Spectroscopic Factors and ASpectroscopic Factors and ATLTL from from Quasielastic (e,e'p) Reaction Quasielastic (e,e'p) Reaction

in in 208208Pb, Pb, 1212C and C and 1616O at JLabO at JLabJ.L. Herraiz1, J.M. Udías1

J.C. Cornejo2, A. Camsonne3, A. Saha3, K. Aniol4, G.M. Urciuoli5

L.B. Weinstein6, K.G. Fissum7 and the Hall A collaboration

1 Universidad Complutense, Madrid, Spain2 The College of Williams and Mary, VA, USA3 Thomas Jefferson National Accelerator Facility, Newport News, VA, USA4 California State University, Los Angeles, California, USA5 INFN, Sezione di Roma, Rome, Italy6 Old Dominion University, VA, USA7 Lund University, Sweden

1) QUASIELASTIC (e,e’p) REACTION 1) QUASIELASTIC (e,e’p) REACTION 2) SIMULATIONS 3) DESCRIPTION OF THE EXPERIMENT4) DATA ANALYSIS5) RESULTS 6) SUMMARY AND CONCLUSIONS

2

Unpolarized electron beams with an Energy of several GeV.

Typical targets are doubly-magic, closed-shell nucleus like 16O, 208Pb. Their bound-nucleon wave functions are well known and relatively easy to calculate.

The scattered electron is detected in coincidence with an ejected proton. The three-momentum of these particles are measured and based on this information we obtain the properties of the proton in the nucleus.

QuasielasticQuasielasticA(e,e’p)B ExperimentsA(e,e’p)B Experiments

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

3

KinematicsKinematics

(e,e’p) reaction in the Born

ApproximationIncident Electron

Scattered Electron

Ejected Proton

Residual Nucleus

Virtual Photon

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

4

• Exclusive conditions • Unpolarized particles

Simple Description Simple Description of the (e,e’p) Reactionof the (e,e’p) Reaction

Single-photon Exchange and Impulse Approximation (IA)

Mean-Field and Independent Particle Shell Model (IPSM)

Plane-Waves (PWIA)

( )6

,ep miss missf e p p

dK S E p

dE d dE d

ss= × ×

W W

Measured Cross

Section

Kin. Factor

electron-proton Cross

Section

Spectral

Function( )miss( , ) p ( - )miss miss a missS E p E Er d= ×

Probability of finding a proton in the nucleus with binding energy

Emiss and momentum pmiss.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

5

MeV

Emiss (MeV)

S(E

mis

s,pm

iss)

[MeV

]-1(G

eV/c

)-3

Other Effects in theOther Effects in the (e,e’p) Reaction (e,e’p) Reaction

A more accurate description of the (e,e’p) reaction includes:

Final-State Interactions: Interactions of the extracted proton with the residual nucleus. This is modeledby an optical potential from elastic (p,p)data. Proton is described by DistortedWaves (DWIA).

Coulomb Distortion and Internal Radiative Corrections: The momentum of the electrons at the reaction point is different to their asymptotic measured values.

External Effects (From atomic interactions in the target) Energy Loss, External Radiative Corrections, Straggling, Proton Absorption.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

6

For a Emiss peak (shell)

51red

ep e p

dK R d d d

ss

s wº ×

× × W W

Reduced cross-section (Distorted Momentum Distribution)

Spectroscopic Factors – Scale factor required to fit the simulated reduced cross section with the measured one.

. . (exper.) (theor.)red redspect fact s s=

(e,e’p) (e,e’p) ObservablesObservables1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

( )5

, ( )

miss

ep miss miss ep misse p E

dK R S E p K R p

d d d

ss s r

w» × × × = × × ×

W W ò

7

5

TL 5

5

5

1800

0 180dd

ddA

Transverse-longitudinal assymetry (ATL)

q

ki kf

ppmiss< 0

ppmiss >

0

1) Momentum Distribution of protons – Measurement of the reduced cross section for different shells in the nucleus in a large pmiss range. Search for correlation effects at high pmiss.

208Pb is one of the best nucleus to observe these effects.

