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
E. Penel-Nottaris
2 other PhD students : F. Benmokhtar and M. Rvachev
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
1
General
context
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
NN and 3-body forces
Short range correlations
Relativistic effects
E. Penel-Nottaris
July, 7th, 2004
(e,e’p) experiments study the
nucleon inside the nucleus
- energy and momentum distribution
of nucleon
- electromagnetic properties of bound
proton
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
2
Quasi-elastic scattering
3He
on
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.
d 2σ ep
dσ

 S(E miss , p miss )
dΩe'dΩ p'dE'
dΩe'
5
ep : electron-(off shell) proton
elastic cross section
E. Penel-Nottaris
July, 7th, 2004
p   p miss
S(Emiss, pmiss) : spectral function
of 3He
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
3
Quasi-elastic scattering
3He
on
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 (MeV)
Emiss  7.7 MeV
 2.2 MeV energy separation between the 2 processes
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
4
Reaction
mechanisms
PWIA
• Final State Interactions (FSI) :
beyond
• Exchange term :
p   p miss
d 2σ ep
dσ
 K
 SD (E miss , p miss , p' )
dΩedΩ p'de'
dΩe'
5
• Meson Exchange Currents (MEC)
and Isobaric Currents (IC) :
E. Penel-Nottaris
July, 7th, 2004
• modify the extracted nuclear
information
• involve more general crosssection formulation
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
5
Longitudinal and transverse
response functions
h=0
• Virtual photon polarization :
- h=0
longitudinal polarization
h=-1
- h=1 transverse polarizations
h=+1
ε
q
ε

q
ε
σ L : longitudinal response function
q
 coupling to nuclear charge
σT : transverse response function
 coupling to nuclear transverse current
σ
LT
σ

 interference terms


TT 
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
6
Longitudinal and transverse
response functions
d5σ
 Γ(σT  ε σ L  ε(ε  1) σ LT cos  ε σTT cos2 )
dΩedΩp'dE'
Γ
2
θ
q
ε  (1  2 2  tan 2 e )
Q
2
q
E'
1
 2
E0 Q 1  ε
• Parallel kinematics :
p miss // q
p’
pmiss
E. Penel-Nottaris
July, 7th, 2004
d5σ
 Γ(σT  ε σ L )
dΩedΩp'dE'
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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Experimental
settings
• Extracting the response functions :
- forward electron angles : Fw (Fw  1)
- backward electron angles : Bw (Bw  0)
Γ Bw σ Fw  Γ Fw σ Bw

σ L  Γ Γ (ε  ε )

Fw Bw
Fw
Bw

σ  Γ Bw ε Bw σ Fw  Γ Fw ε Fw σ Bw
 T
Γ Fw Γ Bw (ε Fw  ε Bw )
E. Penel-Nottaris
July, 7th, 2004
at fixed hadronic vertex variables
Fw - Bw
pmiss
q
(MeV/c)
(GeV/c)
0
1.0
0.7
0
1.5
0.7
0
2.0
0.6
0
3.0
0.5
- 300
1.0
0.4
- 300
2.0
0.7
+ 300
1.0
0.6
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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)
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
9
CEBAF
Continuous Electron Beam
Accelerator Facility
Frequency = 1497 MHz
 499 MHz in the halls
E. Penel-Nottaris
July, 7th, 2004
Duty cycle
100 %
Beam energy
0.8 – 6 GeV
Energy dispersion
2.5 10-5
Beam emittance
2 10-9
Beam current
200 A
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Jlab
E. Penel-Nottaris
July, 7th, 2004
Hall
A
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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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 %
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
12
3He
target
• Luminosity monitoring
nb. singles eL rate 
charge
L rate
ρ
ρ ref
L rate_ref
relative
density
corrected for dead time and prescales
density of the 1st run
• Target density stability : max. fluctuation < 3% ( 0.6 %)
relative density
density from luminosity monitoring
density from P and T sensors
run number
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
13
High Resolution
Spectrometers HRS
45° vertical deflexion
Acceptance
Resolution
±5%
2.5 10-4
Horizontal angle
 30 mrad
2.0 mrad
Vertical angle
 65 mrad
6.0 mrad
Momentum
(FWHM)
Separates momentum resolution (vertical plane) from
vertex position resolution (horizontal plane)
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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Detectors
E. Penel-Nottaris
July, 7th, 2004
Set
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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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)
Relative calibration by analysis software
E. Penel-Nottaris
July, 7th, 2004
Absolute gains calibration (pe = 3581 MeV/c)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
16
Scintillators
S1 ADC (channel)
S1 ADC (channel)
Two planes of 6 scintillator paddles in each arm : S1 and S2 planes
Trigger electronics :
- Coincidence between the 2
PM of the hit paddle.
xrot (m)
xrot (m)
Single event
 S1 & S2 & 45° track
Coincidence event
S1 ADC (channel)
S1 ADC (channel)
 Electron event & Hadron event
Relative calibration by analysis software
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
17
Vertex
reconstruction
• In each detection arm :
VDC tracks
 detector variables
(x det , θdet , ydet , Φdet )
detector position offsets / focal plane
Spectrometer focal plane variables
(x fp , θfp , yfp , Φfp )
spectrometer optics tensor + beam position
Spectrometer target variables
(x tg , θtg , y tg , Φtg , δ)
spectrometer absolute position / hall
Vertex variables
E. Penel-Nottaris
July, 7th, 2004
vertex position (react_z)

