Impulse Approximation limitations to the e,ep reaction on 208Pb

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Impulse Approximation limitations to the (e,ep)
reaction on 208Pb Identifying correlations and
relativistic effects in the nuclear medium
K. Aniol, A. Saha, J. M. Udías, G. Urciuoli
Spokepersons PAC 29, January 12, 2006
J.M. Udias, PAC 29, Jan 12, 2006
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PR89-046 Conditionally approved Should
demonstrate that the experiment can extract
information from states separated by 0.35 MeV
Spokespersons B. Frois C. N. Papanicolas L.
Lapikas J. Mougey
J.M. Udias, PAC 29, Jan 12, 2006
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PAC-28 PR-05-105, Impulse Approximation
limitations to the (e,ep) reaction in 208Pb,
identifying correlations and relativistic effects
in the nuclear medium deferred with regret
Since inevitably it is extremely difficult at
such high energies to separate completely the
individual states, procedures for fitting
simultaneously the response as a function of Em
and pm, should be further developed.  
J.M. Udias, PAC 29, Jan 12, 2006
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Renewed proposal for the PAC-29

• We have added two kinematical setups to measure
  spectroscopic factors at higher Q2. This will
  help finding (or ruling out) a possible Q2
  dependence of the spectroscopic factors up to 2
  (GeV/c)2
• We have run the theory through detailed GEANT
  simulations of the experimental setup. The
  simulated data were analyzed with the same tools
  designed to deal with the actual data

J.M. Udias, PAC 29, Jan 12, 2006
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Presentation to PAC-29

• Review of the physics goals
• Results from the simulations

J.M. Udias, PAC 29, Jan 12, 2006
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1. Physics Motivation (i)
How well do we understand nuclear structure
? The underlying physical picture Dense system
of fermions whose motions to first order can be
treated as independent particles moving in a mean
field Electromagnetic interactions Best
probes for investigating the validity of the
independent particle picture because they are
sensitive to a large fraction of the nuclear
volume Realistic microscopic calculations of the
spectroscopic factors are not possible for
medium-heavy (Agt20) nuclei. Approximations are
made that build on top of the shell model (mean
field or independent particle picture) that is
still the basic building block upon which most
calculations of complex nuclei rely
J.M. Udias, PAC 29, Jan 12, 2006
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1. Physics Motivation (ii)
Deviations from independent particle motion for
orbits near the Fermi surface are attributed to
effects beyond mean field (correlations) which
reveal their pressence in two ways (i) Changes
in the occupation and spectroscopic factors with
respect to mean-field predictions (ii) Changes
in the momentum distribution of particles,
especially at high momentum and binding
energies V.R. Pandharipande, I. Sick and P.K.A.
deWitt Huberts, Independentparticle motion and
correlations in fermions systems, Reviews of
Modern Physics 69 (981) 1997
J.M. Udias, PAC 29, Jan 12, 2006
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1. Physics Motivation (iii)

• The (e,ep) reaction at quasielastic kinematics
  and in exclusive conditions, for the outermost
  shells, becomes one of the most powerful and
  cleanest test of the mean field and the
  correlations needed to supplement it
• 208Pb is the most suitable candidate to employ
  the mean field prediction, and thus it has been
  measured in the past in order to measure
  spectroscopic factors
• The reaction has been measured in the past,
  mainly in parallel kinematics and for moderate
  values of Q2. Spectroscopic factors have been
  measured

J.M. Udias, PAC 29, Jan 12, 2006
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• Shell model (mean field) calculations the shape
  of the cross-section is well described, but the
  measured spectroscopic factors are below the mean
  field prediction. How large/small must be the
  spectrocopic factors?

