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07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 2
Contains
• Introduction
• Design of Mott polarimeter
• Measurements• Results
• Conclusion
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 3
MAMI polarimeter technique
• Mott scattering: electron at gold nuclei (Z=79), due to spin-orbit coupling of electron spin appears asymmetry in backscattering,
• Used in MAMI 14 MeV and JLAB 2-8 MeV • Main parameters: Asymmetry at foil zero thickness -A0, beam
Polarization - P, Sherman Function - S are related by: A0=P x S
• To measure beam polarization need to know both Sherman function and asymmetry
• Sherman function needs theoretical calculation• Asymmetry needs experimental measurements:
• A=(Nl-Nr)/(Nl+Nr)
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 4
Analyzing Power - Sherman Function
• For spherical symmetric potentials, the Sherman function can be calculated exactly by the Mott phase shift formula
• Low energy region (< 1 MeV) must take into account electron cloud (theory) and strong multiple scattering increases experimental problems.
• High energy region (>5 MeV) must take into account nuclear size effect. (P. Uginčius,et. al. 1970.) Considerable deviations from point nucleus values appear above 5 MeV.
• For energies from 1 MeV to 3.5 MeV scattering in Coulomb field with negligible nuclear size effect and electron cloud is possible. This region has preference.
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 5
Nuclear size effect
-0.60
-0.55
-0.50
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
130 135 140 145 150 155 160 165 170 175 180
angle, [degrees]
SF
,[a
.u.]
Pb 10 MeV exten
Pb 10 MeV point
Pb 5 MeV exten
Pb 5 MeV point
Pb 1 MeV point
Pb 1 MeV exten
Au 3,5 MeV exten
Au 3.5 MeV point
Au Coulomb
For Pb from P. Uginčius, H. Überall and G.H. Rawitscher. 1970
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 6
Polarised electron source
Polarised beam produced by photo cathodes based on super lattice A3B5 cathodes from Sankt Petersburg State Technical University, Russia and SVTA, USA
Activation by Cs:O layers. by illuminating by circular polarised laser light wave length 780-830 nm.
Quantum efficiency of photo cathodes about 1%
Beam polarisation more then 80 %
Manipulation of spin direction using Wien filter
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 7
Mott layout
• Mott polarimeter located in the 3.5 MeV region of the MAMI accelerator • Beam energy: variable from 1.0 to 3.6 MeV • Beam current: 5 nA to 45 µA• Scattered electron energy selection by magnetic spectrometers• Empty Target / Target signal ratio > 1000:1 typically • Targets: 0.1 to 15 µm Au foil (Z=79)• Fixed scattering angle 164 degree, yields Sherman function S>0.45 for all
energies
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 8
Mott design
Au target
ScintillatorCollimator
Ø 4 mm
Primary beamBending magnets
Photo multiplier
Spin direction
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 10
Asymmetry measurements
0,1 1 100,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,096 0,098 0,100 0,102 0,104
0,36
0,38
0,40
0,42
1.0 MeV 2.0 MeV 2.5 MeV 3.0 MeV 3.5 MeV
Asy
mm
etr
y, [1
= 1
00
%]
Foil thickness, [mkm]
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 11
Measured asymmetry in a range from 0.005 to 45 μA
0.001 0.01 0.1 1 10 10012.8
12.9
13.0
31.8
31.9
32.0
32.1
36.5
36.6
36.7
36.8
Beam current, mkA
foil thickness 1 mkm
foil thickness 100 nm
foil thickness 15 mkm
Relative variation ±0.5% for each foil.
Required measurement times between 2 min to 2 hours per point
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 12
Extrapolation procedure
Fit procedure and extrapolation to foil zero thickness should have an the property: A(∞)=const and ≠ 0 because of the energy resolution of the detector system.
Exponential extrapolation proposed by Gay, Khakoo, RSI 1992, based on phenomenological model:
A(t)=Ac + Av exp(-t/d)Where t- foil thickness, Ac , Av , d - fit parameters, evidently A(0)= Ac +Av
Wegener 1958 proposed detector count rate as:
Nl,r ~(1 ± P Ao) t + α t2
proposed rational or polynomial fit:
A(t)=Ao /(1+a t)But double scattering term can (should) depend on beam polarisation:
α -> (α l , α r)
Nl,r ~(1 ± P Ao) t + α l,r t2
following fit function: A(t)=Ac + Av /(1+a t)
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 13
Fit example at 2.0 MeV
0,1 1 100,0
0,1
0,2
0,3
0,4
Asymmetry 2.0 MeV Exponential Fit 95% Confidence Limit Rational Fit 95% Confidence Limit
Me
asu
red
asy
yme
try,
[1=
10
0%]
Foil thickness, [mkm]
Both fits predict A(t=0) with accuracy better than 1.5%
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 14
Measured beam polarisation vs beam energy
1,0 1,5 2,0 2,5 3,0 3,5 4,00,79
0,80
0,81
0,82
0,83
0,84
ExpFit PolFit
Bea
m P
olar
isat
ion,
[1=
100%
]
Beam Energy, [MeV]
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 15
Error Sources• The main source is presently the quality of the fit (± 1.5%), which can be
further improved by better thickness measurement or more targets.
• Statistical error by each asymmetry measurement is smaller than ∆A/A= ± 0.2 % negligible.
• Sherman Function. Nucleus extended or point. At energy from 1.0 to 3.5 MeV at gold the effect smaller than ∆S/S=±0.5 %.
• Choice of approximation function – no significant difference for two reasonable fit functions.
• Target induced Background? A(0) reduction due to background would have to be the same for all energies.
07.09.09 V. Tioukine, Inst. of Nuclear Physics, Mainz, Germany 16
Conclusion•A Mott electron polarimeter has been developed for MAMI
•Background discrimination by magnetic spectrometers allows for a good signal to noise ratio
•High beam energy allows to measure asymmetries at ‘robust’ target thicknesses from 0.10 to 15 µm
• Accuracy of extrapolation better than 1.5% in an energy range between 1 and 3.5 MeV
• Asymmetry measurements are independent of the primary beam current in a range from 0.005 to 45 microamperes at a level of 0.5% relative variation.
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