On Compton Ionization of Positronium by Twisted Photons

The process of Compton decay of positronium by a twisted photon is considered in the A 2 approximation. In the case of a Bessel cylindrical wave, the matrix element of such a process is closely related to a similar matrix element for a plane electromagnetic wave. Taking into account the conservation momentum law and within the framework of standard scattering theory, it is shown that in the expression for the probability of this process, practically all the most important characteristics of a cylindrical wave of a twisted photon are lost. Moreover, it is shown that the differential probability of positronium decay by a twisted photon is equal to the probability of decay by a plane-wave photon with a certain momentum moving at a certain angle to the z axis, averaged over the azimuthal angle of the incident photon.