kinematica l variables
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
18
Transverse position
reconstruction
Transverse position
tensor coefficients optimized from vertex
position along beam line (react_z)
ytg
ylab
scattered e-
ztg
tg
ytg
beam
react_z
zlab
target
Scattering off 4 targets :
E. Penel-Nottaris
July, 7th, 2004
- carbon foil at z = 0
- aluminum foils at z = ± 2 cm
z = ± 5 cm
z = ± 7.5 cm
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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Transverse position
before reconstruction
after
Low electron
momentum
electron react_z (cm)
electron react_z (cm)
electron react_z (cm)
hadron react_z (cm)
High proton
momentum
hadron react_z (cm)
E. Penel-Nottaris
July, 7th, 2004
hadron react_z (cm)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
20
Momentum
reconstruction
Emiss (MeV)
Emiss (MeV)
Momentum tensor coefficients optimized on missing energy spectra :
remove dependence on dispersive variables (xfp, fp)
hadron rot (rad)
E. Penel-Nottaris
July, 7th, 2004
hadron rot (rad)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
21
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
electron react_z (mm)
E. Penel-Nottaris
July, 7th, 2004
electron react_z (mm)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
22
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
E. Penel-Nottaris
July, 7th, 2004
=>
3He(e,e’p)d
Cross-sections
=> Simulated 3He(e,e’p) events
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
23
Background
Coincidence
rejection
events
selection
• Corrected time of coincidence : tc_cor
resolution   0.6 ns
2 ns beam
structure
tc (ns)
tc_cor (ns)
Time of coincidence window width = 12 ns
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
24
Background
e
-
-
identification
preshower (MeV)
preshower (MeV)
Electrons
rejection
eshower (MeV)
shower (MeV)
signal in the Cerenkov detector
+ signal in the showers



tc_cor (ns)
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
25
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
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
26
Background
Protons
selection
after cuts
hadron S2 ADC
hadron S2 ADC
before cuts
d
p
rejection
+
hadron 
hadron 
 No need to remove deuterons or pions
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
27
Parallel kinematics
selection
p'
Parallel configuration : p miss // q
pq
q
pmiss
pmiss=0 MeV/c
 Cone aperture = 45 °
pmiss=+300 MeV/c
bq (°)
E. Penel-Nottaris
bq
July, 7th, 2004
pmiss=-300 MeV/c
bq (°)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
bq (°)
28
Accidental coincidences
subtraction
Subtraction of missing energy spectra :
Δt f1  Δt f2  50ns

