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