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Nuclear Structure and Dynamics in the 3He(e,e’p)d and 3He(e,e’p)pn
Reactions
Two high resolution spectrometers (Two high resolution spectrometers (p/p p/p 10 10-4-4); ); δΩδΩ = 6 msr= 6 msr High current, high polarization (High current, high polarization (80%) cw beam80%) cw beamHigh pressure High pressure 33He target - luminosity ≈ 10He target - luminosity ≈ 103838 cm cm22 sec sec-1-1
Focal-plane hadron polarimeterFocal-plane hadron polarimeter
JLAB Hall A
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A(e,e’p)
i = viRi
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Kinematics of Measurements
•Fixed electron kinematics:
q=1.5 GeV/cω=0.837 GeVquasi-elastic: xB~1
•“Perpendicular” proton kinematics
•High energy of ejected proton:
Tp›0.8 GeV
•3 virtual photon polarizations:
0.108‹ε‹0.943
•Parallel kinematics – poster, Eric Voutier
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2bbu x-sections; distorted S(pm)
M. M. Rvachev et al., PRL 94, 192302 (2005)
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Comparison to previous data
Florizone:“Parallel” kinematicsxB≈ 1
Kozlov:“Parallel” kinematicsxB > 1
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ModelsLaget: 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)
Ciofi degli Atti: PWIA+FSI; factorized; CC1Gswf generated from AV18Kinematics is relativisticFSI using generalized Eikonal approximation (“frozen”, only mom. Trans.)Single-, double re-scattering2bbu: pm; 3bbu: Em(pm)
3-Body graphs
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Models (cont.)
Schiavilla: Variational GSWF generated using AV18+UIX Hamiltonian using
Correlated hyperspherical harmonics (CHH); un-factorizedRelativistic one and two-body current operator (Jeschonnek &
Donnely)FSI using Glauber approx. retaining spin & isospin dependenciesSingle-double re-scattering2bbu: 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 dynamicsFSI 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
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3 regions in pm
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X-sections for -150 < pm < 150 MeV/c
NNN forces important at very low pm (~25%)
FSI starts to break factorization around |pm| > 150 MeV/c
Laget Schiavilla
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150 < pm < 700 MeV/c
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Affect of different NN potentials
R. Schiavilla et al., nucl-th/0508048
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Pm > 600 MeV/c
Laget: 3-body diagram(s) Ciofi: double scattering Schiavilla: double scattering Non-hadronic? “Exotic”?
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ATL
No structure in PWIA -factorized
Factorization broken by FSI
No ATL from Ciofi – factorized calculations
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3He(e,e’p)pn – 3bbu
Em - Eth (MeV)
For 2-body kinematics with a spectator A-2 – relationship between Em and pm
Low pm: correlations?
F. Benmokhtar et al., PRL 94, 082305 (2005)
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3bbu – high pm
Em – Eth (MeV)
High pm: dominated by FSI
Note: similarly good calculations by Ciofi
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2bbu, 3bbu “distorted” spectral functions
meppepe
6
m dE)K/dddEdE
d()p(
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
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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/cx-section over 6 decadesmany kinematicsmany 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 x-sections dominated by FSI
All models reproduce data reasonably well; some better than others
Ciofi - (factorized) has problems with ATL
Laget - problems with GSWF, diagramatic approach not transparent
Schiavilla – most sound and sophisticated; does best job for 3He(e,e’p)d
Udias – does surprisingly well using RDWIA – o. p. for FSI in 3He(e,e’p)d
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Summary, conclusions and outlook (cont.)
Must Test models with other reactions, kinematics, and on deuteron (measured), 4He (experiment approved for Hall A)
Ciofi – does ok with 2bbu, 3bbu, d, some predictions for 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
Exciting times are aheadM. 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, 0052502 (2005)C. Ciofi degli Atti and L. P. Kaptari, Phys. Rev. C71, 024005 (2005)R. Schiavilla et al., nucl-th/0508048J. M. Udias, private communications