Generation of relativistic positrons carrying intrinsic orbital angular momentum

High-energy positrons can be efficiently created through high-energy photons splitting into electron-positron pairs under the influence of the Coulomb field. Here we show that a new degree of freedom-the intrinsic orbital angular momentum (OAM)-can be introduced into relativistic positrons when the incident photons are twisted. We develop the full-twisted scattering theory to describe the transfer of angular momentum before and after the interaction. It is found that the total angular momentum (TAM) of the photon is equally distributed between the positron and electron. For each photon TAM value, the generated leptons gain a higher average OAM number when the photon spin is antiparallel to its TAM. The impact of photon polarization on the OAM spectrum profile and the scattering probability is more significant at small photon TAM numbers, owing to the various interaction channels influenced by flipping the photon spin. Our work provides the theoretical basis to study OAM physics in particle scattering and to obtain copious relativistic vortex positrons through the Beth-Heitler process.