Coulomb Sum Rule Experiment

Seonho Choi Seoul National University

!June 25, 2014

Electron-Nucleus Scattering XIII, Isola d’Elba

1

Overview

• Probing nucleons in nuclei with electrons

• Quasi-elastic scattering and Coulomb Sum Rule

• One of the long standing puzzles in nuclear physics

• New experiment at JLab

• Preliminary results and summary

2

Electrons as a Probe

• Electron scattering has been an excellent tool to study properties of nucleons, nuclei etc.

• Charge/Magnetization distribution of various nuclei

• Elastic form factors of nucleons free or inside nuclei

• Surprises from JLab on

• Polarization transfer from 4He

3

µGpE/G

pM

QE Scattering

• Elastic scattering on bound nucleons

• We can study the nucleon properties inside the nucleus

• Scattering on the moving nucleons

• Response functions instead of Form Factors

4

Response Functions• Momentum

Transfer

• Energy Transfer

5

q = |k k|

= E E

d2

dd= Mott

Q4

q4RL(q,) +

Q2

2q2

1RT (q, )

=1 +

2q2

Q2tan2

1

Spin Structure

Seonho Choi

Introduction

Spin Structure of the

Nucleon

Interesting Quantities

Spin Structure atJefferson Lab

Experiments

Jefferson Lab

Results

Structure Function g1

Virtual Photon Asymmetry

Structure Function g2

Burkhardt-Cottingham Sum

Rule

Higher Twist Effects

Summary & Future

Backup

Kinematic Coverages

Polarized3He Target

Neutron Spin Structure

Functions

Spin Polarizabilities

Completed Experiments at

JLab

Future Experiments at JLab

Structure Functions

q = k - k’

k’

Xp

k !

! 4-momentum transfer

Q2 = −q2 = 4EE′ sin2 θ

2

! Energy transfer

ν = E − E′

d2σ

dΩdE′=

4α2E′2 cos2θ

2Q4

!

F2

ν+ 2

F1

Mtan2 θ

2

"

d2σ

dE′dΩ(↓⇑ − ↑⇑) =

4α2

MQ2

E′

νE

!

(E + E′ cos θ)g1 −Q2

νg2

"

d2σ

dE′dΩ(↓⇒− ↑⇒) =

4α2 sin θ

MQ2

E′2

E

1

ν2(νg1 + 2Eg2)

Response Functions

• Roughly RL corresponds to GE2!

• One complication: the separation of quasi-elastic and inelastic scattering is not a clear cut.

• Fortunately, inelastic scattering contributes mainly to RT, leaving RL mostly from quasi-elastic

6

d2

dd= Mott

Q4

q4RL(q,) +

Q2

2q2

1RT (q, )

Coulomb Sum

• Integral of RL to be compared to GE

• Denominator = contribution from electric form factors of protons and neutrons

7

SL(q) =

+el

dRL(q, )

ZGE2(Q2)

GE2(Q2) =

[Gp

E(Q2)]2 + (N/Z)[GnE(Q2)]2

1 + Q2/4M2

1 + Q2/2M2

Coulomb Sum Rule in One Page

• Coulomb Sum Rule

• SL(q)→1 at sufficiently large q*

• Deviation from unity

• at small q

• Pauli blocking

• NN long range correlations

• at large q(>>2kF)

• Short range correlations

• Nucleon properties in the nuclear medium

8

S(q)

1

q2kF

* McVoy and Van Hove, Physical Review 125, 1034 (1962)