Objectives of this Objectives of this (e,e’p) Experiment (I)(e,e’p) Experiment (I)

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

With correlations

Without correlations

pmiss (MeV/c)

Cro

ss S

ecti

on 208Pb(e,e’p)

Valence States

8

2) Spectroscopic Factors - Deviation from the mean field occupation prediction expected for each shell in the Shell Model. It is obtained as the factor required to fit theoretical calculations to measured data.

It was argued that there could be a dependence of spectroscopic factors with Q2.

Objectives of this Objectives of this (e,e’p) Experiment (II)(e,e’p) Experiment (II)

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

In this work this possible dependence was studied in two different nucleus: 12C and 208Pb, obtaining the spectroscopic factor at three different Q2 values: 0.8, 1.4 and 2.0 (GeV/c)2.

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3) Dynamical Relativistic Effects – Enhancement of the lower components of the proton spinor inside the nucleus.

Relativistic DWIA: Nucleon current computed with a fully relativistic operator. The wave functions are four-component spinor solutions of the Dirac equation with scalar and vector potentials and their lower components are dynamically enhanced with respect to a solution of Dirac equation without potentials (a free spinor).

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) DESCRIPTION OF THE EXPERIMENTS 3 ) SIMULATION 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

The effect of spinor distortions is visible in ATL observable. This was seen in a previous Jlab experiment for the 1p1/2 shell in 16O, whose (relativistic) lower component is a 1s1/2 shell

Objectives of this Objectives of this (e,e’p) Experiment (III)(e,e’p) Experiment (III)

10

1) QUASIELASTIC (e,e’p) REACTION 2) SIMULATIONS 2) SIMULATIONS 3) DESCRIPTION OF THE EXPERIMENT4) DATA ANALYSIS5) RESULTS 6) SUMMARY AND CONCLUSIONS

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SpectrometerSpectrometerAcceptancesAcceptances

THEORETICAL CALCULATIONS:

Assume central values for the spectrometer

acceptances

EXPERIMENTS: Spectrometers with

significant angular and momentum

acceptances

1) Acceptance effects may be removed from data via stringent cuts (statistics suffer).2) Assuming factorization, acceptances effects can be removed via reduced cross section and significant cuts.3) Calculations may be averaged over acceptance (requires combination of theory and simulation).

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1 ) QUASIELASTIC (e,e’p) REACTION2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

MCEEPMCEEP

MCEEP (Monte Carlo for (e,e’p) experiments) is a simulation open source code written in Fortran. It was designed to simulate coincidence (e,e’X) experiments by averaging theoretical models over the experimental acceptances.

MCEEP employs a uniform random sampling method to populate the experimental acceptance.

It has an important limitation: it uses very simple models of the (e,e’p) reaction to avoid long computational time.

MCEEP V3.9 (June 2006) P. E. Ulmer et al.

http://hallaweb.jlab.org/software/mceep/mceep.html

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1 ) QUASIELASTIC (e,e’p) REACTION2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

MCEEPMCEEP + DWIA + DWIA

In an extended-acceptance experiment, each event can correspond to somewhat different kinematics. Evaluating the cross section with the DWIA code for each event simulated with MCEEP requires too much time.

In our approach the Response Functions (RL,RT,RLT,RTT), which contain the information of the nuclear charge and current densities, are precomputed in a grid (Emiss,pmiss,q,) which spans the experimental phase space.

After that, we interpolate within this grid in MCEEP for extracting the cross section on an event-by-event basis.

Radiation effects are included in MCEEP simulations than thus can be directly compared to data.

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1 ) QUASIELASTIC (e,e’p) REACTION2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Theory:Theory:IngredientsIngredients

208208PbPb 1212C C 1616O O Bound-nucleonwave function

HS NLSH NLSH-P

Optical model EDAI-PB EDAI-C EDAI-ONuclear spinor

distortionRelativistic and non-relativistic

(projected)Electron distortion (Can be included in simulation)

Kinematics RelativisticCurrent operator CC2

Nucleon form factors Rosenbluth data fitGauge Coulomb

15

1 ) QUASIELASTIC (e,e’p) REACTION2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1) QUASIELASTIC (e,e’p) REACTION 2) SIMULATION 3) DESCRIPTION OF THE EXPERIMENT3) DESCRIPTION OF THE EXPERIMENT4) DATA ANALYSIS5) RESULTS 6) SUMMARY AND CONCLUSIONS

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Experiment E00-102 Experiment E00-102 1616O(e,e’p)O(e,e’p)

Data acquisition October-December, 2001

Requirements Luminosity from H(e,e) Contamination from H(e,e’p)

events Low pmiss region not

available.