About 30 depletion is observed for states near
the Fermi level. This cannot be explained only
with short-range correlations Shape at moderate
pm and parallel kinematics is well
understood Long range correlations are predicted
to be visible at large pm
J.M. Udias, PAC 29, Jan 12, 2006
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Still open issues (i) possible dependence on Q2
of the spectroscopic factors?
data 4, theory 5.
12C(e,ep) data over wide range of Q2. There
appears to be a Q2 dependence to the
spectroscopic factors observed in this
reaction2. This interpretation has been
disputed and the Q2 dependence attributed to
analysis methods of SRC3 208Pb(e,e'p) has been
studied in the past at low momentum transfers and
spectroscopic factors in the range of 0.6 to 0.7
have been reliably extracted from parallel
kinematics 4,5,6 at low Q2 A measurement at
several high values of Q2 will directly address
the question of momentum transfer dependence of
the spectroscopic factors
J.M. Udias, PAC 29, Jan 12, 2006
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Open issues (ii) Long range correlations and
cross-sections at high pm (gt 300 MeV/c)
Excess strength at high pmiss
xB 0.18
E. Quint, thesis, 1988, NIKHEF
I. Bobeldijk et al., PRL 73 (2684)1994
J. M. Udias et al. PRC 48(2731) 1994
J.M. Udias et al. PRC 51(3246) 1996
If long range correlations are the reason for
the small spectroscopic factors, then they should
produce a large effect at high missing momentum.
An experiment was performed at NIKHEF-K to
measure the large momentum region, but the
kinematics was far from XB1. Additional strength
was indeed found, but this can be explained
either via long-range correlations Bobeldijk,6
or by relativistic effects in the mean field
model Udias,7.
J.M. Udias, PAC 29, Jan 12, 2006
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Still open issues (iii) are there any signatures
of relativistic dynamics in the nuclei?
It seems that TL-observables (that change sign
when the cross-section is measured when the
knocked out proton is at both sides of the
transferred momentum) are sensitive to dynamical
relativistic effects A measurement at both sides
of q will directly measure ATL and address the
possible dynamical relativisitc effects. Yet such
a measurement for 208Pb has never been attempted
Red dotted lines non relativistic calculation.
Black lines different relativistic calculations.
Data from Saclay (left) and NIKHEF-K (right) at
moderate Q2 (0.2-0.3 (GeV/c)2) on 16O(e,ep)
J.M. Udias, PAC 29, Jan 12, 2006
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Cross Section Asymmetry ATL
The cross section asymmetry is defined about q
The data taken at NIKHEF 6 were backward of q
where both theoretical (relativistic and
nonrelativistic) are relatively closer. But
forward of q the theories can disagree by two
orders of magnitudeLooking for unmistakable
signatures of correlations at high pmiss from
(e,ep) cross sections alone is a hard task for
xB ltlt1
Data from 6 I. Bobeldijk et al., PRL 73
(2684)1994
J.M. Udias, PAC 29, Jan 12, 2006
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ATL in 3He, 4He and 16O
If there are relativistic dynamical effect, a
strong effect on ATL would be seen, particularly
at moderate pm There is a notable difference in
ATL between 3He and 4He due to the density
difference and in 16O
16O ATL
p1/2
p3/2
M. Rvachev et al. PRL 9412320,2005
J. Gao et al. PRL843265, 2000
E04-107,2004
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1. What is being proposed

• Use 208Pb, a doubly magic, complex nuclei, a
  textbook case for the shell model. Measure
  208Pb(e,ep)207Tl cross sections at true
  quasielastic kinematics and at both sides of q.
  This has never been done before for Agt16 nucleus
• Study low lying states in 207Tl
• g.s. 3s1/2
• 0.351 2d3/2
• 1.348 1h11/2
• 1.683 2d5/2
• 3.470 1g7/2
• Quasielastic kinematics xB 1, q 1 GeV/c , ?
  0.433 GeV/c
• Determine momentum distributions 0 lt pmiss lt
  500 MeV/c
• Determine ATL by measuring cross sections on
  either side of q