Δt 2 bbu  12ns
tc_cor (ns)
E. Penel-Nottaris
July, 7th, 2004
S2-bbu – 12/50  Saccid
before accidental subtraction
after accidental subtraction
Emiss (MeV)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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Missing
energy
spectra
forward
backward
Emiss (MeV)
Emiss (MeV)
pmiss = 0 MeV/c
forward
backward
pmiss = +300 MeV/c
Emiss (MeV)
E. Penel-Nottaris
July, 7th, 2004
Emiss (MeV)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
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space
• Limit simulated and
experimental phase space
to the same volume

tg (rad)
tg (rad)

ytg (m)
E. Penel-Nottaris
simulation
tg (rad)
tg (rad)
Phase
July, 7th, 2004
• Optimize statistics by
considering maximal phase
space volume
Cuts on target variables :
δ, θtg , Φtg , y tg
(same cuts for both arms)
tg (rad)
(R-function defined by M. Rvachev)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
31
Angular and transverse
position resolutions
• Angular resolutions :
tg = 2 mrad
FWHM tg = 4 mrad
FWHM
• Transverse position resolution :
fitted from ytg distributions on scattering off carbon foils data
Quasi-elastic 3He data
Carbon foil data

ytg (mm)
 1.4 mm < FWHM ytg < 9.7 mm
E. Penel-Nottaris
July, 7th, 2004
electron react_z - hadron react_z (cm)
data
simulation
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
32
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.
kin # FWHM 
kin # FWHM 
16
4.8 10-4
17
6.5 10-4
01
4.0 10-4
03
6.3 10-4
18
4.8 10-4
19
5.8 10-4
20
5.2 10-4
21
4.4 10-4
22
6.2 10-4
23
7.0 10-4
24
5.2 10-4
25
6.5 10-4
26
4.3 10-4
27
8.0 10-4
 4 10-4 < FWHM  < 8 10-4
Emiss (MeV)
data
E. Penel-Nottaris
July, 7th, 2004
simulation
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
33
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 crosssection averaged on phase-space
data
simulation
Emiss (MeV)
Two theoretical models :
- unit cross-section
Emiss (MeV)
E. Penel-Nottaris
July, 7th, 2004
- PWIA model
d5σ
 σ cc1  S(p miss )
de' dΩedΩp
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
34
Preliminary results
• Experimental data analysis shows reliable 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 improvements could 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)
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
35
Experimental results
= 0 MeV/c
cross-section (b.MeV-1.sr-2)
Forward
electron angles
:
De Forest / Salme PWIA
Laget PWIA
Laget full calculation
cross-section (b.MeV-1.sr-2)
Backward
electron angles
pmiss (MeV/c)
E. Penel-Nottaris
Pmiss
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
pmiss (MeV/c)
36
Experimental results:
= +300 MeV/c
Pmiss (MeV/c)
wave function
E. Penel-Nottaris
Salme
Urbanna
Paris
July, 7th, 2004
De Forest / Salme PWIA
Laget PWIA
Laget full calculation
cross-section (b.MeV-1.sr-2)
cross-section (b.MeV-1.sr-2)
Forward
electron angles
Pmiss
Backward
electron angles
Pmiss (MeV/c)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
37
Pmiss
De Forest / Salme PWIA
Laget PWIA
Forward
electron angles
cross-section (b.MeV-1.sr-2)
cross-section (b.MeV-1.sr-2)
Experimental results:
= -300 MeV/c
Backward
electron angles
Pmiss (MeV/c)
wave function
E. Penel-Nottaris
Salme
Urbanna
Paris
July, 7th, 2004
Pmiss (MeV/c)
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
38
Longitudinal and transverse
response
functions
Pmiss = -300
MeV/c
T (b.sr-2)
L (b.sr-2)
•  and q matching for forward and backward kinematics
• 50 MeV/c pmiss bins
• achieving forward and backward cross-sections
Pmiss (MeV/c)
De Forest / Salme
PWIA
Pmiss (MeV/c)
Sensitivity to interference terms and imperfect (, q) matching
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
39
Overview on E89-044 results
Parallel kinematics
•Preliminary results show 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)
E. Penel-Nottaris
July, 7th, 2004
Laboratoire de Physique Subatomique et de Cosmologie de Grenoble
40