On the exchange of orbital angular momentum between twisted photons and atomic electrons

We obtain an expression for the matrix element for scattering of a twisted (Laguerre-Gaussian profile) photon from a hydrogen atom. We consider photons incoming with an orbital angular momentum (OAM) of l (h) over bar, carried by a factor of e(il phi) not present in a plane-wave or pure Gaussian profile beam. The nature of the transfer of +2l units of OAM from the photon to the azimuthal atomic quantum number of the atom is investigated. We obtain simple formulas for these OAM flip transitions for elastic forward scattering of twisted photons when the photon wavelength lambda is large compared with the atomic target size a, and small compared with the Rayleigh range z(R), which characterizes the collimation length of the twisted photon beam.