core shell model (NCSM)2,…
1 S.C. Pieper, V.R. Pandharipande, R.B. Wiringa and J. Carlson: Phys. Rev. C 64 (2001)
2 P. Navratil, J P. Vary, B. R. Barrett: Phys. Rev. Lett. 84 (2000) 5728.
Scattering A4 !!! Faddeev-Yakubovski eq3, Hyperspherical Harmonics4
3Deltuva et al. Phys.Rev.C76 (2007 ):021001
3,4Lazauskas et al., Phys.Rev. C71 (2005)
restrictive A=5: Resonating group model5, GFMC, NCSM
5Hofmann et al.,Phys.Rev. C64 (2001)

4. ? NN Interaction What to do? Np r N
NN interaction models only effective tools!
Exact description is possible only fully taking into account N structure underlaying theory (QCD) but…
What to do?

5. Kitchen of NN Interaction? p r N
Kitchen of NN Interaction
Analyze nucleon-nucleon scattering data (only pp & np data exist)
Extract S-matrix from experimental cross section (Partial wave analysis), i.e. extract data related with 1-dimensional QM problem
Experiment (3D data)
Data related with 1D Schrodinger eq.
c2/datum
1992 pp database (1787 entries)
1.00
Total pp database (2932 entries)
1.09
Construct potential model reproducing data of Partial wave analysis

6. h ? p r N
NN Interaction
Extreme sports: realistic potentials
=C f(x)
Freestyle: non(semi)-relistic potentials
ann=-18.6 fm
anp=-23.7 fm
app=-17.5 fm
Paris
Nijmegen: Nijm I, Nijm II, Reid
Urbana/Argonne: Av.14, Av18
Bonn: Bonn B, CD Bonn, cPT…
INOY,ISUJ (Doleschall), …
JISP
Manufactures of parameters: fitting experimental NN (n-p and p-p) data. Description with c2data 1.01 ( n~40 free parameters...).
No n-n data! Rely on isospin symmetry…

7. NN Interaction ? Underestimation of 3N energies (~10%)!!! p r h
2N does not contain off energy shell physics  One more fit…3NF?

8. NN interaction ? Question of taste? … Non-localh ? p r N
NN interaction
Underestimation of 3N energies (~10%)!!!
2N does not contain off energy shell physics  One more fit…3NF?  
Question of taste? …
Three-nucleon force vs nonlocal NN interaction:
Non-local

9. NN interaction ? … neither equivalents nor fully complementary
Underestimation of 3N energies (~10%)!!!
2N does not contain off energy shell physics  One more fit…3NF?   …
Three-nucleon force vs nonlocal NN interaction:
neither equivalents nor fully complementary
One has infinite freedom to construct phase-equivalent NN interaction models. These models are related by nonlocal unitary transformations, which gives different off-shell physics
cPT models: 3N & 2N fits are related..

10. NN interaction ? Non-localh ? p r N
NN interaction
Off energy shell structure of NN interaction?
Deuteron 3D1 -state probabilities in (%):
INOY
cPT-N3LO
CD-Bonn
AV18
3.60
2.73…3.63
4.85
5.76
Bd= (1) MeV hd=0.0256(4)
Non-local

11. Can we do anything with these transformations?
System of a few-identical bosons with Gaussian separable potential!
B4/B2
B3/B2
Simple pot. with single
attractive region
More complex pot.
Two body phase-equivalence
up to E~50B2

12. Back to nuclear physics!
B3/B2
B4/B2
J. Kirscher, arXiv:
Something similar?

13. a-particle Can we avoid 3NF? Pure NN models too soft.. INOY04 6Li
rmsp (fm)
INOY04
Exp
6Li
2.29(4)
2.54(3)
7Li
2.20(5)
2.39(3)
8Li
2.16(5)
2.281(3)
9Li
2.07(6)
2.185(3)
11Li
2.06(6)
2.43(3) 3H
4He
rmsp (fm)
B (MeV)
INOY04’
1.57
8.464
1.38
29.09
AV18+UIX
1.59
8.473
1.44
28.50
Exp.
1.60
8.482
1.47
28.30
C. Forssén et al., Phys. Rev. C 79, (2009)

14. a-particle Can we avoid 3NF? 1S0 3S1 3D1 3P0 3P1 3P2 1P1 3H 4He 2H 4He
57.94
47.85
29.24
36.85
12.78
14.83
0.151
0.002
-0.381
-0.213
0.166
0.052
-0.045
-0.021 2H
4He
PD(%)
B (MeV)
INOY04’
3.6
5.95
29.09
AV18+UIX
5.76 16
28.50
Exp. -
28.30

15. Radiative capture Thermal n+3He->4He+g capture process
Ln3He=0; Jn3He=1
E (MeV)
n+3He
0.76 MeV
p+3H
sn3He(mb)
Model
sn3He [mb]
3an3He [fm]
B (4He) [MeV]
Av18
80(12.2) i
24.23
I-N3LO
57.3(7.9) i
25.36
I-N3LO+UIX*
44.4(6.7) i
28.12
Av18+UIX
49.4(8.5) i
28.47
INOY
34.4(4.5) i
29.08
Exp.
55(3); 54(6)
3.28(5)-0.001(2)i
28.3
=c(PD)2/3q
Surprisingly low!

16. Why >3N systems? ? Underestimation of 3N energies (~10%)!!!p r N
Why >3N systems?
Underestimation of 3N energies (~10%)!!!
Only two 3N bound states: 3He & 3H, too little to understad 3NF & off shell energy structure of 2N
Unfortunate 3N scattering
V(3S1) 2H

17. Scattering ? Unfortunate 3N scattering + spin dependent 3NF p r h N
A. Deltuva, private comm.
S. Ishikawa, Phys. Rev. C 75, (R) (2007)

18. Scattering ? Unfortunate 3N scattering V(3S1) 2H p r h N
A. Deltuva, private comm. 2H

19. But scattering wave functions diverge!
What is wrong?
To what the phaseshifts are sensible?
In bound state we calculate mean values:
But scattering wave functions diverge!
Integral representation of phaseshifts: i r
B.S.
Jp E(MeV)
1S0
3S1
3D1
3P0
3P1
3P2
1P1
76.0
22.8
-1.43
-1.30
1.94
-0.81
3.60
79.8
19.7
-1.84
-1.05
1.91
-0.58
3.41
64.2
70.1
-41.9
32.8
-29.7
2.31
-0.38
39.8
54.9
-3.18
1.06
-6.90
14.3
-0.16

20. Smoking gun (Charge dependence)
Binding energies…
C. Pieper et al.: Phys. Rev. C 64 (2001) ; Phys. Rev. Lett. 89 (2002) ; Phys. Rev. C 66 (2002)

21. Conclusions
During the last two decades realistic potentials have made real progress, however have still several open issues:
Problem with negative parity states (P-waves)
Isospin breaking effects?
Short-range tensor force strength
3NF may (at least) solve part of these problems, however it should have quite rich structure.