A continuation of experiment E89-003, which measured 16O(e,e’p)N cross section using a waterfall target.

In this experiment, the cross section was measured in the quasielastic peak (Q2=0.9GeV2, =0.5GeV) with a larger missing momentum range and much higher precision.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATION 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

17pmiss (MeV/c)

We measured 208Pb(e,e’p)207Tl and 209Bi(e,e’p)208Pb cross sections at true quasielastic kinem. (xB = 1, q = 1 GeV/c, ω = 0.433 GeV/c) and at both sides of q.

This has never been done before for A>16 nucleus. Additionally we measured 12C(e,e’p) as a reference.

Data acquisition RUN 1 – (March, 3-26, 2007) RUN 2 – (January 2008)

Requirements Good Energy Resolution Rastered Beam & Composed Target (Diamond+Pb+Diamond)

With correlations

Without correlations

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1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATION 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Experiment E06-007Experiment E06-007208208Pb(e,e’p),Pb(e,e’p),209209Bi(e,e’p) & Bi(e,e’p) & 1212C(e,e’p)C(e,e’p)

Experimental SetupExperimental Setupand Kinematicsand Kinematics

ELECTRONSPECTROMETER

PROTONSPECTROME

TER

BEAM LINE

TARGETCHAMBER

Q1 Q2 DIPOLE Q3

19

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATION 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

JLAB - Hall AJLAB - Hall A

Experimental Setup:Experimental Setup:4. - Kinematics4. - Kinematics

208208Pb(e,e’p) and Pb(e,e’p) and 1212C(e,e’p)C(e,e’p)1616O(e,e’p)O(e,e’p)20

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATION 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Experimental Setup:Experimental Setup: Targets: C+Pb+C Targets: C+Pb+C

Beam entrance Beam exit

Diamond/Lead/Diamond cryogenic target (for high beam current) 0.2 mm Lead Foil 0.15 mm Diamond Foils

BeO

C

Pb

Pb

Bi

BeO

C

Pb

Pb

Bi

Diamond 0.0465 g/cm2

Lead 0.194 g/cm2

Diamond 0.0395 g/cm2

21

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATION 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

TARGETS EXPERIMENT

E06-007

1) QUASIELASTIC (e,e’p) REACTION 2) SIMULATIONS 3) DESCRIPTION OF THE EXPERIMENT 4) DATA ANALYSIS4) DATA ANALYSIS5) RESULTS 6) SUMMARY AND CONCLUSIONS

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Acquired Data

Response Functions

(DWIA, CC2) (Relativistic &

Non-Relativistic

Measured Reduced Cross Section

and ATL

Simulated Reduced Cross Section

and ATL

LuminosityNormalization

EfficiencyCorrections

R-FunctionCuts

PS Criterium (PSbin > 50% PSmax)

ep for reduced

cross-sections

Cuts in Emiss Select shell

MCEEPROOT

File

Phase Space

SimulatedYield

MCEEP

Data Analysis:Data Analysis:StepsSteps

Data ROOT

File

RealYield

Hall A Analyzer

Calibration (Beam, Optics)

C++MACRO

Spect. Factors

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

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Beam Calibration:Beam Calibration:RasterRaster

To avoid melting the 208Pb target there exists a raster which spread the incident electrons in the whole target. The position of the beam with raster at each moment was known and it was taken into account in the event reconstruction.

Beam Parameters: Energy Position: (With and Without Raster, Width) Current

24

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Beam Calibration:Beam Calibration:CurrentCurrent

25

The number of incident electrons should be accurately measured. A correct beam charge calibration is crucial for luminosity determination.