Previous Measurements• For the past 30 years, a large experimental program

at Bates, Saclay and SLAC

• Saturation of the Coulomb sum still a puzzle

• Limited kinematic coverage in q and ω due to machine limitations

• Unresolved issue on the control of systematics

• background events for backward scattering

• Coulomb corrections

9

Existing Data for CSR

10

J. Morgenstern, Z.-E. Meziani / Physics Letters B 515 (2001) 269–275 273

Fig. 6. SL obtained in the EMA as a function of qeff usingonly Saclay data (a) and using Saclay data combined with SLACNE3 and Bates data with the new experimental setup (b). N–Mcalculations [38] (solid line), N–M calculations integrated within theexperimental limits: dashed line, same with modified form factors(dotted-dashed line), 208Pb H–F calculations [39] integrated withinthe experimental limits (thick right cross), same with modified formfactors (thin right cross). 56Fe SLAC NE9 [21] (filled circle) andJourdan analysis of 56Fe Saclay data (thick star) are shown in (b).

difference in RT between the previously publishedwork [19] and this analysis the conclusions regardingthe quenching of RL have not changed qualitatively.Fig. 5 also shows that combining the SLAC, Bates andSaclay data to extract RL and RT does not change theresults significantly. We also present in Fig. 5 ((b) and(c) panels) microscopic Nuclear Matter calculations(NM) of RL at 550 and 500 MeV/c [38] (dashedlines) and Hartree–Fock calculations (HF) of RL at500 MeV/c including short-range correlations andfinal-state interaction [39] (solid line). If the integratedstrengths of RL within the experimental limits arequite close (5% more strength for HF; see Fig. 6,compared to NM), the shapes are different. The largeenergy excitation tail of RL is much less important inthe HF than in the NM calculation. Finally, we plottedin Fig. 5(c) the HF calculation with a modified formfactor [40,41] (dotted-dashed curve) (discussed laterin the text) and find a fairly good agreement with thecombined Saclay and Bates-60 data (triangles down).We now turn to the results of the experimental

Coulomb sum but first discuss the quantitative differ-ence between the EMA analysis and that of Ref. [34]

as summarized in Table 1. A comparison between thepresent result of SL for 56Fe and that of Ref. [34] iden-tifies two possible sources for the difference; (a) theCoulomb corrections and (b) the use of the total er-ror in the Saclay data but only the statistical error inthe SLAC data. For (a), we believe that the Coulombcorrections used in [34] following the prescriptionof [31], at variance with the experimental confirmationof the EMA [33], have the wrong sign; they increasethe longitudinal response instead of decreasing it. TheCoulomb corrections within the EMA reduce SL by10% while it is increased by 5% in [34]. For (b), moreweight was given to the SLAC NE3 data by neglectingthe 3.5% systematic error quoted by the authors [36],leading to an artificial enhancement of RL by 4%.Fig. 6 shows the results obtained in the present

analysis for SL of 40Ca, 48Ca, 56Fe and 208Pb. InFig. 6(a) the data shown were obtained using onlycross section measured at Saclay, whereas in Fig. 6(b)the results by combining data from at least twodifferent laboratories among Bates, Saclay and SLACexcept for the data point from SLAC experimentNE9 at qeff = 1.14 GeV/c. Among the Bates crosssection data of 40Ca and 238U we chose to use onlythose measured at forward-angles with the modifiedexperimental setup. In order to evaluate SL we usedthe Simon [42] parametrization of the proton chargeform factor, while for the neutron charge form factorwe have taken into account the data by Herberg etal. [43]. We note that for 208Pb the total error inthe experimental determination of !VC is 1.5 MeVleading to a relative uncertainty of 2% on SL atqeff = 500 MeV/c. We have plotted the total NMCoulomb sum [44] (solid line), a partial NM Coulombsum integrated only within the experimental limits at400 ! qeff ! 550 MeV/c [38] (dashed curve) and apartial HF Coulomb sum in 208Pb integrated withinthe experimental limits at qeff = 500 MeV/c [39](thick right cross). The experimental results are to becompared with the partial sum and not the total sumvalues. We observe a quenching between 20% and30% in all medium and heavy nuclei.The observed quenching is similar to the quench-

ing of the ratio RL/RT observed in a 40Ca (e e′p) 39Kexperiment [45] which was performed at energy trans-fers ω near or below the maximum of the quasi-elasticpeak (ω " ωmax) where the quasi-elastic process isdominant. The observed quenching of RL/RT implies

