  Transfer mechanism of orbital angular moment(OAM) of light to trapped
ground-state atoms under paraxial approximation is well known. Here we show how
optical OAM of a Laguerre-Gaussian(LG) beam under paraxial approximation can be
transferred to trapped Rydberg atoms. Optical OAM is shown to be transferable
to a Rydberg electronic state in dipole transition. The Gaussian part of the
profile of the LG beam, which is generally neglected , is found to have an
important effect on the OAM transfer to the Rydberg atoms. Numerical
calculations are calculated based on this theory for Rubidium Rydberg atoms
trapped in a harmonic potential. Our results exhibit the mixing of final states
of different parities.
