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

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

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) 014001. 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) 034004 restrictive A=5: Resonating group model5, GFMC, NCSM 5Hofmann et al.,Phys.Rev. C64 (2001) 044003

? NN Interaction What to do? N p 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?

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

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…

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

NN interaction ? Question of taste? … Non-local h ? 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

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..

NN interaction ? Non-local h ? 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=-2.2245(1) MeV hd=0.0256(4) Non-local

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

Back to nuclear physics! B3/B2 B4/B2 J. Kirscher, arXiv:0903.5538 Something similar?

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, 021303 (2009)

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

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) 3.43-0.0082i 24.23 I-N3LO 57.3(7.9) 3.56-0.007i 25.36 I-N3LO+UIX* 44.4(6.7) 3.44-0.0055i 28.12 Av18+UIX 49.4(8.5) 3.23-0.0054i 28.47 INOY 34.4(4.5) 3.26-0.0058i 29.08 Exp. 55(3); 54(6) 3.28(5)-0.001(2)i 28.3 =c(PD)2/3q-5 +0.42 Surprisingly low!

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

Scattering ? Unfortunate 3N scattering + spin dependent 3NF p r h N A. Deltuva, private comm. S. Ishikawa, Phys. Rev. C 75, 061002(R) (2007)

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

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 0+ 0.0 76.0 22.8 -1.43 -1.30 1.94 -0.81 3.60 0+ 3.0 79.8 19.7 -1.84 -1.05 1.91 -0.58 3.41 0- 3.0 64.2 70.1 -41.9 32.8 -29.7 2.31 -0.38 2- 3.0 39.8 54.9 -3.18 1.06 -6.90 14.3 -0.16

Smoking gun (Charge dependence) Binding energies… C. Pieper et al.: Phys. Rev. C 64 (2001) 014001; Phys. Rev. Lett. 89 (2002) 182501; Phys. Rev. C 66 (2002) 044310

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.