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Zhihong Ye University of Virginia E08014 Collaboration, Hall-A, JLab Spokespersons: John Arrington, Donal Day, Doug Higinbotham, Patricia Solvignon Study of Short Range Correlations at x>2

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Outline Overview of Nuclear Structure Short Range Correlations E08-014 Experiment in Hall-A @JLab Data Analysis Preliminary Ratio Summary

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A nucleus is a very complicated system Many-body problem: Impossible to directly solve the wave-functions: Overview of Nuclear Structure A dilute nuclear medium Long-Rang Weak Abstraction Tensor Force Repulsive cores Two-Nucleon Interactions Woods-Saxon Potential Mean free path (1.7 fm) is larger than the typical nuclear radius (1.0 fm) Special nucleon-nucleon potentials

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Mean Field Theory (Shell Model): Nucleons move independently in an average potential induced by the surrounding nucleons; Occupying separated energy shells bellow Fermi sea: Predicting nucleons eigen-states and magic numbers. Overview of Nuclear Structure Energy Shells and Magic Number

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Mean Field Theory (Shell Model): Nucleons move independently in an average potential induced by the surrounding nucleons; Occupying separated energy shells bellow Fermi sea: Predicting nucleons eigen-states and magic numbers. Overview of Nuclear Structure Missing Strength: The Spectroscopy Factor should equal to the number of states a nucleon is allowed to occupied: Proton knock-out experiments show 30% -- 40% missing lower than the mean field prediction; Can’t be explained by advanced Hartree-Fock calculation including long range interactions. j number of “shells”

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Strong repulsive force at short-distance (<1 fm); High relative momenta; Zero total momentum. Similar shape for High momentum tails (k>k Fermi ). Short Range Correlations C. Ciofi degli Atti and S. Simula, Phys. Rev. C 53 (1996). Attribute to the missing strength: Slow decreasing momentum distribution is responsible for the missing strength.

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Attribute to the missing strength: Strong repulsive force at short-distance (<1 fm); High relative momenta; Zero total momentum. Similar shape for High momentum tails (k>k Fermi ). C. Ciofi degli Atti and S. Simula, Phys. Rev. C 53 (1996). High-momentum region: SRCs dominated. Mean Field Region k fermi 2N-SRC dominates at 300 < k < 600 MeV/c scaled to Deuterium 3N-SRC dominates at k – 800 MeV/c scaled to He3; Non-Nucleonic D.O.F at extremely high momentum (Dense nuclear matter such as Neutron Stars). p p p p n n 1.7 fm < 1.0 fm p p p p n n 2N-SRC3N-SRC Short Range Correlations

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Probing SRCs with A(e,e’): Short Range Correlations At Quasi-Elastic (QE) Region (PWIA): Extract momentum distribution: Inclusive Cross Section in SRCs (for x bj >1.3): 2N-SRC (1.3<x bj <2) 3N-SRC (2<x bj <3) Scaling (independent of x bj and Q 2 ):

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Probing SRCs with A(e,e’): Short Range Correlations k>k Fermi : No Mean Field contribution; q 0 >>V NN, q>>m N /c : Instantly removes SRCs from intact nucleus; Kinematics conditions to isolate SRCs: Benhar, Day, Sick, Rev. Mod. Phys. 80, 189 (2008) Q 2 >1 GeV : Suppress FSI and MEC; x bj >1.3 : No Inelastic processes contribution; Directly probe high momentum tails.

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Frankfurt, Strikman, Day, Sargsian, PRC48, 2451 (1993) K. Egiyan et al, PRL96, 082501 (2006) CLAS & E02-019 results: Agreement for xbj <2 region Different onset values for 3N plateau CLAS: Q 2 ≈ 1.6 GeV 2, E02-019: Q 2 ≈ 2.7 GeV 2 Large error bars at 3N-SRCs for E02-019 N. Fomin et al, PRL 108,092502 (2012) Previous results of A(e,e’): Short Range Correlations

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Isospin Effect in SRCs: Short Range Correlations Lines np pairs; Dots pp pairs R. Schiavilla et al, PRL98, 132501 (2007) The abstractive NN interaction is mainly due to Tensor Force. In 2N-SRC, iso-singlet np pairs (T=0) dominates. Hall-A results shows 80% of 2N-SRC in np pairs. 2N-SRC R. Subedi et al, Science, 320 1476 (2008) Study in Inclusive measurement: E08-014 using Ca48/Ca40 New Hall-A experiment using He3/H3 : E12-11-112, P. Solvignon, J. Arrington, D. Day, D. Higinbotham

