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Quasi-elastic 3 He(e,e’p) experiment (E89-044) at Jefferson Lab :

E. Penel - Nottaris. Exp é rience E89-044 de diffusion quasi- é lastique sur l’ 3 He au Jefferson Laboratory : analyse des sections efficaces 3 He(e,e’p)d en cin é matique parall è le. Quasi-elastic 3 He(e,e’p) experiment (E89-044) at Jefferson Lab : study of the 2-bbu parallel kinematics.

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Quasi-elastic 3 He(e,e’p) experiment (E89-044) at Jefferson Lab :

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  1. E. Penel - Nottaris Expérience E89-044 de diffusion quasi-élastique sur l’3He au Jefferson Laboratory : analyse des sections efficaces 3He(e,e’p)d en cinématique parallèle. Quasi-elastic 3He(e,e’p) experiment (E89-044) at Jefferson Lab : study of the 2-bbu parallel kinematics. Hall A collaboration 2 other PhD students : F. Benmokhtar and M. Rvachev

  2. Generalcontext Electromagnetic probe - interaction described by QED - electron is a point like particle - small coupling (Z1) - kinematical flexibility 3He nucleus - exact calculations for 3-body systems - ingredients of complex nuclei • (e,e’p) experimentsstudy the • nucleon inside the nucleus • energy and momentum distribution of nucleon • electromagnetic properties of bound proton NN and 3-body forces Short range correlations Relativistic effects

  3. Quasi-elastic scattering on 3He Born Approximation : one photon exchange • Plane Wave Impulse Approximation •  absorbed by the detected nucleon • independent particles model for the • nucleus • particles described by plane waves. S(Emiss, pmiss) : spectral function of 3He ep : electron-(off shell) proton elastic cross section

  4. Quasi-elastic scattering on 3He Missing energy : Emiss= Mp + Mrecoil – M3He Emiss =  - Tp - Tr • 2-body-break-up : 3He(e,ep)d • Emiss = 5.5 MeV • 3-body-break-up : 3He(e,ep)pn • Emiss 7.7 MeV Emiss (MeV)  2.2 MeV energy separation between the 2 processes

  5. Reaction mechanisms beyond PWIA • Final State Interactions (FSI) : • Exchange term : • Meson Exchange Currents (MEC) • and Isobaric Currents (IC) : • modify the extracted nuclear information • involve more general cross-section formulation

  6. : longitudinal response function  coupling to nuclear charge : transverse response function  coupling to nuclear transverse current Longitudinal and transverse response functions h=0 • Virtual photon polarization : • h=0 longitudinal polarization • h=1 transverse polarizations h=-1 h=+1 interference terms

  7. Longitudinal and transverse response functions • Parallel kinematics : p’ pmiss

  8. Experimental settings • Extracting the response functions : • -forward electron angles : Fw(Fw  1) • -backward electron angles : Bw (Bw  0) at fixed hadronic vertex variables

  9. Jefferson Lab Hall A Basic Equipment • Coincidence experiment =>100% duty cycle • - High luminosity (1038 cm-2 s-1) => high beam current and target density • Identification of processes separated by 2.2 MeV at momenta of few GeV=> low beam energy dispersion (2.10 -5) and high momentum resolution (2.10 -4)

  10. CEBAF CEBAF Continuous Electron Beam Accelerator Facility Frequency = 1497 MHz  499 MHz in the halls

  11. Jlab Hall A

  12. Cryogenic 3He gaseous target Cylindrical target (tuna can) :  = 10.3 cm High density : T = 6.3 K P  7.6 or 11 atm •  = 0.055 or 0.070 g.cm-3 • Density measurements : • temperature and pressure sensors + state equation of 3He • elastic electron scattering on 3He at each beam energy Preliminary normalization by density from sensors Systematic error on density from sensors : 7 %

  13. density from luminosity monitoring density from P and T sensors 3He target relative density • Luminosity monitoring corrected for dead time and prescales density of the 1st run • Target density stability : max. fluctuation < 3% ( 0.6 %) relative density run number

  14. High Resolution Spectrometers HRS 45° vertical deflexion (FWHM) Separates momentum resolution (vertical plane) from vertex position resolution (horizontal plane)

  15. Detectors Set

  16. Electron identification Gas Cerenkov detector Shower counters pe > 17 MeV/c p > 4.8 GeV/c preshower and shower counters e- e- - - Cerenkov (channel) preshower + shower (MeV) Absolute gains calibration (pe = 3581 MeV/c) Relative calibration by analysis software

  17. S1 ADC (channel) S1 ADC (channel) xrot (m) xrot (m) Scintillators Two planes of 6 scintillator paddles in each arm : S1 and S2 planes • Trigger electronics : • Coincidence between the 2 PM of the hit paddle. Single event  S1 & S2 & 45° track Coincidence event  Electron event & Hadron event S1 ADC (channel) S1 ADC (channel) Relative calibration by analysis software

  18. VDC tracks  detector variables Spectrometer focal plane variables Spectrometer target variables Vertex variables Vertex reconstruction • In each detection arm : detector position offsets / focal plane spectrometer optics tensor + beam position spectrometer absolute position / hall

  19. Transverse position reconstruction Transverse position tensor coefficients optimized from vertex position along beam line (react_z) ylab scattered e- ytg ztg tg ytg beam zlab react_z target Scattering off 4 targets : - carbon foil at z = 0 - aluminum foils at z = ± 2 cm z = ± 5 cm z = ± 7.5 cm

  20. Transverse position reconstruction before after Pe = 694 MeV/c Low electron momentum electron react_z (cm) electron react_z (cm) Pe = 3850 MeV/c electron react_z (cm) Ph = 1295 MeV/c hadron react_z (cm) High proton momentum Ph = 2999 MeV/c hadron react_z (cm) hadron react_z (cm)

