Background Rejection Activities in Italy Francesco Longo University and INFN, Trieste, Italy
Geant4 Low Energy Polarized Processes Gerardo Depaola * Francesco Longo + Francesco Longo + *...
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Geant4 Low Energy Polarized Processes
Geant4 Low Energy Polarized Processes
Gerardo DepaolaGerardo Depaola**
Francesco LongoFrancesco Longo++
* National University of Córdoba (Argentina)
+ University of Ferrara and INFN (Italia)
Talk OutlineTalk Outline
Compton Effect Compton Effect · Angular Distribution for Scattered gamma.· Angular Distribution for Scattered gamma.
· Vector Polarization distribution.· Vector Polarization distribution.
Pair ProductionPair Production · Azimuthal distribution.· Azimuthal distribution.
Effect of polarizationEffect of polarization · Asymmetric ratio.· Asymmetric ratio.
COMPTON SCATTERINGCOMPTON SCATTERING
2
0
020
220 cos42
h
h
h
h
h
hr
4
1
d
d
The Klein Nishina cross section:
Where,h0 : energy of incident photon.h : energy of the scattered photon. : angle between the two polarization vector
Angles in the Compton EffectAngles in the Compton Effect
Polar angle Polar angle Azimuthal angleAzimuthal angle Polarization vectorPolarization vector
O
x
A
Cyy
O z
x
h
h A
C
Angular distribution Scattered Radiation compose of two components: ’
and ’
respect to AOC plane
Angular distribution Scattered Radiation compose of two components: ’
and ’
respect to AOC plane
’
’
CO
Ah
’
x
Summing over the two direction the cross section can be write as: Summing over the two direction the cross section can be write as:
22
0
020
220 cossin2
h
h
h
h
h
hr
2
1
d
d
Sample Methods implemented in G4LowEnergyPolarizedCompton class :• Integrating over • Sample • Theta - Energy Relation Energy• Sample of from P() = a (b – c cos2 ) distribution
ResultsResults
Class inserted in next G4 release Class inserted in next G4 release To be compared with Experimental resultsTo be compared with Experimental results Scattered PolarizationScattered Polarization
distribution obtained with the class
Scattered Photon PolarizationScattered Photon Polarization
is obtain from cos = cos N and is sample from Klein Nishina cross section
Ncossin1sincossincos 22
coskcoscossin
N
1jcossinsin
N
1iN 2'
||
sinksinsinjcosN
1'
Test of the distribution:
a) low energy b) high energy
Low energy: ho << mc2 => h ho => =1 => a = 0
the distribution reduces to the Thompson distribution
=> the probability that the two polarization vectors are perpendicular is zero.
2cosbaba
1)(PThe distribution function is: where
and = h / h0.
4b,21
a
High energy: small => h ho => equal to low energy
high : it is possible to demonstrate that b/(a+b) ->0, so in this case the distribution tend to be isotropic.
ResultsResults
Scalar product between the two polarization vectors for three different energies.Scalar product between the two polarization vectors for three different energies.
Upper histograms: Upper histograms: Low polar angle Low polar angle
Lower histograms:Lower histograms: High polar angle High polar angle
100 keV 10 MeV1 MeVThese distributions are in agreement with the limits obtained previously.
Cross Section:Cross Section:
PAIR PRODUCTION
]m)1)(cosE(
)1(cosE)coscoscossinsin1)(E(E[2q
cos2sin
sin
E
)E(
sin
sin
E
E
cos1
sin
cos1
sin
cos1
)cos(sin
cos1
cossinq
cos1
)cos(sinE
cos1
cossinE4
q
EEddEd
mr
2
Z2d
2
2
2
22
2
43
20
2
2
Angles occurring in the pair productionAngles occurring in the pair production
z
y
x
k
p- p+
- +
Azimuthal Distribution of a Pair Created by 100 MeV Photon.
0.00 0.52
1.05 1.57
2.09 2.62
3.14 3.00 3.02
3.04 3.06
3.08 3.10
3.12 3.14 4
6
8
10
12
14
16
1 d (Zr 0 )
2 d d
[rad] [rad]
Effects of polarization
Asymmetric ratio for pair production
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1000 MeV
R
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
500 MeV
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
100 MeV
ε [rad]
Asymmetric Ratio nº of pairs contains in plane parallel to the vector polarization to nº of pairs perpendicular
Asymmetric ratio for Compton scattering
Polar aperture
Polar aperture
In progressIn progress
• Test the Compton class with experimental data.
• Include the binding effect in the Compton class.
• Build the class for pair production.
• Develop a class for :
1) Rayleig scattering
2) Photoelectric effects