K. Aniol, California State University, Los Angeles 1

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Detailed Study of the 4He Nuclei through Response
Function Separations at High Momentum Transfers
Spokespersons Konrad Aniol CSULA, Los
Angeles, CA Shalev Gilad M.I.T.,
Cambridge, MA Doug Higinbotham Jefferson Lab,
Newport News, VA Arun Saha
Jefferson Lab, Newport News, VA Contact person
saha_at_jlab.org
K. Aniol, California State University, Los
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Physics Motivation
Provide a large and precise data set for testing
and constraining theoretical models
Microscopic wave functions
relativisitic dynamics Relativistic
mean-field models
Short range structure of 4He (and other nuclei)
Is RL quenched in 4He? Measure the q dependence
Look for NN correlations at high pmiss and emiss
Response function separations
Find the limits of hadronic degrees of freedom in
the nucleus
Fruitful comparison to 3He(e,ep) in same
kinematics
K. Aniol, California State University, Los
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Why Study 4He ?
It is a tightly bound system so NN correlations
may be more important here than in a lighter
nucleus.
It is a bridge between 2/3 body systems and
heavier nuclei. Its density is similar to that of
a heavier nucleus.
Microscopic calculations are possible, which help
establish the baseline for looking for exotic
effects.
Study the A dependence, A 2,3,4 of the high
pmiss region as a measure of final state
interactions or initial state correlations.
High quality data exist for 2H and 3He. 4He data
are needed to complete the systematic survey of
the few body nuclei.
K. Aniol, California State University, Los
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Kinematics
Perpendicular Kinematics, xB 1
E 4.8 GeV and 1.25 GeV, q 1.5 GeV/c, w 0.84
GeV Cross Sections pmiss from 0 to 1.2
GeV/c ATL,RTL pmiss from 0 to 0.5
GeV/c RT, RLTT pmiss 0, 0.4, 0.5 GeV/c
Parallel Kinematics
Cross Sections, RT, RL, RL/RT
E 0.85 to 4.8 GeV xB 1, pmiss0 q 1.0,
1.5,2.0, 3.0 GeV/c
E 1.25 and 4.8 GeV xB1.86, pmiss 0.4
GeV/c q 1.5 GeV/c
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3,4He(e,e)X
4He
3He
RT
RL
Quasielastic peak and the Bjorken variable xB
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One photon exchange cross section for two body
breakup
p
em
g
q
w Ee Ee
q
em
q pe - pe
f
Response functions RX depend on q, w, p, and g.
VX and frec are known kinematical factors.
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Definition of perpendicular kinematics, S1 , S2 ,
S3
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Perpendicular Kinematics
Measurements in quasielastic kinematics ( xB 1)
emphasize the single nucleon aspect of the
reaction.
RLTT from pmiss 0.4 to 0.5 GeV/c may reveal
the long sought minimum in the 4He wave function.
Low pmiss allows both relativistic mean field
models and microscopic models to be compared to
the data.
High pmiss allows investigation of short range
structure.
Extreme pmiss and q may reveal non-hadronic
degrees of freedom in nuclear structure.
K. Aniol, California State University, Los
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New response function calculations by J. M. Laget
A 4
Perpendicular kinematics
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Looking for the minimum in 4He wave function
Spectral function fit from Van Leeuwe data
The minumum should be evident as a break in the
slope according to Lagets prediction.
expected errors
Laget prediction
pmiss, MeV/c
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Perpendicular kinematics
New cross section calculation by J. M. Laget
A 4
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Relativistic calculations for 4He(e,ep)
ATL
Nucl. Phys. A278 (2003) 226 J. Ryckebusch et al.
Response functions at proposed kinematics
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Preliminary JLab data, 4He(e,ep)3H, Bodo
Reitz Calculation by C. Ciofi degli Atti and H.
Morita, private communication
A 4
Distorted spectral function from JLab experiment
E97-111, in parallel (Py2) and perpendicular
(cq2) kinematics
cq2, (w,q)(0.53,1.70)GeV/c py2, 0.59ltQ2lt.89
(GeV/c)2
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A4
4He(e,ep)3H
Preliminary E97111 data from Bodo Reitz,
calculation by J. M. Laget, private
communication.
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A 3
3He(e,ep)2H, E89044 data Marat Rvachev, MIT
thesis, 2003
Data exceed calculation by a factor of 26 at
pmiss 1 Gev/c
This region must be studied in 4He.
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A 3
Calculations M. Avioli et al.,
arXivnucl-th/03123123v1 29Dec, 2003
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A 3
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A 3
3He(e,ep)2H, E89-044 Marat Rvachev, MIT thesis,
2003
Calculations, Madrid group, private communication
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A 3
3He(e,ep)2H, E89044 data Marat Rvachev, MIT
thesis, 2003
Calculations Madrid group, private communications
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A 2
P. E. Ulmer, et al., PRL 89
(2002) 062301
JLab data, P. E. Ulmer et al., calculations M.
Avioli et al., arXivnucl-th/0312123v1 29 Dec 2003
2H(e,ep)n, JLab data and recent theoretical fits
Also E01-020 finished data taking. Q2 survey to
study short range structure, FSI, and to obtain
RLT . Data analysis in progress
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Parallel Kinematics
Only RL and RT contribute to the cross section.
FSI are minimized.
At low pmiss ( 0 MeV/c) both relativistic mean
field theory and microscopic theory should be
able to predict the nucleon wave function.