xB0.18
Lumproposed/LumNIKHEF-K 170
J.M. Udias, PAC 29, Jan 12, 2006
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1) Determine spectroscopic factors from the data
for separate states at low pm kinematics (kin01
to kin07)
J.M. Udias, PAC 29, Jan 12, 2006
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1) Determine spectroscopic factors from the low
pm kinematics (kin01 to kin07). Expected data
were extracted with the peak fitting procedure
after averaging the theory over the acceptance
with a detailed GEANT simulation
J.M. Udias, PAC 29, Jan 12, 2006
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... Determine spectroscopic factors from the low
pm kinematics (kin01 to kin07)
J.M. Udias, PAC 29, Jan 12, 2006
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... Determine spectroscopic factors from the low
pm kinematics (kin01 to kin07)
J.M. Udias, PAC 29, Jan 12, 2006
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2) Measure ATL for separated states at least for
the low pm kinematics (kin01 to kin07)
J.M. Udias, PAC 29, Jan 12, 2006
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ATL in 208Pb
The solid blue line (and black circle points)
shows a calculation that includes the
relativistic dynamical effects of the enhancement
of the lower components of the four spinors (and
the expected data after acceptance averaging).
The magenta line (and cyan squared points) is a
calculation that neglects these dynamical
relativistic effects.
1h11/2
Non Rel.
After running through the simulations and
acceptance averaging, the calculations show the
same sensitivity to relativistic dynamics as the
raw curves. Relativistic results tend
systematically to produce larger (in absolute
value) ATL
Rel.
J.M. Udias, PAC 29, Jan 12, 2006
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1g7/2
Simulated data obtained from a realistic
simulation that includes folding with the
acceptances and the extraction from the peak
fitting procedure
ATL in 208Pb
2d3/2
3s1/2
2d5/2
J.M. Udias, PAC 29, Jan 12, 2006
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Non relativistic dynamics
Relativistic dynamics
ATL for all the shells added up, compared with
the acceptance averaged simulations
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3) Measure the cross-section at high pm and look
for effects of long-range correlations
(kin06-kin11)
J.M. Udias, PAC 29, Jan 12, 2006
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Look at large pmiss for correlations.
xB 1
With correlations
Without correlations
(I) Mahaux and Sartor (SF0,6) (II) Ma and
Wambach (SF0,7) (III) Pandharipande et al
(SF0,8)
208Pb(e,ep)207Tl(3.470 MeV)
Long range correlations are needed to explain the
30 depletion. At xB 1 neither Nonrel. or Rel.
theory produces large strength at high pm if long
range correlations are excluded. This is in
contrast to the ambiguous signature at xB ltlt 1 of
former experiment at NIKHEF-K
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Look at large pmiss for correlations.
xB 1
With correlations
We compare to theoretical predictions after
acceptance averaging. We do not attempt to
separate the five shells in this region nor to
compute ATL. If cross-sections are higher than
the mean field prediction, the improved
statistics might eventually allow for shell
separation and ATL measurement
Without correlations
(II) Mahaux and Sartor (SF0,6) (I) Ma and
Wambach (SF0,7)
208Pb(e,ep)207Tl(all 5 shells)
Long range correlations are needed to explain the
30 depletion. If correlations are excluded,
neither Nonrel. or Rel. theory can produce large
strength at high pmiss. This is in contrast to
the ambiguous signature at xB ltlt 1 of former
experiment at NIKHEF-K
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High pmiss predictions are robust at
xB 1
With correlations
Without correlations
(II) Mahaux and Sartor (SF0,6)
208Pb(e,ep)207Tl(all 5 shells)
The different ingredients of the calculation
(relativity, off-shell prescriptions) will not
change appreciably the results at high pm,
long-range correlations will be seen unmistakably
if they are as large as predicted to explain
spectroscopic factors
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Target Issues and Peak Extraction

• Two tested targets configurations capable of high
  current running
• (i) Cold Lead in diamond sandwich
• E03-011 has demonstrated that a 0.5 mm lead foil
  sandwiched between two 0.15 mm diamond foils at
  cryogenic temperatures can withstand currents up
  to 80 uA and calculations indicate that they can
  operate at 100 µ A. Thinner (0.2mm) lead foil is
  not a problem
• Preferred Target Configuration, has been
  employed in all the simulations
• (ii) Stacked lead foils in a 15 cm beer can LH2
  target
• Test run showed that the upstream foil can
  withstand at least 60 µA with only the horizontal
  sweep of the raster working at the time

