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

In this work, we report calculation for Compton scattering of a gamma-ray vortex with Laguerre Gaussian wave function on an electron in the framework of the relativistic quantum mechanics. We have found the following unexpected feature. The momentum of scattered photon distributes outside of the reaction plane determined by the incident photon and the scattered electron, and hence the energy of the scattered photon also distributes. This novel result indicates that one can identify a gamma-ray vortex by measuring coincidentally the scattered angles of the electron and photon.