J. Morgenstern, Z.-E. Meziani / Physics Letters B 515 (2001) 269–275 273

Fig. 6. SL obtained in the EMA as a function of qeff usingonly Saclay data (a) and using Saclay data combined with SLACNE3 and Bates data with the new experimental setup (b). N–Mcalculations [38] (solid line), N–M calculations integrated within theexperimental limits: dashed line, same with modified form factors(dotted-dashed line), 208Pb H–F calculations [39] integrated withinthe experimental limits (thick right cross), same with modified formfactors (thin right cross). 56Fe SLAC NE9 [21] (filled circle) andJourdan analysis of 56Fe Saclay data (thick star) are shown in (b).

difference in RT between the previously publishedwork [19] and this analysis the conclusions regardingthe quenching of RL have not changed qualitatively.Fig. 5 also shows that combining the SLAC, Bates andSaclay data to extract RL and RT does not change theresults significantly. We also present in Fig. 5 ((b) and(c) panels) microscopic Nuclear Matter calculations(NM) of RL at 550 and 500 MeV/c [38] (dashedlines) and Hartree–Fock calculations (HF) of RL at500 MeV/c including short-range correlations andfinal-state interaction [39] (solid line). If the integratedstrengths of RL within the experimental limits arequite close (5% more strength for HF; see Fig. 6,compared to NM), the shapes are different. The largeenergy excitation tail of RL is much less important inthe HF than in the NM calculation. Finally, we plottedin Fig. 5(c) the HF calculation with a modified formfactor [40,41] (dotted-dashed curve) (discussed laterin the text) and find a fairly good agreement with thecombined Saclay and Bates-60 data (triangles down).We now turn to the results of the experimental

Coulomb sum but first discuss the quantitative differ-ence between the EMA analysis and that of Ref. [34]

as summarized in Table 1. A comparison between thepresent result of SL for 56Fe and that of Ref. [34] iden-tifies two possible sources for the difference; (a) theCoulomb corrections and (b) the use of the total er-ror in the Saclay data but only the statistical error inthe SLAC data. For (a), we believe that the Coulombcorrections used in [34] following the prescriptionof [31], at variance with the experimental confirmationof the EMA [33], have the wrong sign; they increasethe longitudinal response instead of decreasing it. TheCoulomb corrections within the EMA reduce SL by10% while it is increased by 5% in [34]. For (b), moreweight was given to the SLAC NE3 data by neglectingthe 3.5% systematic error quoted by the authors [36],leading to an artificial enhancement of RL by 4%.Fig. 6 shows the results obtained in the present

analysis for SL of 40Ca, 48Ca, 56Fe and 208Pb. InFig. 6(a) the data shown were obtained using onlycross section measured at Saclay, whereas in Fig. 6(b)the results by combining data from at least twodifferent laboratories among Bates, Saclay and SLACexcept for the data point from SLAC experimentNE9 at qeff = 1.14 GeV/c. Among the Bates crosssection data of 40Ca and 238U we chose to use onlythose measured at forward-angles with the modifiedexperimental setup. In order to evaluate SL we usedthe Simon [42] parametrization of the proton chargeform factor, while for the neutron charge form factorwe have taken into account the data by Herberg etal. [43]. We note that for 208Pb the total error inthe experimental determination of !VC is 1.5 MeVleading to a relative uncertainty of 2% on SL atqeff = 500 MeV/c. We have plotted the total NMCoulomb sum [44] (solid line), a partial NM Coulombsum integrated only within the experimental limits at400 ! qeff ! 550 MeV/c [38] (dashed curve) and apartial HF Coulomb sum in 208Pb integrated withinthe experimental limits at qeff = 500 MeV/c [39](thick right cross). The experimental results are to becompared with the partial sum and not the total sumvalues. We observe a quenching between 20% and30% in all medium and heavy nuclei.The observed quenching is similar to the quench-

ing of the ratio RL/RT observed in a 40Ca (e e′p) 39Kexperiment [45] which was performed at energy trans-fers ω near or below the maximum of the quasi-elasticpeak (ω " ωmax) where the quasi-elastic process isdominant. The observed quenching of RL/RT implies

