Nuclear Structure and Dynamics in the 3He(e,e

1
Nuclear Structure and Dynamics in the 3He(e,ep)d
and 3He(e,ep)pn Reactions
JLAB Hall A
Two high resolution spectrometers (?p/p ? 10-4)
dO 6 msr High current, high polarization
(?80-85) cw beam High pressure 3He target -
luminosity 1038 cm2 sec-1 Focal-plane hadron
polarimeter
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Inclusive electron scattering (e,e)
Can vary independently the transferred energy and
momentum
xB Q2/2m?
3
A(e,ep)B
, ?
Em ? - Tp - TB
B A-1 (bound), A-2 N, other
4
Plane-Wave Impulse Approximation (PWIA)
Not an observable!!
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Final-state interactions

• Calculate FSI in terms of
• Optical potential
• Glauber (or Eikonal) approximation

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A(e,ep) x-section in term of responses
?i viRi
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Kinematics of Measurements

• Quasi-elastic xB1
• Fixed electron kinematics
• q1.5 GeV/c
• ?0.837 GeV
• 3 virtual photon polarizations
• 0.108e0.943
• Perpendicular proton kinematics
• High energy of ejected proton
• Tp0.8 GeV
• Parallel kinematics in analysis

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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 kinematics xB 1
Kozlov Parallel kinematics xB gt 1
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Models

• Laget
• Gswf generated from solution to Faddeev eqn. with
  Paris NN potential
• (also variational calculations using AV18UIX)
• Kinematics, nucleon meson propagators are
  relativistic un-factorized MottFF
• 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!
• PWIAFSI 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)

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Models (cont.)

• Schiavilla
• Variational GSWF generated using AV18UIX
  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
  AV8central 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

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3 regions in pm
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X-sections for -150 lt pm lt 150 MeV/c
Laget
Schiavilla

• NNN forces important at very low pm (25)
• FSI starts to break factorization around pm gt
  100-150 MeV/c

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150 lt pm lt 700 MeV/c
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Affect of different NN potentials
R. Schiavilla et al., nucl-th/0508048
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Pm gt 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,ep)pn 3bbu
For 2-body kinematics with a spectator A-2 - a
relationship between Em and pm
Low pm (still gt kf) correlations?
Em - Eth (MeV)
F. Benmokhtar et al., PRL 94, 082305 (2005)
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3bbu high pm
High pm dominated by FSI Note similarly good
calculations by Ciofi
Em Eth (MeV)
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2bbu, 3bbu distorted spectral functions
High Q2 xB 1 ? Reduced MEC, ?
contributions At pm gt 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,ep)d
  and 3He(e,ep)pn
• -750 gt pm gt 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,ep)d. 3He(e,ep)pn by fall?
• Udias does surprisingly well using RDWIA o.
  p. for FSI in 3He(e,ep)d

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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,epp)n, 4He
• Laget does reasonably well with 2bbu, 3bbu,
  3He(e,epN)N, d
• Schiavilla working on 3He(e,ep)pn,
  4He(e,ep)3H, ingredients tested on d
• Udias has predictions for 4He(e,ep)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