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EMC vs SRCs: J. Arrington et al., PRC 86, 065204 (2012) L. Weinstein et al, PRL 106, 052301 (2011) O. Hen et al, PRC 85, 047301 (2012) D.O.F: Nucleus -> Nucleon -> Quarks&Gluons ? Data contributed by JLab: Egiyan, et al. (2006 PRL, Hall B) J. Seely, et al. (2009, Hall C) N. Fomin, et al. (2012, Hall C) And SLAC data Understanding how EMC connects to SRCs will be one of the major studies in 12 GeV. Short Range Correlations (Several experiments to systematic study EMC and SRC have been approved in Hall-C)

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Study the onset of 3N-SRC scaling plateau at x>2; Extract absolute cross section to study momentum distribution, FSI, etc; E08-014 Experiment in Hall-A@JLab

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Study the onset of 3N-SRC scaling plateau at x>2; Extract absolute cross section to study momentum distribution, FSI, etc; Isospin effect at SRCs (Ca40 & Ca48) Theory of SRCs assumes Isospin independent; For 2N-SRC, n-p (T=0) pairs dominate. 25% difference E08-014 Experiment in Hall-A@JLab E12-11-112 using H3/He3: 40% difference, no mass difference

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E08-014 Experiment in Hall-A@JLab Configurations: Un-polarized Electron Beam at 3.356 GeV; Two HRSs taking data Simultaneously; Standard Detector Packages; One DAQ system. Modified Triggers: T1&T3: S1 + S2m + GC, main production triggers. T6&T7: S1 + S2m, for efficiencies and PID study. T3&T4: Efficiencies Study Mis-Match RQ3 HRS-R Q3 was scaled down to 87.72% due to a power supply problem. Targets: Cry-Targets: LH2, He3, He4 Non-uniform density (“bump”)! Solid Targets : C12, Ca40, Ca48, and other calibration targets. Kin3.1 Kin3.2 Kin4.1 Kin4.2 Kin5.1 Kin5.2 Kin5.0 Kin6.5 Kin5.05 E0 = 3.356GeV First time used in Hall-A

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The flow-chart to extract inclusive cross sections Initial Raw Data Reply Beam Calibration (BCM, BPM, Raster) Beam Calibration (BCM, BPM, Raster) Detector Calibration (VDC, Scin, GC, Calo) Detector Calibration (VDC, Scin, GC, Calo) Optics Calibration PID Cuts Study Detectors’ Efficiencies Detectors’ Efficiencies Final Raw Data Reply Several Raw Data Reply Target Density (Boiling, Thickness) Target Density (Boiling, Thickness) Live Time Kinematics Settings Electron Charge Cuts Binning Yield_EX Monte Carlo Simulation (SAMC) Wider Acceptance than HRSs Non Uniform Cryo-Target Correction Reconstructed DeltaP Correction Reconstructed DeltaP Correction Cross Section Model (XEMC) σ DIS F1F2IN09 σ QE F(y) Radiation Correction Cuts Binning σ Born σ Radiated Target Luminosity Yield_MC Other Corrections Iterating Cross Section Models Efficiencies E08-014 Data Analysis Experimental Data Analysis Ratio

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The flow-chart to extract inclusive cross sections Initial Raw Data Reply Beam Calibration (BCM, BPM, Raster) Beam Calibration (BCM, BPM, Raster) Detector Calibration (VDC, Scin, GC, Calo) Detector Calibration (VDC, Scin, GC, Calo) Optics Calibration PID Cuts Study Detectors’ Efficiencies Detectors’ Efficiencies Final Raw Data Reply Several Raw Data Reply Target Density (Boiling, Thickness) Target Density (Boiling, Thickness) Live Time Kinematics Settings Electron Charge Cuts Binning Yield_EX Monte Carlo Simulation (SAMC) Wider Acceptance than HRSs Non Uniform Cryo-Target Correction Reconstructed DeltaP Correction Reconstructed DeltaP Correction Cross Section Model (XEMC) σ DIS F1F2IN09 σ DIS F1F2IN09 σ QE F(y) σ QE F(y) Radiation Correction Cuts Binning σ Born σ Radiated Target Luminosity Yield_MC Other Corrections Iterating Cross Section Models Efficiencies E08-014 Data Analysis Experimental Data Analysis Ratio To be discussed.

