  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.
