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Geant4 Low Energy Polarized Processes Gerardo Depaola * Francesco Longo + Francesco Longo + * National University of Córdoba (Argentina) + University of Ferrara and INFN (Italia)
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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.
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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
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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
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Angular distribution Scattered Radiation compose of two components : ’ and ’ respect to AOC plane ’ ’ CO A h ’ x
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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
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Results ä Class inserted in next G4 release ä To be compared with Experimental results ä Scattered Polarization distribution obtained with the class
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Scattered Photon Polarization is obtain from cos = cos N and is sample from Klein Nishina cross section
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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.
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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.
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Cross Section: PAIR PRODUCTION
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Angles occurring in the pair production z y x k p- p- p+ p+ - - + +
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Azimuthal Distribution of a Pair Created by 100 MeV Photon.
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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
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Asymmetric ratio for Compton scattering Polar aperture
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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
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