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Cross Section Package - XEMC: Several Born Cross Section Models coded; Radiation Correction Subroutines; Stand alone subroutines in C++, easily included by other codes; (Tech note is available). E08-014 Data Analysis - XEMC

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Cross Section Package - XEMC: Quasi-Elastic Cross Section: (1), XEM -- F(y) Function, from Hall-C EMC&X>1 collaboration (from D. Gaskell, N. Fomin, etc.). Converted into C++. Parameters are updated by fitting data from E02-019 (2), QFS -- From Temple Univ. group (K. Slifer, D. Flay, H. Yao, etc.); (3), F1F2QE09 -- P. Bosted and V. Mamyan In FORTRAN – f1f209.f (arXiv:1203.2262v2). Born Cross Section Models: Several Born Cross Section Models coded; Radiation Correction Subroutines; Stand alone subroutines in C++, easily included by other codes; (Tech note is available). E08-014 Data Analysis - XEMC

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Cross Section Package - XEMC: Quasi-Elastic Cross Section: (1), XEM -- F(y) Function, from Hall-C EMC&X>1 collaboration (from D. Gaskell, N. Fomin, etc.). Converted into C++. Parameters are updated by fitting data from E02-019 (2), QFS -- From Temple Univ. group (K. Slifer, D. Flay, H. Yao, etc.); (3), F1F2QE09 -- P. Bosted and V. Mamyan In FORTRAN – f1f209.f (arXiv:1203.2262v2). Inelastic Cross Section: (a), XEM - F1F2IN06 (P. Bosted & E. Christy) + special corrections in different regions (b), QFS - DIS + Delta + Resonances + DIP (c), F1F2IN09 - P. Bosted and V. Mamyan – f1f209.f Born Cross Section Models: Several Born Cross Section Models coded; Radiation Correction Subroutines; Stand alone subroutines in C++, easily included by other codes; (Tech note is available). E08-014 Data Analysis - XEMC

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Cross Section Package - XEMC: Quasi-Elastic Cross Section: (1), XEM -- F(y) Function, from Hall-C EMC&X>1 collaboration (from D. Gaskell, N. Fomin, etc.). Converted into C++. Parameters are updated by fitting data from E02-019 (2), QFS -- From Temple Univ. group (K. Slifer, D. Flay, H. Yao, etc.); (3), F1F2QE09 -- P. Bosted and V. Mamyan In FORTRAN – f1f209.f (arXiv:1203.2262v2). Inelastic Cross Section: (a), XEM - F1F206 F1F206 (P. Bosted & E. Christy) + special corrections in different regions (b), QFS - DIS + Delta + Resonances + DIP (c), F1F2IN09 - P. Bosted and V. Mamyan – f1f209.f Born Cross Section Models: Several Born Cross Section Models coded; Radiation Correction Subroutines; Stand alone subroutines in C++, easily included by other codes; (Tech note is available). E08-014 Data Analysis - XEMC In E08-014 analysis, XEM + F1F2IN09 were used

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Comparing with E02-019 data from Hall-C: He3 Red dots -> Exp. Blue dots -> XEMC C12 E08-014 Data Analysis - XEMC D2 He4

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He3 Red dots -> Exp. Blue dots -> XEMC C12 E08-014 Data Analysis - XEMC D2 He4 Comparing with data from QE-Archive: (D. Day, Rev. Mod. Phys. 80, 189-224, 2008)

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Radiation Correction: Basic Idea: Mo&Tsai Rev. Mod. Phys. 41. 205 (1969), S. Stein et al, Phy. Rev. D 12 1884 (1975) Old XEM code has a Radiation Correction subroutine with full radiation tail integrals (but in FORTRAN, specified for x<1, and runs very slow). Peak-Approximation method based on subroutines from RadCor package (from Temple Univ.). NEED Plots here!!! E08-014 Data Analysis - XEMC Comparing with E02-019 Radiated Cross Sections He3C12

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E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Focal Plane Target Plane Q1 Q2 Dipole Q3 Optics Calibration:

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E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Ideally Focal Plane Target Plane Practically Q1 Q2 Dipole Q3 Optics Calibration: An optics calibration procedure is to obtain the parameters in the polynomial functions.

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E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Ideally Focal Plane Target Plane Sieve Slit Practically Q1 Q2 Dipole Q3 Optics Calibration: An optics calibration procedure is to obtain the parameters in the polynomial functions. Calibration Data: Unrastered Beam, QE region, 7-foils carbon targets, Sieve Slit Plate; & Survey reports.

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E08-014 Data Analysis - Optics Beam -7.5 -5.0 -2.5 0 2.5 5.0 7.5 (cm) Ideally Focal Plane Target Plane Sieve Slit Practically Q1 Q2 Dipole Q3 Optics Calibration: LHRS: Initial optics works well; only updated with offsets. An optics calibration procedure is to obtain the parameters in the polynomial functions. Calibration Data: Unrastered Beam, QE region, 7-foils carbon targets, Sieve Slit Plate; & Survey reports.