Calibration measurements at different currents were done.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Target Center

Q1Q2

Dipole

Q3

VDC first plane(focal plane)

Particle trajectories

26

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Spectrometer Calibration:Spectrometer Calibration:Optics OptimizationOptics Optimization

Elastic 12C(e,e’) data used for optics calibration. The common optics calibration procedure in Hall A is based on a gradient-based 2 minimization (Optimize++):

The optics calibration was improved by developing a code based on a genetic algorithm for the 2 minimization. This way, all database coefficients could be optimized simultaneously and there were no problems with local minima.

27

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Spectrometer Calibration:Spectrometer Calibration:Optics OptimizationOptics Optimization

SIEVE SLITSIEVE SLIT

NO CALIBRATEDCALIBRATED

The angles measured by the spectrometers are calibrated using data acquired with a sieve slit plate placed at the detector’s entrance.

28

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Spectrometer CalibrationSpectrometer CalibrationOptics Optimization: AnglesOptics Optimization: Angles

Emiss (MeV)

ONLINE SPECTRU

M12C

208Pb

- With the optimized database and with the appropriate raster correction, good resolution has been achieved.

- Two peaks can be separated in this 208Pb Emiss spectrum (pmiss=0).

Ex (MeV) Shell

0 3s1/2

0.351 2d3/2

1.348 1h11/2

1.683 2d5/2

3.470 1g7/2

Low lying states in 207Tl

12C208Pb

OPTIMIZED

SPECTRUM

Emiss (MeV)29

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Spectrometer CalibrationSpectrometer CalibrationOptics Optimization: EnergyOptics Optimization: Energy

30

Calibrated CT spectrum for the experiment E06-007.

(12C, Kin7, pmiss= -300 MeV/c).Resolution 3 ns

Particles with different momentum and trajectory within the spectrometers will have a different time-of-flight (TOF). This effect can be corrected and the CT is improved.

A good coincidence time (CT) resolution is important to remove random coincidences, by applying a narrow cut in the CT peak.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Spectrometer Calibration:Spectrometer Calibration:Coincidence TimeCoincidence Time

Deadtime – Good events not recorded due to electronics or computer deadtime.

Trigger efficiency – Good events not detected by the scintillators. Obtained from redundant measurements.

Tracking efficiency – Good events not properly reconstructed from the VDC measurements. Obtained from the number of events reconstructed with unphysical values.

Proton absorption – Protons lost during interactions with material prior to detection.

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1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Efficiency correctionsEfficiency corrections

Measured data are corrected by efficiencies, dead-time, and random coincidences. All these events are histogrammed into the relevant variables

(Emiss,pmiss,q,,) and cross section is obtained as:

The phase-space volume of each bin is obtained with a simulation with uniform distribution over the acceptances.

32

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Data Analysis:Data Analysis: Cross-Section Cross-Section

1) QUASIELASTIC (e,e’p) REACTION 2) DESCRIPTION OF THE EXPERIMENT 3) SIMULATION 4) DATA ANALYSIS5) RESULTS 5) RESULTS 6) SUMMARY AND CONCLUSIONS

33

1212C(e,e’p) EC(e,e’p) Emissmiss

34

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Pmiss = 0-100MeV/c

35

Spec. factor = 0.85 0.05

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1212C(e,e’p) – 1pC(e,e’p) – 1p3/23/2 shell shell Reduced Cross SectionReduced Cross Section

36

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1212C(e,e’p) - 1pC(e,e’p) - 1p3/23/2 shell shellAATLTL

2 /DOF=1.59 (Rel.)2 /DOF=2.09 (No Rel.)

208208Pb(e,e’p) EPb(e,e’p) Emissmiss

37

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

38

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

208208Pb(e,e’p) – Valence States Pb(e,e’p) – Valence States Reduced Cross SectionReduced Cross Section

Simulations are based on DWIA (RMF) and do not include

correlations

39

Spectroscopic Factors

3s1/2

0.52 0.06

2d3/2

0.59 0.06

1h11/2

0.65 0.06

2d5/2

0.52 0.06

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

208208Pb(e,e’p) – Valence States Pb(e,e’p) – Valence States Reduced Cross SectionReduced Cross Section

Experimental 208Pb(e,e'p) reduced cross section (for the aggregate of valence states) together with the results from relativistic DWIA for the contributions from individual shells.

