1 Three-nucleon interaction dynamics studied via the deuteron-proton breakup Elżbieta Stephan Institute of Physics, University of Silesia
2 Studies of the 1 H(d,pp)n Breakup at 130 MeV University of Silesia, Katowice, Poland Jagiellonian University, Kraków, Poland KVI, Groningen, The Netherlands Kraków-Bochum Group EFT/ChPT Group Hannover/Lisboa Group Theory Support
3 Motivation Faddeev framework provides exact treatment for the 3N system Various approaches to construct the interaction (2N and 3N): Realistic potentials + phenomenological 3NF models Chiral Perturbation Theory Coupled-Channels formalism with explicit Δ
4 Motivation Three-nucleon system is the simplest non-trivial environment to test predictions of the NN and 3N potential models Elastic scattering data demonstrate both success and problems of modern calculations Very few breakup data at medium energies (earlier PSI experiments provided only 14 kinematical configurations) In order to reach meaningful conclusions about the interaction models needed experimental coverage of large phase space regions
5 Small Area Large Acceptance Detector 140 ΔE-E telescopes 3-plane MWPC Angular range : θ = (12º, 38º), φ = (0º, 360º) SALAD KVI
6 Cross Section Results Summary Nearly 1800 cross section data points θ 1, θ 2 = 15 o 30 o ; grid 5 o ; θ = ±1 o an additional set for θ 1, θ 2 = 13 o φ 12 = 40 o 180 o ; grid 10 o -20 o ; φ = ±5 o S [MeV] = ; grid 4; ΔS = ±2 Statistical accuracy Data very clean accidentals below 2% Systematic errors 3% 5% Global comparisons with theory (χ 2 test for all points, χ 2 = f(φ 12 ), χ 2 = f(e rel ), tests of normalization)
7 Cross Section Results Example Coupled EFT/ChPT Faddeev channels calculations calculations NNLO Realistic 2N NN only potentials: (CD NNLO Bonn, 2N (modif.) NijmI, + 3 N NijmII, + Δ Av18) 3NF model: TM99, UIX
8 Cross Section Results Exploring Phase Space Relative χ 2 as a function of the relative azimuthal angle φ 12 between the two proton trajectories For large E rel 3NF s improve description of the data when combined with the NN potentials In general: Including 3NF s reduces global χ 2 by about 30% [Phys. Rev. C 72 (2005) ]
9 Cross Section Results Discrepancies
10 Cross Section Results Discrepancies Cured Coupled Channel calculations Coupled Channel calculations with Coulomb effects Predictions with Coulomb reproduce data much better!
11 Discrepancies at low E rel cured Coupled Channel calculations
12 Cross Section Results Coulomb Effects Possible sources of differences: Peak magnitude exp. averaging? Total width relativistic effects? Acceptance limit of KVI experiment
13 Coulomb effects dedicated experiment Θ: 3º-14º φ: 2π Small sample result of FZJ experiment (arbitrary normalization)
14 Vector and Tensor Analyzing Powers A few times more additional data points (supplementing cross sections) Potentially stronger sensitivity to small ingredients (sums of interfering amplitudes) Small Coulomb effects - it can be easier to trace 3NF 7 states: Δ P z Δ P zz P max z P max zz P z P zz +1/ / / /
15 Analyzing Power Results Summary Vector (A x, A y ) and tensor analyzing powers (A xx, A yy, A xy ) determined in the large part of the phase space Nearly 800 data points per observable θ 1, θ 2 = 15 o 30 o ; grid 5 o ; Δθ = ±2 o φ 12 = 40 o 180 o ; grid 20 o ; Δφ = ±10 o S [MeV] = ; grid 4; ΔS = ±4 Statistical accuracy Systematic errors analysis under way Global comparisons with theory (χ 2 test) nonnegligible averaging
16 Vector Analyzing Power Results ChPT N2LO
17 Tensor Analyzing Power Results Description not satisfactory!
18 Tensor Analyzing Power Results configurations with predicted strong 3NF effects
19 Tensor Analyzing Power Results NN, ChPT N3LO
20 Conclusions: Systematic, precise set of cross sections and analyzing power data obtained at E d = 130 MeV basis for comparing different approaches which predict the 3N system observables Significant 3NF effects observed in cross section Found large influence of Coulomb force Vector analyzing powers reveal very low sensitivity to 3NF best description given by ChPT (2NLO) will this fact be confirmed by full calculation at 3NLO or at lower energy? Tensor analyzing power sensitive to 3NF, but... current models of 3NF do not provide precise description of A xx and A xy problems with spin part of 3NF?
21 BINA detection system at KVI BINA Detector Phoswich Ball ΔE Wall Stopping (E) Wall MWPC
22 Investigations of 3N/4N continuum Summary Rich set of high precision cross sections and analyzing powers data: Data at E d = 130 MeV supplemented with results for forward proton angles Complete set for E d =100 MeV (BINA) Measurements for pd systems at 180 and 135 MeV (BINA) Developments in theoretical calculations for 3N system (3N force, Coulomb interaction, relativistic effects, higher order in ChPT ) Studies of breakup processes in dd system (BINA) at 130 MeV
23 Thank you for your attention!
24 3 3 ς = ( θ1, θ2, ϕ12, S) σ p ( ς, ϕ1) = σ 0( ς ) 1 + Pz sinϕ1ax + cosϕ1ay Pzz ( sinϕ1 cosϕ1axy ) + Pzz sin ϕ1axx + cos ϕ1ayy a = Pz Ax ( ς ) 2 3 b = Pz Ay ( ς ) 2 c = P A ( ς ) zz xy 1 d = Pzz A 2 1 e = Pzz A 2 xx yy ( ς ) ( ς ) N P N N 0 0 = a sin ϕ b cosϕ1 + c sin ϕ1 cosϕ1 + d sin ϕ1 + e cos θ = 25 1 o θ = 20 ϕ 2 12 o = 120 o S = 96MeV ϕ 1 ϕ 1
25 Tensor Analyzing Power Results examples of A xx, symmetric configurations with ϕ 12 =60 o, 120 o
26 Analyzing Power Results odd observables: A x, A xx, A xy; e.g.: A x ( ϕ12) = Ax ( ϕ12);