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E08-014 Data Analysis - Optics Good: a)Only need one set of optics matrix b)SNAKE can easily reproduce Bad: Bad reconstruction using an initial optics matrix, and more … Reconstructed with original optics! Target Vertex Sieve Slit Pattern Optics Calibration - RHRS: Scaled down Q3 field by 87.72% for each HRS central momentum setting.

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E08-014 Data Analysis - Optics Good: a)Only need one set of optics matrix b)SNAKE can easily reproduce Bad: Bad reconstruction using an initial optics matrix, and more … Optics Calibration - RHRS: Scaled down Q3 field by 87.72% for each HRS central momentum setting. Reconstructed with new optics! Target Vertex Sieve Slit Pattern Remain Issues: Unknown DeltaP optics (could not take the calibration data since ran at QE region). Additional DeltaP Correction using Monte Carlo Simulation.

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DeltaP Correction for HRS-R Data: Two sets of RQ3 “DeltaP-Optics” in SAMC: “Old” -> DeltaP functions with Q3 field equal to Dipole field; “New” -> DeltaP functions with Q3 field equal to 87.72% of Dipole field. In SAMC, generating two sets of data with the same seeds: 1, New Forward + Old Backward Simulate the REAL DeltaP reconstruction on HRS-R (δp wrong ); 2, New Forward + New Backward Simulate the CORRECTED DeltaP reconstruction (δp right ). but wrong! E08-014 Data Analysis -DeltaP HRS Optics Polynomials functions Transportation functions in SNAKE Forward transportation Functions: Target Plane Focal Plane Backward transportation Functions: Focal Plane Target Plane Asked John LeRose to generate new transportation functions for HRS-R, with Q3 field scaled down by 87.72% compared to Dipole field. 31

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DeltaP Correction for HRS-R Data: higher order residuals Correcting Data by defining the polynomial correction function E08-014 Data Analysis -DeltaP 32

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DeltaP Correction for HRS-R Data:.vs. x fp.vs. θ fp.vs. y fp.vs. ϕ fp.vs. δp old higher order residuals Correcting Data by defining the polynomial correction function: δp right - δp wrong E08-014 Data Analysis -DeltaP Using MC (Data#1 & Data #2); Fitting the correction function by correlating with focal plane variables: δp right - δp wrong 2-D Profile-Y Residual From MC data, the correction function can recover DeltaP reconstruction as good as near 0.03%. 33

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DeltaP Correction for HRS-R Data: E08-014 Data Analysis -DeltaP Apply the correction function on experimental data 34 Conclusion: 1, HRS optics with distorted Q3 field still can be extracted (need a good optics run plan); 2, Gain additional Yields due to Q3 enlarging the acceptances (Q3 -13% +5% Yield); 3, Pay attention to the acceptance effect.

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Cryo-Target Density Uniformity Cryogenic Coolant distribute along 20 cm cells; Non-uniform target density on H2, He3 and He4 targets; Higher current, bigger effect (bump!). Problem: Hard to evaluate target luminosity; Complicated boiling effect correction; Complicated radiation corrections. 20 cm Cryogenic flow Beam E08-014 Data Analysis - Target Warmer! For LH2 (7 K), He3 (20 K), and He4 (20 K)

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In Real Data: 1-D histogram for Z react (Vertex Z) distribution (includes the density distribution, cross section weighting and the acceptance effects). In MC Data: 1-D histogram for Z react assuming the target density is uniform, and weighted by cross section model (only the cross section weighting and the acceptance effects). Extract the distribution: 2 histograms with the same range and bin, normalize the statistics, and then take the ratio: Extract the density distribution from data: E08-014 Data Analysis - Target Red-> Real Data Blue -> MC Data (Cross Section Weighted) Absolute density at the entrance or exit of cells can be calculated from pressure and temperature readings.

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In Real Data: Z react (Vertex Z) distribution includes the density distribution and the acceptance effects. In MC Data: Assuming the target density is uniform, Z react (Vertex Z) distribution includes only the acceptance effects. Extract the distribution: Plot the histogram of Z react for Real data and MC data with the same range and bin, normalize the statistics, and take the ratio of two histograms: Extract the density distribution from data: E08-014 Data Analysis - Target Absolute density at the entrance or exit of cells can be calculated from pressure and temperature readings.

