1. Geant4 Low Energy Polarized Processes Gerardo Depaola * Francesco Longo + Francesco Longo + * National University of Córdoba (Argentina) + University of Ferrara and INFN (Italia)

2. Talk Outline ä Compton Effect · Angular Distribution for Scattered gamma. · Angular Distribution for Scattered gamma. · Vector Polarization distribution. · Vector Polarization distribution. ä Pair Production · Azimuthal distribution. · Azimuthal distribution.  Effect of polarization · Asymmetric ratio. · Asymmetric ratio.

3. COMPTON SCATTERING The Klein Nishina cross section: Where, h 0 : energy of incident photon. h : energy of the scattered photon.  : angle between the two polarization vector

4. Angles in the Compton Effect ä  Polar angle ä  Azimuthal angle ä  Polarization vector  O x  A Cy y O z x     h h   A C

5. Angular distribution Scattered Radiation compose of two components :  ’  and  ’   respect to AOC plane  ’   ’  CO  A h  ’   x

6. Summing over the two direction the cross section can be write as: Sample Methods implemented in G4LowEnergyPolarizedCompton class : Integrating over  Sample  Theta - Energy Relation Energy Sample of  from P(  ) = a (b – c cos 2  ) distribution

7. Results ä Class inserted in next G4 release ä To be compared with Experimental results ä Scattered Polarization  distribution obtained with the class

8. Scattered Photon Polarization  is obtain from cos  = cos  N and  is sample from Klein Nishina cross section

9. Test of the distribution: a) low energy b) high energy Low energy: h o h  h o =>  =1 => a = 0 the distribution reduces to the Thompson distribution => the probability that the two polarization vectors are perpendicular is zero. The distribution function is: where and  = h / h 0. High energy: small  => h  h o => 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.

10. Results Scalar product between the two polarization vectors for three different energies. Upper histograms: Low polar angle  Upper histograms: Low polar angle  Lower histograms: High polar angle  Lower histograms: High polar angle  100 keV 10 MeV1 MeV These distributions are in agreement with the limits obtained previously.

11. Cross Section: PAIR PRODUCTION

12. Angles occurring in the pair production z y x  k p- p- p+ p+   - - + +

13. Azimuthal Distribution of a Pair Created by 100 MeV Photon.

14. Effects of polarization Asymmetric ratio for pair production Asymmetric Ratio nº of pairs contains in plane parallel to the vector polarization to nº of pairs perpendicular

15. Asymmetric ratio for Compton scattering Polar aperture

17. In 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