  Usually, photons are described by plane waves with a definite 4-momentum. In
addition to plane-wave photons, "twisted photons" have recently entered the
field of modern laser optics; these are coherent superpositions of plane waves
with a defined projection hbar*m of the orbital angular momentum onto the
propagation axis, where m is integer. In this paper, we show that it is
possible to produce high-energy twisted photons by Compton backscattering of
twisted laser photons off ultra-relativistic electrons. Such photons may be of
interest for experiments related to the excitation and disintegration of atoms
and nuclei, and for studying the photo-effect and pair production off nuclei in
previously unexplored experimental regimes.
