Electronic and centre of mass transitions driven by Laguerre-Gaussian beams

We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the centre of mass wavefunction in comparison with the waist of the Laguerre-Gaussian beam and taking into account the centre of mass motion of the atomic system. Using the properties of regular spherical harmonics the internal and centre of mass dynamical variables are separated without making any multipolar expansion. The features of angular momentum exchange process assisted by Laguerre-Gaussian beams and the influence of their winding number on the selection rules and transition probability of internal and centre of mass motion are discussed.