About electrons and position in Triplet Production: some remarks

Taking into account the increasing interest in measuring high energy gamma ray polarization, Boldishev et. at. \cite{[Boldy]} published an extensive and very comprehensive work on the possibility of using the recoil electrons in the production of pairs on electrons. However, this work is based on using only 2 Feynmann diagrams of the 8 that the process has. This eliminates the difficulty of distinguishing, in the theory, which is the recoil electron and which is the created In this work we have analyzed the eight Feynman diagrams and we have shown that for energies lower to $\sim 1000mc^2$, the assumption just described is not a good approximation, so we propose a different way to work \cite{Marcos}: we classify the electrons into the less energetic and the most energetic ones without taking into account their origin. Under these conditions (lower or higher energy value), we have calculated the contribution of the different diagrams to the distribution(we compare the sum of them with that obtained by Haug \cite{Haug_e+}\cite{Haug_e-}, and how these distributions are modified by introducing a threshold for the momentum detection for electrons. For the study of polarization we presented on the angular distribution of particles for high-energy gamma rays (where only Borsellino diagrams predominate). Our results on the azimuthal distribution show that it is highly influenced by the orientation (in the plane perpendicular to the direction of the photon), prior to the interaction, that the polarization vector has with respect to the position of the electron in whose field the pair will be generated.