Compton Scattering of γ-Ray Vortex with Laguerre Gaussian Wave Function

In this work, we report calculation for Compton scattering of a γ-ray vortex with a wave function of Laguerre Gaussian on an electron in the framework of the relativistic quantum mechanics. We consider the coincidence measurement of the scattered photon and the scattered electron from each Compton scattering. The momentum of the scattered photon distributes outside of the reaction plane determined by the incident photon and the scattered electron, and the energy of the scattered photon also distributes, when the scattered angle of the electron is simultaneously measured. These distributions depend on the angular momentum and the node number of the Laguerre Gaussian function of the incident photon. Thus, the coincident measurement for Compton scattering is useful to identify the nature of the vortex photon wave function.