1. 1 March 2006 Nikolas Meitanis

2. 2 Outline  Theoretical Framework  Experimental Apparatus  Data Analysis  Results and Conclusion

3. 3 THEORETICAL FRAMEWORK

4. 4 Motivation Importance of Nucleon Form Factors  Fundamental quantities: describe electro-magnetic structure  Tests of theoretical calculations  Necessary for parity-violation experiments NOTE: Due to the absence of free neutron targets: Neutron form factors known less precisely compared to proton.

5. 5 Electron-Nucleon Elastic Scattering Unpolarized target: Rosenbluth cross section Mott cross section: (spin ½ electron, spinless+structureless nucleon) Polarized target:

6. 6 Electron-Nucleon Elastic Scattering Forming asymmetries: Asymmetry in terms of Sachs form factors: ( θ *, φ * ) : Angles between the target polarization and the momentum transfer vector. θ* = 0 deg. : parallel kinematics θ* = 90 deg. : perpendicular kinematics.

7. 7 Electron-Deuteron Elastic Scattering Unpolarized Cross Section Polarized Cross Section Deuteron Properties: Simplest nuclear system in nature Spin 1, Isospin 0 Proton and Neutron loosely bound, spins aligned Ground state: admixture of S and D

8. 8 Electrodisintegration  QE: Special case of electrodisintegration  QE: Electron scatters off single nucleon  PWBA: No excited states, no FSI Polarized cross section Beam-target vector asymmetry EXCLUSIVE: both scattered electron and hadron detected. Scattering off either proton or neutron. Quasi-Elastic

9. 9 Inclusive Electron-Deuteron Quasi-elastic Scattering Beam-target vector asymmetry 10 Structure Functions remaining after integration. Only electron detected. Cross section derived from integral of exclusive structure functions over n-p phase space. This asymmetry exhibits sensitivity to G M n in the inclusive electro- disintegration reaction of polarized electrons and polarized deuterium. NEW MEASUREMENT.

10. 10 Sensitivity to G M n ASYMMETRIES NOTE: Asymmetries vary with opposite sign in the two sectors. This can be exploited in a linear combination of the two. Polarized deuteron: Incoherent sum of pol. neutron and pol. proton

11. 11 Sensitivity to G M n (2) Same sensitivity across W spectrum.

12. 12 Sensitivity to G M n (3) The ratio enhances sensitivity to the form factor. The form factor enters the ratio squared. RATIO OF ASYMMETRIES

13. 13 Calculation by H. Arenhovel Incorporated in Monte Carlo. Friedrich & Walcher form factors for proton, Galster form factor for GEn. Incorporates: 1. Final State Interactions (FSI) 2. Meson Exchange Currents (MEC) 3. Isobar Configurations (IC) 4. Relativistic Corrections (RC) A model of Deuteron structure using the Bonn potential.

14. 14 Friedrich&Walcher Parametrization Expressed form factors as “smooth“ part plus “bump” smooth bump

15. 15 F&W Parametrization (2) The effect of changing the proton form factors from dipole to the FW parametrization. The Galster parametrization is used for Gen and the dipole for GMn.

16. 16 Previous G M n Measurements  Unpolarized electron-deuteron quasi-elastic. Inclusive. Proton contributions subtracted (model dependent).  Ratio of cross sections D(e,e’n) and D(e,e’p) in QE kinematics. Less sensitive to nuclear structure. Needed to know neutron detection efficiency.  Quasi-elastic scattering of polarized electrons off polarized Helium-3. Inclusive. Nuclear structure model an issue

17. 17 World’s Data for G M n  Holzwarth B1, B2: Soliton  Simula: CQM  Lomon: VMD model  Miller: Cloudy Bag model  FW: Friedrich & Walcher par.  Faessler: ChPT THEORETICAL CALCULATIONS

18. 18 EXPERIMENTAL APPARATUS

19. 19 MIT-Bates Linear Accelerator Siberian Snakes  Polarized Source  Linac  Recirculator  South Hall Ring (SHR)  Siberian Snakes  BLAST detector in SHR  ABS: BLAST target embedded in the beamline

20. 20 The BLAST Detector  ABS target  Wire Chambers  Cerenkov Counters  TOFs  Neutron Counters  Magnetic Coils

21. 21 The BLAST Detector + Coils  ABS target  Wire Chambers  Cerenkov Counters  TOFs  Neutron Counters  Magnetic Coils

22. 22 Atomic Beam Source (ABS)  RF Dissociator  Sextupole System  RF Transition Units  Storage Cell  Breit-Rabi Polarimeter

23. 23 RF Dissociator Critical parameters for optimizing performance: Nozzle temperature Gas through-put Vacuum Matching Network – RF power Oxygen Admixture Dissociates molecules into atoms Consists of an RF coil, connected to an RF power supply and wrapped around a glass tube.

24. 24 Dissociation Results HYDROGENDEUTERIUM

25. 25 Sextupole System 24 segments glued together. Create radial field. RAYTRACE simulations used to optimize location / opening of apertures, location of sextupoles. Used to focus atoms with pos. atomic electron spin and de-focus the rest.

