A 5D, polarised, Bethe-Heitler event generator for $\gamma \to e^+e^-$ conversion

We describe a new version of the 5D, exact, polarised, Bethe-Heitler event generator of $\gamma$-ray conversions to $e^+e^-$, developed in the context of the HARPO project, that is able to simulate successive events with different photon energies and on different atomic targets without any substantial CPU overhead. The strong correlation between kinematic variables in the divergence of the five-dimensional differential cross section are mitigated by performing each step of the conversion in the appropriate Lorentz frame. We extend the verification range down to 1 keV above threshold and up to 1 EeV. This work could pave the way to the precise simulation of the high-performance $\gamma$-ray telescopes and polarimeters of the post-Fermi-LAT area.