  We present a simple technique for studying collisions of ultracold atoms in
the presence of a magnetic field and radio-frequency radiation (rf). Resonant
control of scattering properties can be achieved by using rf to couple a
colliding pair of atoms to a bound state. We show, using the example of 6Li,
that in some ranges of rf frequency and magnetic field this can be done without
giving rise to losses. We also show that halo molecules of large spatial extent
require much less rf power than deeply bound states. Another way to exert
resonant control is with a set of rf-coupled bound states, linked to the
colliding pair through the molecular interactions that give rise to
magnetically tunable Feshbach resonances. This was recently demonstrated for
87Rb [Kaufman et al., Phys. Rev. A 80:050701(R), 2009]. We examine the
underlying atomic and molecular physics which made this possible. Lastly, we
consider the control that may be exerted over atomic collisions by placing
atoms in superpositions of Zeeman states, and suggest that it could be useful
where small changes in scattering length are required. We suggest other species
for which rf and magnetic field control could together provide a useful tuning
mechanism.
