Off-axis vortex scattering of electron-positron annihilation into a photon pair

The off-axis triple-vortex scattering process of $e^-e^+\to\gamma\gamma$ is studied theoretically, in which the positron is in a plane-wave state and the electron and photons are in vortex states. We develop a theoretical formalism for the process, which allows us to study the effects of various vortex parameters and scattering angle. We adopt a Bessel-Gaussian type wave packet for the initial vortex electron for the purpose of normalization. Numerical calculations are performed for an electron and a positron with a moderate energy around $1~\textrm{MeV}$. Our results demonstrate strong impacts of the scattering angle and the topological charges on the cross section and distributions in the energy and cone angles of the vortex photons. This could provide insight into off-axis vortex scattering and also a possible approach to distinguishing and detecting vortex electrons by off-axis vortex scattering.