Morgenstern & Meziani PLB 515 (2001) 269

CSR Puzzle

• Early data show significant quenching of the CSR

• With the addition of forward angle data, some analysis claims no significant quenching

• Jourdan NPA 603, 117 (1996)

• Other, new analysis claims that quenching persists

• Morgenstern & Meziani, PLB 515, 269 (2001)

11

Major Issues of the CSR Experiments

• Coulomb Corrections

• Effect of the nuclear Coulomb field to the incoming and outgoing electrons

• Actual incident & scattered energy inside the nucleus are modified

• Corrections are necessary before the comparison of elastic & quasi-elastic

• Experimental Systematics

• Machine limitations (too low or too high)

• Relatively small lever arm for LT separation

• Control of background events in the detector

12

Coulomb Corrections• Up to now, two methods have been suggested

• Approximated Distorted Wave Impulse Approximation (DWIA) calculations

• Leading to LEMA(Local EMA)

• Jourdan, PLB 353(1995) 189, NPA603(1996) 117

• Approximate corrections via Effective Momentum Approximation (EMA)

• Morgenstern & Meziani, PLB 515, 269 (2001)

• To make things more complicated

• MIT/Bates experiments have used LEMA

• Saclay experiments used EMA

13

What is EMA?• Corrections to incident and scattered electron energies by

average potential

• Response functions after EMA corrections are

• Comparison of positron vs electron scattering on Pb nuclei

• P. Gueye et al., Physical Review C 60 044308 (1999)

14

VC

E Ee = E VC

E Ee = E VC

qe , Q2

e

d2

dd= Mott(E,E, )

Q4

e

q4e

RL(qe , ) +Q2

e

2q2e

1e

RT (qe , )

New Development on Coulomb Corrections

• 4 independent theory groups have worked on the subject

• A. Aste (Basel), K. Kim (Korea), J. Tjon (Maryland), J. Udias (Madrid), S. Wallace (Maryland), L. Wright (Ohio)

• Workshops organized by Jefferson Lab and College of William & Mary

• Mini-workshop on Coulomb Corrections (Mar. 2005)

• A session during JLab/INT workshop (Aug. 2005)

15

New Conclusions• EMA is a reasonable approximation, especially

• for medium-light nuclei

• for incident electron energies higher than 500 MeV

• EMA should be a reasonable approximation for Coulomb corrections up to 56Fe

• How good is EMA for RL in the case of 208Pb?

• For different nucleus, the effect goes roughly as

• Coulomb corrections significant

• Have to work with theorists

16

1 V (0)

E

2

References for CC

• Wallace & Tjon, PRC78, 044604 (2008)

• Aste, NPA806, 191 (2008)

• Benhar, Day & Sick, RMP 80, 189 (2008)

• Aste & Trautmann, EPJA33, 11 (2007)

• Tjon & Wallace, PRC74, 064602 (2006)

• Kim & Wright, PRC72, 064607 (2005)

• Aste, von Arx & Trautmann, EPJA26, 167 (1005)

17

* References only after 2005 CC Workshop have been listed.

