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
4He(e,ep)3H and 4He(e,ep)X
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
Angeles - 1
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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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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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Definition of perpendicular kinematics, S1 , S2 ,
S3
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3,4He(e,e)X
4He
3He
RT
RL
Quasielastic peak and the Bjorken variable xB
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Physics Motivation
Provide a large and precise data set for testing
and constraining theoretical models in few-body
nuclei Microscopic
wave functions relativistic kinematics
Relativistic mean-field models
Study short range structure of 4He (and other
nuclei)
Is RL quenched in 4He(e,ep)3H? RL seems to be
quenched in 4He(e,e). Measure the q dependence.
Look for NN correlations at high pmiss and emiss
Response function separations
We need to understand the impact of reaction
dynamics, relativity, and final state interaction
effects on the observables.
Find the limits of hadronic degrees of freedom in
the nucleus
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Why Study 4He ?
It is a tightly bound system so NN correlations
should 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 may
help establish the baseline for looking for
exotic effects.
Study the A dependence, A 2,3,4 and density
dependence 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.
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Perpendicular Kinematics
Measurements in quasielastic kinematics ( xB 1)
emphasize the electron-single nucleon interaction
aspect of the reaction.
RLTT from pmiss 0.4 to 0.5 GeV/c may show
effects due to the minimum in the 4He wave
function.
Low pmiss allows both relativistic mean field
models and microscopic models to be compared to
the data.
The asymmetry ATL is predicted to be sensitive to
dynamical relativistic effects in the 4He wave
function.
High pmiss allows investigation of short range
structure.
Extreme pmiss and q may reveal non-hadronic
degrees of freedom in nuclear structure.
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Parallel Kinematics
Only RL and RT contribute to the cross section.
FSI are minimized but not negligible. See
preliminary data of E97111
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. Experience from e89044 at xB1
shows strong FSI effects.
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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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Experiment is Ready to Run There is a strong
collaboration of experimentalists and theorists
on the proposal.
The standard Hall A equipment was designed for
high resolution experiments.
Sister experiment has educated three PhD students
so far 1 thesis (MIT) completed, 1 thesis
(Rutgers) to be submitted this summer, 1 thesis
still being worked on.
Drafts of two Physical Review Letters are
circulating among the collaboration.
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Some Recent Theoretical Calculations for 4He at
JLab energies
Fully relativistic models
Non-relativistic models
Microscopic 4He wave function generated from
modern nucleon-nucleon potentials, e.g., R.
Schiavilla others.
Mean field wave function
Ghent
Madrid
Relativistic multiple scattering Glauber
approximation
Optical potential
J. M. Laget
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 of w. f. on ATL
Glauber approximation, Finite Formation Time
effects,
Generally improved spectroscopic factors for Agt4
Rome INFN, Juelich, Landau Institute
Glauber/eikonal approx. color transparency
Medium modifications of nucleon EM form factors
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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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Is there a q dependence to the quenching of the
longitudinal vs transverse response?
PRL 69 (1992) 41 Z.-E. Meziani et al.,
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4He(e,ep)3H Response function
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The minimum in the pt spectral function should
produce an observable break in the slope of RLTT.
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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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New response function calculations by J. M. Laget
A 4
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Perpendicular kinematics
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4He(e,ep)3H
In 4He the RPWIA produces significant oscillation
in ATL. In 3He the RPWIA gives a monotonic
dependence of ATL on pm.
Ee4.8 GeV q1.5 GeV/c w 0.84 GeV
ATL
For 4He ATL depends both on FSI and on the lower
component of the wave function.
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The enhancement of the lower component of the
bound state wave function is evident in the
relativistic calculation. See the result for
3He(e,ep)2H.
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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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4He(e,ep)3H
pm 30 MeV/c
1.0
Data - J. E. Ducret et al., NP A556 (1993) 373
R
pm 90 MeV/c
0.5
pm 190 MeV/c
A
R
ratio of corrected longitudinal to corrected
transverse spectral function, SL(corr)/ST(corr)
0.
0
300
600
900
1.0
A ratio calculated by J.-M. Laget B ratio
calculated by R. Schiavilla
R
0.5
However, at q685 MeV/c R. Florizone et al. did
not observe a quenching of the longitudinal
response. (MIT thesis 1999)
B
0.
300
600
900
0
q MeV/c
Is the longitudinal response quenched?
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Preliminary JLab data, 4He(e,ep)3H, Bodo
Reitz Calculation by C. Ciofi degli Atti and H.
Morita, private communication
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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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Perpendicular kinematics
New cross section calculation by J. M. Laget
A 4
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A 3
Calculations M. Avioli et al.,
arXivnucl-th/03123123v1 29Dec, 2003
Note Calculations by J.-M. Laget show a similar
strong FSI effect
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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
The oscillation in the calculated ATL is caused
by FSI.
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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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A 3
E89044, Parallel kinematics
Theoretical curves by J.-M. Laget
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RL
RL fm3
fm3
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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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K. Aniol, California State University, Los Angeles
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Spectral function fit from Van Leeuwe data
Both the magnitude and shape of the response
function are sensitive to the 4He wave function
and reaction dynamics
RL
The minimum in the W.F. should produce a break in
the slope according to Lagets prediction.
Laget prediction
pmiss, MeV/c
Looking for the effect of the minimum in 4He wave
function
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4He(e,ep)X
J.J. van Leeuwe et al., Phys. Lett. 523B(2001)6
w 215 MeV q 401(MeV/c) xB 0.28 Q2 0.11
(GeV/c)2
Calculation Laget Variational Monte Carlo wf,
Urbanna NN potential
dashed 1 bodyFSI solid includes MEC and IC
MECIC more important for large gpq.
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Effects of Short Range Correlations in
4He(e,ep)X at high pmiss and Emiss
From 4He(e,ep)X of van Leeuwe et al and
calculations by Laget
Q2 0.11 (GeV/c)2 , xB 0.28
Minimize gpq to minimize MEC and IC do response
function separations
From 3He(e,ep)X of E89044 and calculations by
Laget
Q2 1.55 (GeV/c)2 , xB 0.96
Large Q2 suppresses MEC even at small gpq FSI
dominant the cross section
From 4He(e,e)X of K. Egiyan et al. Phys. Rev.
C68, 014313 (2003)
SRC dominate the nuclear wave function for pmiss
gt 300MeV/c and are seen clearly for Q2gt1.4
(GeV/c)2 and xBgt1.5 because of the scaling of
(e,e) cross sections with A.
proposal separate RL/RT , xB 1.86, Q2 1.94
(GeV/c)2
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