  21. Emiss (MeV) Emiss (MeV) hadron rot (rad) hadron rot (rad) Momentum reconstruction Momentum tensor coefficients optimized on missing energy spectra : remove dependence on dispersive variables (xfp, fp)

  22. electron react_z (mm) electron react_z (mm) Spectrometers absolute position • - May not point at the hall center • Angle orientation may be different from floor marks •  Use scattering off carbon foil at z = 0

  23. 3He(e,e’p)d Cross-sections => Data Analysis and Simulation • Background rejection=> experimental 3He(e,e’p) events • 2-bbu and 3-bbu separation • Radiative corrections • Phase space calculation • => Monte Carlo Simulation => Simulated 3He(e,e’p) events

  24. 2 ns beam structure Background rejection Coincidence events selection • Corrected time of coincidence : tc_cor • resolution   0.6 ns tc (ns) tc_cor (ns) Time of coincidence window width = 12ns

  25. Background rejection Electrons identification e- preshower (MeV) preshower (MeV) - e- shower (MeV) shower (MeV) - signal in the Cerenkovdetector + signal in the showers tc_cor (ns)

  26. Target walls rejection : vertex position cuts | react_z | < 4 cm cut on the arm with best resolution on react_z electron react_z (cm) electron react_z - hadron react_z (cm) | react_ze arm – react_zh arm | < 2 cm

  27. Background rejection Protons selection before cuts after cuts d hadron S2 ADC hadron S2 ADC + p hadron  hadron   No need to remove deuterons or pions

  28. Parallel kinematics selection Parallel configuration : pq bq  Cone aperture = 45 ° pmiss pmiss=0 MeV/c pmiss=+300 MeV/c pmiss=-300 MeV/c bq (°) bq (°) bq (°)

  29. Accidental coincidences subtraction Subtraction of missing energy spectra : before accidental subtraction after accidental subtraction tc_cor (ns) Emiss (MeV)

  30. Missing energy spectra forward backward pmiss = 0 MeV/c Emiss (MeV) Emiss (MeV) forward backward pmiss = +300 MeV/c Emiss (MeV) Emiss (MeV)

  31. Phase space simulation • Limit simulated and experimental phase space to the same volume • Optimize statistics by considering maximal phase space volume tg (rad) tg (rad)   Cuts on target variables : tg (rad) tg (rad) (same cuts for both arms) (R-function defined by M. Rvachev) ytg (m) tg (rad)

  32. electron react_z - hadron react_z (cm) data simulation Angular and transverse position resolutions • Angular resolutions : FWHMtg= 2 mrad FWHMtg= 4 mrad • Transverse position resolution : • fitted from ytg distributions on scattering off carbon foils data Carbon foil data Quasi-elastic 3He data  ytg (mm)  1.4 mm < FWHMytg< 9.7 mm

  33. data simulation Momentum resolution • Adjusted in the simulation to get same resolution on missing energy for 2-bbu as experimental resolution •  same momentum resolution for electron and hadron arms.  4 10-4 <FWHM < 8 10-4 Emiss (MeV)

  34. Emiss (MeV) Emiss (MeV) Extracting 3He(e,e’p)d cross-sections By fitting simulated missing energy spectrum to experimental data • takes into account 3-bbu contribution (1 % systematic error on subtraction) • simulates energy losses and radiative effects • extracts unradiated cross-section averaged on phase-space data simulation Two theoretical models : - unit cross-section -PWIA model

  35. Preliminary results • Experimental data analysis showsreliable background control and pretty good transport variables resolutions • Simulation reproduces rather well kinematical variables resolutions => used to extract unradiated cross-section averaged on phase-space • Possible improvementscould come from spectrometer optics optimization, simulated resolutions and absolute normalization by density from elastic data. • Systematic error on preliminary cross-sections is 8.8 % (mainly due to target density)

  36. De Forest / Salme PWIA Laget PWIA Laget full calculation Experimental results : Pmiss = 0 MeV/c Forward electron angles cross-section (b.MeV-1.sr-2) Backward electron angles cross-section (b.MeV-1.sr-2) pmiss (MeV/c) pmiss (MeV/c)

  37. Salme wave functionUrbanna Paris Experimental results: Pmiss = +300 MeV/c Forward electron angles De Forest / Salme PWIA Laget PWIA Laget full calculation cross-section (b.MeV-1.sr-2) Backward electron angles cross-section (b.MeV-1.sr-2) Pmiss (MeV/c) Pmiss (MeV/c)

  38. Salme wave functionUrbanna Paris Experimental results: Pmiss = -300 MeV/c De Forest / Salme PWIA Laget PWIA Forward electron angles cross-section (b.MeV-1.sr-2) Backward electron angles cross-section (b.MeV-1.sr-2) Pmiss (MeV/c) Pmiss (MeV/c)

  39. Longitudinal and transverse response functions Pmiss = -300 MeV/c •  and q matching for forward and backward kinematics • 50 MeV/c pmiss bins • achieving forward and backward cross-sections L (b.sr-2) T (b.sr-2) De Forest / Salme PWIA Pmiss (MeV/c) Pmiss (MeV/c) Sensitivity to interference terms and imperfect (, q) matching

  40. Overview on E89-044 results Parallel kinematics • Preliminary resultsshow unexpected effects for forward electron angles kinematics at pmiss = 0 and rather good agreement for the other kinematics that should constraint theoretical models. • Elastic data analysis would allow final cross-sections extraction. • Longitudinal and transverse separation looks promising • Very interesting results on perpendicular kinematics (2-bbu and 3-bbu) that constrained models. • Other experiments at Jlab study few body interactions models through (e,e’p)

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