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 (80-85%) cw beam80-85%) 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

Inclusive electron scattering (e,e’)

Can vary independently the transferred energy and momentum

xB = Q2/2m

A(e,e’p)B

B = A-1 (bound), A-2 + N, other

,

Em = - Tp - TB

Plane-Wave Impulse Approximation (PWIA)

Not an observable!!

Final-state interactions

Calculate FSI in terms of:

Optical potential

Glauber (or Eikonal) approximation

A(e,e’p) x-section in term of responses

i = viRi

Kinematics of Measurements

•Quasi-elastic: xB~1

•Fixed electron kinematics:

q=1.5 GeV/cω=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

2bbu x-sections; distorted S(pm)

M. M. Rvachev et al., PRL 94, 192302 (2005)

Comparison to previous data

Florizone:“Parallel” kinematicsxB≈ 1

Kozlov:“Parallel” kinematicsxB > 1

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: More recent results next talk by Morita! 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

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 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

3 regions in pm

X-sections for -150 < pm < 150 MeV/c

NNN forces important at very low pm (~25%)

FSI starts to break factorization around |pm| > 100-150 MeV/c

Laget Schiavilla

150 < pm < 700 MeV/c

Affect of different NN potentials

R. Schiavilla et al., nucl-th/0508048

Pm > 600 MeV/c

Laget: 3-body diagram(s) Ciofi: double scattering Schiavilla: double scattering Non-hadronic? “Exotic”?

ATL

No structure in PWIA -factorized

Factorization broken by FSI

No ATL from Ciofi – factorized calculations

3He(e,e’p)pn – 3bbu

Em - Eth (MeV)

For 2-body kinematics with a spectator A-2 - a relationship between Em and pm

Low pm (still > kf): correlations?

F. Benmokhtar et al., PRL 94, 082305 (2005)

3bbu – high pm

Em – Eth (MeV)

High pm: dominated by FSI

Note: similarly good calculations by Ciofi

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

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 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

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, dSchiavilla – working on 3He(e,e’p)pn, 4He(e,e’p)3H,

ingredients tested on dUdias – 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