A Bethe-Heitler 5D polarized photon-to-e+e-pair conversion event generator
Past and current pair gamma-ray space telescopes use tungsten converters interleaved with tracker layers, for which the contribution of multiple scattering of the pair electrons in the tungsten dominates the single-photon angular resolution (example the Fermi LAT) and polarimetry with pairs has never been performed by a space polarimeter.
All-silicon telescopes could provide an angular resolution improvement of a factor of 3 at 100 MeV. With a gaseous active target a factor of 10 is within reach [NIM A 701 (2013) 225] and the single-track angular resolution is so good that polarimetry with pairs becomes possible [NIM A 729 (2013) 765] and has actually been demonstrated experimentally on beam [SPIE (2016) 99052R]. For these excellent telescopes, the recoil momentum dominates the single-photon angular resolution over most of the usable photon energy range and therefore an event generator that describes accurately the kinematic configuration of the particles in the final state must be used in simulations.
Current pair-conversion event generators (e.g. geant4 and EGS5 physics models) don't sample the five-dimensional differential cross section (5D DCS), but instead a product of 1D DCSs. In addition, most of them use high-energy and/or small angle approximations. Also the electron and positron polar angles are often generated independently so that energy-momentum is not conserved. Few of them generators can simulate the conversion of linearly polarized photons, and only at high energy and none of them accurately [Astropart. Phys. 88 (2017) 60].
I have written an event generator that is sampling exactly the 5D Bethe-Heitler DCS, including for photons with a non-zero linear polarization fraction [NIM A 729 (2013) 765]. This event generator is using the BASES/SPRING instantiation of the VEGAS method : at a given energy, for a given target nucleus (nuclear conversion) or atom (triplet conversion), after a 5D grid has been optimized for DCS integration precision that is for event generator efficiency, the DCS is tabulated and stored, something that needs several seconds of computation. Then zillions of gamma conversions can be generated quickly at that energy and for that target. The polarization asymmetry properties of the Bethe-Heitler DCS were examined with that tool in Astropart. Phys. 88 (2017) 30, especially at low energy where most of the statistics is for cosmic sources.
I am now developing a VEGAS-free version of that code, that will allow the fast generation of the conversion of a photon of a given energy on a given target, with the same other properties as for the VEGAS-based generator, i.e., 5D, exact, polarized and strictly energy-momentum conserving.
My goal is to make this generator available to the community as a Geant4 physics model.