Nuclear Structure and Dynamics in the 3 He(e,e’p)d and 3 He(e,e’p)pn Reactions

1. Nuclear Structure and Dynamics in the 3He(e,e’p)d and 3He(e,e’p)pn Reactions JLAB Hall A Two high resolution spectrometers (p/p  10-4); δΩ= 6 msr High current, high polarization (80-85%) cw beam High pressure 3He target - luminosity ≈ 1038 cm2 sec-1 Focal-plane hadron polarimeter Shalev Gilad - MIT

2. Inclusive electron scattering (e,e’) Can vary independently the transferred energy and momentum xB = Q2/2m Shalev Gilad - MIT

3. A(e,e’p)B ,  Em =  - Tp - TB B = A-1 (bound), A-2 + N, other Shalev Gilad - MIT

4. Plane-Wave Impulse Approximation (PWIA) Not an observable!! Shalev Gilad - MIT

5. Final-state interactions • Calculate FSI in terms of: • Optical potential • Glauber (or Eikonal) approximation Shalev Gilad - MIT

6. A(e,e’p) x-section in term of responses i= viRi Shalev Gilad - MIT

7. Kinematics of Measurements • Quasi-elastic: xB~1 • Fixed electron kinematics: • q=1.5 GeV/c • ω=0.837 GeV • 3 virtual photon polarizations: • 0.108‹ε‹0.943 • “Perpendicular” proton kinematics • High energy of ejected proton: • Tp›0.8 GeV • Parallel kinematics – in analysis Shalev Gilad - MIT

8. 2bbu x-sections; distorted S(pm) M. M. Rvachev et al., PRL 94, 192302 (2005) Shalev Gilad - MIT

9. Comparison to previous data Florizone: “Parallel” kinematics xB≈ 1 Kozlov: “Parallel” kinematics xB> 1 Shalev Gilad - MIT

10. Models Laget: • Gswf generated from solution to Faddeev eqn. with Paris NN potential • (also variational calculations using AV18+UIX) • Kinematics, nucleon & meson propagators are relativistic; un-factorized; Mott+FF • One-, two- & 3-body interactions • FSI globally parameterized from LANL, SATURN &COSY data • No angular restriction (Glauber type) imposed on loop integrals • 2bbu: pm, ATL; 3bbu: pm,Em(pm) 3-Body graphs • Ciofi degli Atti: More recent results next talk by Morita! • PWIA+FSI; factorized; CC1 • Gswf generated from AV18 • Kinematics is relativistic • FSI using generalized Eikonal approximation (“frozen”, only  mom. Trans.) • Single-, double re-scattering • 2bbu: pm; 3bbu: Em(pm) Shalev Gilad - MIT

11. Models (cont.) • Schiavilla: • Variational GSWF generated using AV18+UIX Hamiltonian using Correlated hyperspherical harmonics (CHH); un-factorized • Relativistic one and two-body current operator (Jeschonnek & Donnely) • FSI using Glauber approx. retaining spin & isospin dependencies • Single + double re-scattering • 2bbu: pm, ATL; 3bbu: in near future • Udias: • GSWF generated by Faddeev technique using AV8+central NNN (Gaussian or exponential, adjusted for binding energy); un-factorized; CC2 • Fully relativistic kinematics and dynamics (RDWIA) • FSI using optical potential generated by relativistic folding model – fold effective £ with residual nuclei. Parameters of effective £ reproduce elastic p-d & p-He scattering data • 2bbu: pm, ATL Shalev Gilad - MIT

12. 3 regions in pm Shalev Gilad - MIT

13. X-sections for -150 < pm < 150 MeV/c Laget Schiavilla • NNN forces important at very low pm (~25%) • FSI starts to break factorization around |pm| > 100-150 MeV/c Shalev Gilad - MIT

14. 150 < pm < 700 MeV/c Shalev Gilad - MIT

15. Affect of different NN potentials R. Schiavilla et al., nucl-th/0508048 Shalev Gilad - MIT

16. Pm > 600 MeV/c Laget: 3-body diagram(s) Ciofi: double scattering Schiavilla: double scattering Non-hadronic? “Exotic”? Shalev Gilad - MIT

17. ATL No structure in PWIA - factorized Factorization broken by FSI No ATL from Ciofi – factorized calculations Shalev Gilad - MIT

18. 3He(e,e’p)pn – 3bbu For 2-body kinematics with a spectator A-2 - a relationship between Em and pm Low pm(still > kf): correlations? Em - Eth (MeV) F. Benmokhtar et al., PRL 94, 082305 (2005) Shalev Gilad - MIT

19. 3bbu – high pm High pm: dominated by FSI Note: similarly good calculations by Ciofi Em – Eth (MeV) Shalev Gilad - MIT

20. 2bbu, 3bbu “distorted” spectral functions High Q2; xB ≈ 1  Reduced MEC, Δ contributions At pm > pF spectral function is much larger for 3bbu than for 2bbu due to correlations (SRC) Calculations reproduce both 2bbu and 3bbu - confidence Awaiting calculations by Schiavilla Shalev Gilad - MIT

21. Summary, conclusions, and outlook • Extensive and precise data set for 3He(e,e’p)d and 3He(e,e’p)pn -750 > pm > 1000 MeV/c x-section over 6 decades many kinematics many observables (x-sections ATL, RL, RT) This is the only way to test ingredients of theory in details!!!! • Data illuminates details of 3He gswf (NN, NNN potentials, correlations) and reaction dynamics although much of the x-sections is dominated by FSI • All models reproduce data reasonably well; some better than others Ciofi - (factorized) did not yet produce ATL.Coming soon!! Laget - problems with GSWF, diagramatic approach not transparent Schiavilla – most sound and sophisticated; does best job for 3He(e,e’p)d. 3He(e,e’p)pn by fall? Udias – does surprisingly well using RDWIA – o. p. for FSI in 3He(e,e’p)d Shalev Gilad - MIT

22. Summary, conclusions and outlook (cont.) • Must Test models with other reactions, kinematics, and on deuteron (measured), 4He (measured, more comprehensive experiment approved for Hall A) Ciofi – does ok with 2bbu, 3bbu, d, 3He(e,e’pp)n, 4He Laget – does reasonably well with 2bbu, 3bbu, 3He(e,e’pN)N, d Schiavilla – working on 3He(e,e’p)pn, 4He(e,e’p)3H, ingredients tested on d Udias – has predictions for 4He(e,e’p)3H • Are we close to having a good model for understanding few-nucleons dynamics? M. M. Rvachev et al., PRL 94, 192302 (2005) F. Benmokhtar et al., PRL 94, 082305 (2005) J. M. Laget, Phys. Lett. B609, 49 (2005) J. M. Laget, Phys. Rev. C72, 024001 (2005) C. Ciofi degli Atti and L. P. Kaptari, PRL 95, 052502 (2005) C. Ciofi degli Atti and L. P. Kaptari, Phys. Rev. C71, 024005 (2005) R. Schiavilla et al., Phys. Rev. C72, 064003 (2005) J. M. Udias, private communications Shalev Gilad - MIT