4He(e,ep) data show a
reduction in RL at lower q. J.
E. Ducret et al., NP A556 (1993) 373 Study q
dependence of RL and RT.
For pmiss 0.4 GeV/c and xB 1.86 we expect
minimal effects from MEC and pion production for
NN correlations. This was the main piece of
E97011 (jeopardy casualty).
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A 3
E89044, Parallel kinematics
Theoretical curves by J.-M. Laget
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Theories and Models
Few body systems have attracted a great deal of
interest. Many wave functions and reaction models
are available.

Standard Nuclear Model Approach Microscopic 4He
wave function generated from modern
nucleon-nucleon potentials, e.g., R. Schiavilla
others.
Diagrammatic expansion used by J.-M. Laget with
success.
Relativisitic mean field wave functions and fully
relativistic dynamics used by the Madrid group,
Ghent group.
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Some Recent Theoretical Calculations for 4He at
JLab energies
Fully relativistic models
Non-relativistic models
Mean field wave function
Realistic wave functions
Ghent
Madrid
J. M. Laget
Relativistic multiple scattering Glauber
approximation
Optical potential
Diagrammatic approach allows incorporation of
MEC, FSI rescattering
U. Perugia, INFN, Dubna, St. Petersburg, Sapporo
Gakuin U., U. Trieste, Heidelberg, others
Effect of lower component on ATL
Glauber approximation, Finite Formation Time
effects,
Rome INFN, Juelich, Landau Institue
Generally improved spectroscopic factors for Agt4
Glauber/eikonal approx. color transparency
Medium modifications of nucleon EM form factors
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Beam Time Request
Perpendicular Kinematics
(i) Response function separations (0-0.5 GeV/c)
227 hours
(ii) High pmiss(0.6 1.2 GeV/c)
128 hours
Parallel Kinematics ( xB 1)
12 hours
Parallel Kinematics (xB 1.86)
57 hours

• Setup and Calibrations
• Spectrometer changes (fields and angles)
  16 hours
• (ii) Energy measurements (Arc and ep)
  12 hours
• (iii) Optics studies
  16 hours
• (iv) Elastic scattering measurements
  12 hours

Total time requested 480
hours 20 days
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Summary
In perpendicular kinematics (xB 1)

• Cross sections will be measured over an
  unprecedented
• Range of pmiss, up to 1.2 GeV/c

(ii) Response functions will be extracted to 0.5
GeV/c
Parallel kinematics (xB 1) measure RL/RT vs. q
Parallel kinematics (xB 1.86) look for NN
correlations

• This will produce high quality data to be
  compared to
• 3He(e,ep) over the same kinematical conditions
• (ii) Modern theoretical interpretations

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K. Aniol, California State University, Los Angeles