New Experiment at JLab

• Beam: 16 energies from 0.4 to 4.0 GeV

• Scattering angles: 15o, 60o, 90o, 120o

• Targets: 4He, 12C, 56Fe, 208Pb

• Spectrometer momenta range from 4 GeV down to 100 MeV

• Covers q from 550 to 1000 MeV/c

18

Jefferson Lab / Experimental Hall A

AB

C

19

• Up to ~6 GeV polarized electron beam • 100 μA for Hall A / C • Now under 12 GeV upgrade with Hall D construction

Jefferson Lab Hall-A

20

Electron beam from the accelerator

Nuclear targetTwo spectrometers

To the beam dump

Spectrometer

21

Q1 Magnet

Detector Packages

Dipole Magnet

Q3 Magnet

Q2 Magnet

Path of scattered electrons

What’s New?

• Comfortable high values of q • From 550 MeV/c to 1000 MeV/c

• High enough for clean observation of CSR

• Previously unexplored region

• Comprehensive single experiment • Largest lever arm

• Measurement at 4 angles

• Better control of background with NaI detector

22

Kinematic Coverage

23

15o

120o90o

60o

0 200 400 600 800 1000

! (MeV)

0.4

0.6

0.8

1

1.2

1.4

q (

GeV

/c)

1.256 GeV

1.645 GeV

2.139 GeV

2.445 GeV

2.839 GeV

3.245 GeV

3.683 GeV

4.045 GeV

0 200 400 600 800 1000

! (MeV)

0.4

0.6

0.8

1

1.2

1.4

q (

GeV

/c)

0.400 GeV

0.528 GeV

0.645 GeV

0.739 GeV

0.845 GeV

0.959 GeV

1.028 GeV

0 200 400 600 800 1000

! (MeV)

0.4

0.6

0.8

1

1.2

1.4

q (

GeV

/c)

0.645 GeV

0.739 GeV

0.845 GeV

0.959 GeV

1.028 GeV

1.100 GeV

1.256 GeV

0 200 400 600 800 1000

! (MeV)

0.4

0.6

0.8

1

1.2

1.4

q (

GeV

/c)

0.400 GeV

0.528 GeV

0.645 GeV

0.739 GeV

0.845 GeV

0.959 GeV

(MeV)!0 100 200 300 400 500 600 700 800 900

)c| (

MeV

/ef

fq|

200

400

600

800

1000

1200

1400

°15

°60

°90

°120

=938/1232/1300 MeVW

Kinematic Coverage

24

Lever arm for Rosenbluth Separation

250 200 400 600 800 1000

ω (MeV)0.0

0.2

0.4

0.6

0.8

1.0∆ε

|q| = 550 MeV/c|q| = 750 MeV/c|q| = 900 MeV/c

NaI Detector

• Electrons reflected inside the spectrometer

• Source of background at low energy backward angle

• Reduction of the background

• Careful geometry cut at the focal plane

• Independent energy measurement of the electrons using NaI detector

26

NaI Detector

• NaI Crystal given from BNL

• About 400 crystals of 2.5”x2.5”x12”

• Refurbished at JLab: polishing, assembly in new boxes, sealing

• Final product: 3 boxes of 90 crystals (9x10 arrangement) each

• Covers whole focal plane of L-HRS

27

Installation of NaI detector

28

Performance

29

NaI Box 2 & 3 ADC sum0 50 100 150 200 250

Entri

es

10

210

310

410

Track Y Position (m)-0.03 -0.02 -0.01 0 0.01 0.02

Trac

k X

Posi

tion

(m)

-0.4

-0.2

0

0.2

0.4

NaI Box 2 & 3 ADC sum after Track XY cut0 50 100 150 200 250

Entri

es

0

200

400

600

800

1000

1200

1400

dp/p-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Entri

es

0

200

400

600

800

1000

1200

1400

1600

1800

2000

=97.84%75877423

=97.84%75877423

=98.91%69086833

• Blue: NaI Geometry Cut • Green: Cerenkov + NaI

PeopleKalyan Allada, Korand Aniol, John Arrington, Hamza Atac, Todd Averett, Herat Bandara,

