  The formulation of the interaction of matter with singular light fields needs
special care. In a recent article [Phys.~Rev.~A {\bf 91}, 033808 (2015)] we
have shown that the Hamiltonian describing the interaction of a twisted light
beam having parallel orbital and spin angular momenta with a small object
located close to the phase singularity can be expressed only in terms of the
electric field of the beam. Here, we complement our studies by providing an
interaction Hamiltonian for beams having antiparallel orbital and spin angular
momenta. Such beams may exhibit unusually strong magnetic effects. We further
extend our formulation to radially and azimuthally polarized beams. The
advantages of our formulation are that for all beams the Hamiltonian is written
solely in terms of the electric and magnetic fields of the beam and as such it
is manifestly gauge-invariant. Furthermore it is intuitive by resembling the
well-known expressions in the dipole-electric and dipole-magnetic moment
approximations.