26. 26 Hyperfine Structure DEUTERIUM HYDROGEN Quantum mechanics of spin ½ - spin ½ system. Two Zeeman multiplets: Symmetric triplet, anti-symmetric singlet. Spin 1 – spin ½ system: Quadruplet + Doublet.

27. 27 RF Transition Units MFT UNIT DEUTERIUM TRANSITIONS To induce transitions between the hyperfine states.

28. 28 Storage Cell To limit de-polarization: Cooled to 100 K. Coated with Dryfilm. Used to increase target thickness for internal target. 60 cm long, 15 mm diameter, Al. De-polarization effects: Recombination Spin Relaxation

29. 29 Other Components Target Holding Field : To maintain and control the orientation of the target polarization. Electromagnet with two pairs of coils. Covers ± 20 cm of the cell. Breit-Rabi Polarimeter (BRP) : To monitor transitions. A dipole magnet with a gradient field for electron-spin separation.

30. 30 Polarization Results Beam: Average Pol. ≈ 65% Measured with Compton Pol. Target Vector Pol. ≈ 85% (deuterium) From (e,e’p) analysis off deuterium. Target Tensor Pol. ≈ 80% (deuterium) From ed-elastic analysis.

31. 31 DATA ANALYSIS

32. 32 Data Sets 20042005 Running period June-OctoberMarch-June Total Charge320 kC550 kC Target pol. angle 32 deg.47 deg. Ave. Beam current 100 mA180 mA Cell length60 cm Target thickness 6x10 31 cm -2

33. 33 Inclusive Electron Selection 1. Particles with inbending Wire-Chamber Track (negative charge). 2. Correlated TOF – Cerenkov signals. 3. Invariant mass cuts: essentially limit events to QE regime. 4. The data were divided into four Q 2 bins.

34. 34 Inclusive Electron Selection Data from 3 triggers Trigger 1 : (e,e’p), (e,e’d) Trigger 2: (e,e’n) Trigger 7: (e,e’) singles prescaled by 3 INCLUSIVE: ADD TRIGGERS NOTE: In forming the inclusive cross section, the individual detection efficiencies cancel out when trigger 7 is taken into account. Electron detection efficiency is not crucial when forming asymmetries.

35. 35 Data Spectra Sample of experimental spectra for first Q 2 bin and 2004 data. Bin 1Bin 2 Bin 3 Bin 4 Bin 1

36. 36 Data Spectra (2) Sample of experimental spectra for first Q 2 bin and 2004 data. Bin 1Bin 2 Bin 1 Bin 4Bin 3 Bin 4 Bin 3

37. 37 Experimental Background  Empty target background From cell-wall scattering etc. Uniform across W spectrum, 1-3% Dilutes individual sector asymmetries  Pion contamination Only past pion-threshold (high-W edge) Expected to be negligible  Electro-deuteron elastic scattering Only at low-W edge Varies between 1-5% Sizeable effect on asymmetries and ratio

38. 38 Electron-Deuteron Elastic Events  Monte Carlo of ed elastic versus disintegration events. Resolution convolutes peaks Mostly at low-Q2 Only at low-W edge Varies between 1-5% Effect on asymmetries and ratio QE elastic

39. 39 Electron-Deuteron Elastic Events The contamination was accounted for in the MC.

40. 40 Extraction of G M n The following analysis process was performed for each data set independently: 1.Divide the data into the Q2 bins and form the asymmetries in both perpendicular and parallel kinematics. Within each Q2 bin, divide the data in W bins. Correct the asymmetries for empty target background. Q 2 = 0.189 (GeV/c) 2

41. 41 Extraction of G M n (2) 2. Divide the asymmetries to form the ratio. Q 2 = 0.189 (GeV/c) 2 3.Vary G M n value wrt the dipole form factor in the Monte Carlo. 4. Obtain χ 2 for each calculation. 2004 2005

42. 42 Extraction of G M n (3) Q 2 = 0.189 (GeV/c) 2 5.Find minimum of χ 2 for each Q 2 bin using a parabolic shape. 6. Calculate error by varying χ 2 for each Q 2 bin by 1. 2004 2005

43. 43 Systematic Uncertainties Uncertainty Source % GMn err. 2004 % GMn err. 2005 1.Target Polarization Angle2.5%1.5% 2.Cuts, Recon & Resolution1.5% 3.Value of GEn0.5% 4.Radiative Effects0.5%

44. 44 Target polarization angle uncertainty

45. 45 Uncertainty in G E n A 20% uncertainty in G E n contributes 0.5% uncertainty in G M n.

46. 46 False Asymmetries Negligible Effect.

47. 47 RESULTS & CONCLUSION

48. 48 Final Results

49. 49 Final Results (2) 1. New measurement technique. 2. Includes full deuteron structure. 3. Consistent with recent polarization and other data. 4. Provides a tighter fit to form factor in the low Q2 region.