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Extract the density distribution from simulation: (by Silviu Covrig ) E08-014 Data Analysis - Target Cryogenic target density is important when taking cross section ratio of solid targets to long targets. Big systematic errors to extract target density using data and MC. Running a cryogenic target system simulation for LH2, He3 and He4. Target info, such as design, temperature, pressure and current, etc, are provided by Dave Meekins. Graphics provided by Silviu LD2 Flow in the cell LD2 Density in the cell

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Boiling Effect Study: (by Patricia Solvignon) Density changes at different beam currents: H2He3He4 20cm Cryo-Targets -> Density varies along target length (VZ); Boiling effect varies too, H2He3He4 Yield Slope Boiling(%) E08-014 Data Analysis - Target

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1, Radiation Length is calculated at the center of the target with uniform density. 2, For non-uniform targets, Radiation Correction (RC) differs in reaction locations and paths. 3, Bin on VZ, calculate RC in each location and statistically weight the total RC). RC depends on the location of reactions. Radiation Correction with Non-Uniform Target: E08-014 Data Analysis - Target

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Extracting Cross Sections Experimental differential cross section: (binning in E’, then calculating xbj))

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Experimental Yield: -- Total events in ith bin; -- Total electron charge; -- Total Detectors’ efficiencies. Extracting Cross Sections Experimental differential cross section: (binning in E’, then calculating xbj)

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Experimental Yield: -- Total events in ith bin; -- Total electron charge; -- Total Detectors’ efficiencies. Monte Carlo Yield: -- Total target luminosity; -- Total generated MC events; - Entire phase space in MC (slight larger than HRS) - Radiated Cross Section Sum of all events in each bin Extracting Cross Sections Experimental differential cross section: (binning in E’, then calculating xbj)

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Experimental Yield: -- Total events in ith bin; -- Total electron charge; -- Total Detectors’ efficiencies. Monte Carlo Yield: -- Total target luminosity; -- Total generated MC events; - Entire phase space in MC (slight larger than HRS) - Radiated Cross Section Sum of all events in each bin Extracting Cross Sections Experimental differential cross section: Advantage of Yield Ratio: Study the acceptance effect; Check the difference between data from two HRSs before combining them; Experimental Yield remain untouched, but only apply correction on MC Yield and iterate the XEMC model until the ratio close to one; Reduce model dependence. (binning in E’, then calculating xbj)

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Extracting Cross Sections Cuts & Efficiencies VDC One-Track-Only Cuts (> 99%); Trigger Cuts (>99% since GC included); PID Cuts (very loose cuts, 99% for GC, 99% for Calo); Focal Plane Variables Cuts (removing big-angle events); 20cm Cryo-Target End-Cup Cuts: No dummy subtraction since using long 20cm target cell and good optics reconstruction. Target Plane Acceptance Cuts: (using very tight cuts, will open up when other effects are cleaned); Beam Trip Cuts: Removing events taken during beam trip. Errors Statistic Errors and Systematic Errors from Detectors are included; Final evaluation of Total Errors will be proceeded.

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Extracting Cross Sections 21 0 23 0 25 0 Yield Ratio Y EX /Y MC Preliminary Preliminary Cross Section Results: (He3)

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Extracting Cross Sections 21 0 23 0 25 0 Preliminary Preliminary Cross Section Results: (He4) Yield Ratio Y EX /Y MC

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Extracting Cross Sections Preliminary Cross Section Results: (C12) 21 0 23 0 25 0 Yield Ratio Y EX /Y MC Preliminary

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Extracting Cross Sections Preliminary Cross Section Results: (Ca40 & Ca48) Ca40 Target Thickness not yet fully determined. First High-Q2 cross section for Ca40&Ca48; Need more work on the cross section model. Very Preliminary

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Preliminary Ratio Preliminary E08-014 agrees with E02-019. C12/He3 Ratio (Comparing with E02-019 ):

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Preliminary Ratio Preliminary He4/He3 Ratio (Comparing with CLAS E02-019 ): No 3N-SRC Plateau? Can’t conclude yet!

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Summary SRCs attribute to the 30% - 40% missing strength in nuclei predicted by Mean Field Theory Inclusive QE electron scattering provide a clean tool to probe 2N-SRC, 3N-SRC. E08014 aims to verify the onset of 3N-SRC at x>2 and study Isospin dependence using Ca40 and Ca48. Data analysis is nearly completed. Final results will be available soon. To Do: (1) Cryo-Targets Simulation, (2) Re-measure Ca40 Thickness (3) Iterate Cross Section Model, (4) Evaluate Systematic Errors Several new experiments in Hall-A and Hall-C will continue on studying isospin effects of SRCs and connections between EMC effect and SRCs.

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