Werner Boeglin, Alexandre Camsonne, Mustafa Canan, Jian-Ping Chen, Wei Chen, Khem Chirapatpimol, Seonho Choi, Eugene Chudakov, Evaristo Cisbani, Francesco Cusanno, Raffaele De Leo, Chiranjib Dutta, Cesar Fernandez-Ramirez, David Flay, Salvatore Frullani,

Haiyan Gao, Franco Garibaldi, Ronald Gilman, Oleksandr Glamazdin, Brian Hahn, Ole Hansen, Douglas Higinbotham, Tim Holmstrom, Bitao Hu, Jin Huang, Florian Itard, Liyang Jiang,

Xiaodong Jiang, Hoyoung Kang, Joe Katich, Mina Katramatou, Aidan Kelleher, Elena Khrosinkova, Gerfried Kumbartzki, John LeRose, Xiaomei Li, Richard Lindgren,

Nilanga Liyanage, Joaquin Lopez Herraiz, Lagamba Luigi, Alexandre Lukhanin, Maria Martinez Perez, Dustin McNulty, Zein-Eddine Meziani, Robert Michaels,

Miha Mihovilovic, Joseph Morgenstern, Blaine Norum, Yoomin Oh, Michael Olson, Makis Petratos, Milan Potokar, Xin Qian, Yi Qiang, Arun Saha, Brad Sawatzky,

Elaine Schulte, Mitra Shabestari, Simon Sirca, Patricia Solvignon, Jeongseog Song, Nikolaos Sparveris, Ramesh Subedi, Vincent Sulkosky,Jose Udias, Javier Vignote,

Eric Voutier, Youcai Wang, John Watson, Yunxiu Ye, Xinhu Yan, Huan Yao, Zhihong Ye, Xiaohui Zhan, Yi Zhang, Xiaochao Zheng, Lingyan Zhu

and Hall-A Collaboration

30

Students Post-docs Run Coordinators Collaborators Spokespersons

Data Taking

• Dates: Oct. 23, 2007 - Jan. 16, 2008 86 calendar days - 2 holiday shutdowns

• Data taken: about 3TB over 7000 runs

• Most of the runs are 5 minutes long

• Frequent changes of target and spectrometer momentum

31

Analysis• Measurement of absolute cross sections

• Comparison of two absolute cross sections for two different kinematic conditions

• Forward vs backward angle

• High vs low beam energy

• Almost two extremes of spectrometer momentum configuration

• Finally subtraction of two large numbers to find the small difference

32

Spectrometer Optics Calibration

33

7-foil Carbon targetSieve Slit

Spectrometer Optics

34

-0.1 -0.05 0 0.05 0.10

100

200

300

400

500

600

ReactZ h_reactzEntries 775149Mean -0.01628RMS 0.06916

ReactZ

Phi_tg-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Thet

a_tg

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Foil 4 for Run 1292 h_theta_tg_vs_phi_tg_4Entries 5419Mean x -0.006788Mean y -0.008721RMS x 0.01011RMS y 0.02833

h_theta_tg_vs_phi_tg_4Entries 5419Mean x -0.006788Mean y -0.008721RMS x 0.01011RMS y 0.02833

Foil 4 for Run 1292

Phi_tg-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Thet

a_tg

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Foil 4 for Run 1292 h_theta_tg_vs_phi_tg_4Entries 5633Mean x -0.004972Mean y -0.007006RMS x 0.01042RMS y 0.02801

h_theta_tg_vs_phi_tg_4Entries 5633Mean x -0.004972Mean y -0.007006RMS x 0.01042RMS y 0.02801

Foil 4 for Run 1292

-0.1 -0.05 0 0.05 0.10

100

200

300

400

500

600

ReactZ h_reactzEntries 772727Mean -0.01623RMS 0.07203

ReactZ

Before Optimization

After Optimization

Red lines: Surveyed positions and angles of the target and slit holes

Spectrometer Acceptance

• Realistic acceptance with full simulation considering

• Effect of energy loss

• Multiple coulomb scattering

• Detector resolutions

35

Spectrometer Acceptance

36

With Realistic Acceptance

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

With Geometrical Acceptance

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800D

iffer

entia

l Cro

ss S

ectio

n (n

b/G

eV/s

r)0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

E' (MeV)2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Comparing w/o Acceptance Correction

2200 2300 2400 2500 2600 27000

2

4

6

8

10

12

14

-3310!