Spectroscopic Factors are obtained from a

(Emiss, pmiss) fit.

40

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

208208Pb(e,e’p) - Valence StatesPb(e,e’p) - Valence StatesAATLTL

2 /DOF=1.13 (Rel.)2 /DOF=2.65 (No Rel.)

SpectroscopicSpectroscopicFactorsFactors

-100 < pmiss < 100 MeV/cNucleus Shell

Spect. Factor

12C 1p3/2 0.85 (5)

208Pb

3s1/2 0.52 (6)

2d3/2 0.59 (6)

1h11/2 0.65 (6)

2d5/2 0.52 (6)

No dependence of the spectroscopic factors with Q2 has been found

Spectroscopic Factors for several shells in 16O measured at Q2=0.9 (GeV/c)2 and in 12C and 208Pb measured at Q2=0.8 (GeV/c)2.

41

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1616O(e,e’p) EO(e,e’p) Emissmiss

pmiss = 100-200 MeV/c

p1/2p1/2

p3/2 p3/2

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

42

43

Spec. factor = 0.71 0.05

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1616O(e,e’p) – 1pO(e,e’p) – 1p1/2 1/2 SHELL SHELL Reduced Cross SectionReduced Cross Section

44

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

1616O(e,e’p) – 1pO(e,e’p) – 1p1/2 1/2 SHELLSHELL AATLTL

2dof=1.27 (Rel.)

2dof=7.22 (No

Rel.)

1) QUASIELASTIC (e,e’p) REACTION 1) QUASIELASTIC (e,e’p) REACTION 2) SIMULATIONS 2) SIMULATIONS 3) DESCRIPTION OF THE EXPERIMENT 3) DESCRIPTION OF THE EXPERIMENT 4) DATA ANALYSIS4) DATA ANALYSIS5) RESULTS5) RESULTS 6) SUMMARY AND CONCLUSIONS6) SUMMARY AND CONCLUSIONS

45

SummarySummary

Two (e,e’p) experiments performed at JLab with 16O,12C and 208Pb targets have been analyzed. These experiments have measured the (e,e’p) reaction in perpendicular quasielastic kinematics with Q2~1.

In this talk, results in the pmiss range [-350,350] MeV/c are shown.

208Pb(e,e’p) data have been obtained for the valence states over more complete kinematics than previous experiments, measuring the ATL asymmetry for the first time are shown. 12C(e,e’p) data was also measured. In this talk, results from the knockout of protons from the p3/2 shell have been obtained.

Results of the p1/2 shell of 16O have been obtained with good statistical accuracy. 209Bi(e,e’p) measured data is under analysis.

46

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

ConclusionsConclusions

Experimental cross sections show good agreement in general with DWIA calculations. Spectroscopic factors of 0.6 to 0.85 have been obtained in the shells analyzed in all nuclei. Carbon and Lead results show that there is no significant dependence of spectroscopic factors with Q2 in the 0.8-2 (GeV/c)2 range. Simulations obtained from just relativistic mean field calculations (without long-range correlations included) seem to compare fairly well with data at both low and high missing momentum.

ATL data, which are sensitive to dynamical relativistic effects, clearly favors the results that include relativistic dynamics.

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

47

THANKS FOR THANKS FOR YOUR ATTENTION!YOUR ATTENTION!

CROSS SECTIONCROSS SECTION

The (e,e’p) cross section for a particular shell can be computed in general as a function of kinematical variables and the Response Functions RL,RT,RTL,RTT which contain the nuclear structure information.

1 ) QUASIELASTIC (e,e’p) REACTION2 ) SIMULATIONS 3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALISIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

49

Raster position cut – Required in 208Pb to remove those events that hit the frame.

50

1 ) QUASIELASTIC (e,e’p) REACTION 2 ) SIMULATIONS3 ) DESCRIPTION OF THE EXPERIMENTS 4 ) DATA ANALYSIS5 ) RESULTS 6 ) SUMMARY AND CONCLUSIONS

Efficiency correctionsEfficiency corrections