  Recent experiments involving the interaction of optical vortices with atoms
in quadrupole transitions have been shown to be accompanied by the exchange of
orbital angular momentum (OAM) between the electronic states of the atom and
the optical vortex field. Earlier work by both theory and experiment had ruled
out the transfer of a vortex OAM to the electronic degrees of freedom in an
electric dipole atomic transition and it has been confirmed that the lowest
multipolar order involving an OAM transfer to the electronic motion is indeed
the electric quadrupole. Hitherto, the quadrupole transition involving optical
vortices has not been quantified and we have thus set out to evaluate the
absorption rate accompanied by an OAM transfer with reference to the
$6^2S_{1/2}\rightarrow 5^2D_{5/2}$ in Cs when caesium atoms are subject to the
field of a linearly polarized optical vortex. Our results assuming typical
experimentally accessible parameters indicate that the absorption rate for
moderate light intensities is smaller than the quadrupole spontaneous emission
rate, but should still be within the measurement capabilities of modern
spectroscopic techniques.