° = 15"E = 2845 MeV,

2200 2300 2400 2500 2600 2700

-10

-5

0

5

10

Difference in %E' (MeV)

2200 2300 2400 2500 2600 2700 2800

Diff

eren

tial C

ross

Sec

tion

(nb/

GeV

/sr)

0

2

4

6

8

10

12

14

310!

°2845 MeV, 15

Elastic Cross Sections

37

(fm)effq0.5 1 1.5 2 2.5 3

devi

atio

n fro

m b

est f

it

-610

-510

-410

-310

-210

-110

1 e-C Elastic Scattering

PRELIMINARY

LT Separation

38

6 /1 =5

U60 +

5

U68

(MeV)ω0 100 200 300 400 500

(1/G

eV)

εΣ

0

2

4

6

8

10

156090120

6 = 5

U60 +

5

U68

Slope Intercept

=

+

(/)

12C q=650MeV/c

PRELIMINARY

LT Separation

39

ε0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(1/G

eV)

εΣ

7

7.5

8

8.5

9

9.5

10

=230ωq=650, 0.12(st)+ 0.30(sy)±= 3.66LR 0.15(st)+ 0.29(sy)±=16.60TR

ε0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(1/G

eV)

εΣ

7

7.5

8

8.5

9

9.5

10

=230ωq=650, 0.12(st)+ 0.30(sy)±= 3.66LR 0.15(st)+ 0.29(sy)±=16.60TR

12C q=650 MeV/c ω=230 MeV

15

60

120

90

PRELIMINARY

LT Separation

40

ε0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(1/G

eV)

εΣ

5

5.5

6

6.5

7

7.5

=170ωq=650, 0.07(st)+ 0.20(sy)±= 2.66LR 0.11(st)+ 0.21(sy)±=11.02TR

ε0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(1/G

eV)

εΣ

5

5.5

6

6.5

7

7.5

=170ωq=650, 0.07(st)+ 0.20(sy)±= 2.66LR 0.11(st)+ 0.21(sy)±=11.02TR

12C q=650 MeV/c ω=170 MeV

15

60

120

90

PRELIMINARY

LT Separation

41

ε0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(1/G

eV)

εΣ

5.5

6

6.5

7

7.5

=290ωq=650, 0.12(st)+ 0.27(sy)±= 3.08LR 0.15(st)+ 0.24(sy)±=14.26TR

ε00.10.20.30.40.50.60.70.80.91

(1/GeV

)εΣ

5.5

6

6.5

7

7.5

=290 ω q=650, 0.12(st)+ 0.27(sy) ± = 3.08 L R 0.15(st)+ 0.24(sy) ± =14.26 T R

12C q=650 MeV/c ω=290 MeV

15

60

120

90

PRELIMINARY

Expected Error

42

200 400 600 800 1000 1200qeff (MeV/c)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2S L

(qef

f)

3He 40Ca 56Fe 208Pb 56Fe 56Fe Expected Error on 56Fe

Summary• Precision measurement of RL and RT over the QE scattering range

• Momentum transfer: 550 MeV/c - 1000 MeV/c

• On four nuclei: 4He, 12C, 56Fe and 208Pb

• Analysis in the final stage

• Checking systematic errors etc

• Cross check from two independent analyses

• Absolute cross section measurement

• Cross check with e-C elastic etc

• Help solve the puzzle on Coulomb Sum Rule

• Learn properties of nucleon inside the nuclear medium

43