J.M. Udias, PAC 29, Jan 12, 2006
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GEANT Simulation and Peak Extraction (i)
Use a bismuth run to provide an experimental line
shape, no model dependencies introduced
Previous work on Bismuth Electron and
photon-induced proton knockout from 209Bi, D.
Branford, et al., PRC63, 014310 and Electron
Scattering study of internal target effects and
of the 209Bi(e,ep) reaction, Jan Lac, thesis,
1993, University of Amsterdam
Geant simulation for requested 20 hour run
We will have a factor of 100 increase in
luminosity compared to earlier measurements.
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GEANT Simulation and Peak Extraction (ii)
Comparison of gs profiles at Pmiss 100 MeV/c
(solid) and 200 MeV/c (dashed)
Comparison of Bi and Pb gs profiles
Em profile will be known (measured from Bi
experiment), independent on Pmiss or Emiss Peak
positions are also well known The only unknowns
are the weights for each shell. According to a
realistic simulation, Peak extraction from a
line-shape fit is possible if good statistics is
available, i.e., up to Pmiss lt 300 MeV/c
J.M. Udias, PAC 29, Jan 12, 2006
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GEANT Simulation and Peak Extraction (iii)
Excitation Energy (MeV), pm100MeV/c
A 0.2 mm thick lead target is a good compromise
between resolution and count rate
J.M. Udias, PAC 29, Jan 12, 2006
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Kin4, pm around 200 MeV/c
1h11/2
1g7/2
2d3/2
2d5/2
3s1/2
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Beam Time Request
The time estimates for the data runs have been
adjusted up by 30 to account for radiative
losses Optics data taken with the carbon target
will help establish the missing mass calibration,
which is needed for the peak fitting The
bismuth run will provide a line shape and also
provide a missing mass calibration.
J.M. Udias, PAC 29, Jan 12, 2006
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Summary
(1) The first measurements ever made in
quasielastic kinematics on the paradigmatic shell
model nucleus, 208Pb at high Q2 are proposed.
Accurate spectroscopic factors for separated
shells will be obtained at several values of
Q2.(2) Strength for pmiss gt 300 MeV/c will give
insight into nuclear structure issues and will
settle the long standing question about the
amount of long range correlations. We will see
them for the first time, if they are there. (3)
A new observable ATL for the five low lying
states of 207Tl will be measured. ATL can help
distinguishing between relativistic and
nonrelativistic structure of the wave functions.
J.M. Udias, PAC 29, Jan 12, 2006
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Fitted spectra , 208Pb(e,ep)207Tl for 0.2mm
Pb, cold diamond sandwich
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Fitted spectra , 208Pb(e,ep)207Tl for 0.2mm
Pb, cold diamond sandwich
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Heavy Metal Collaboration
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Pmiss coverage, scale in MeV/c
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Resolution for Various Target Configurations
The realistic spectrometer settings use the
published Hall A spectrometer characteristic. The
ideal spectrometer settings contribute no width.
NIKHEF-target refers to using the NIKHEF two foil
or one foil targets in our spectrometers and
kinematics. NIKHEF-paper refers to the results
from 6. In that experiment the scattered
electron energy was almost 7 times lower than in
the proposed kinematics. A comparison of the
widths for the same target between the realistic
and ideal spectrometers gives us a measure of the
spectrometers' contribution to the experimental
FWHM. Assuming the target effects and
spectrometer effects add in quadrature we
conclude that the spectrometers contribute about
0.5 Mev to the FWHM for our kinematics
K.Aniol, PAC 28, August 24, 2005
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ATL compared to simulated data averaged over
experimental bin, 3s1/2 state, 0.000 MeV
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ATL compared to simulated data averaged over
experimental range, 2d3/2 state, 0.351 MeV
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ATL compared to simulated data averaged over
experimental range, 1h11/2 state, 1.348 MeV
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ATL compared to simulated data averaged over
experimental bin, 2d5/2 state, 1.683 MeV
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ATL compared to simulated data averaged over
experimental bins, 1g7/2 state, 3.470 MeV
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