  We show that radio-frequency spectroscopy on weakly-bound molecules is a
powerful and sensitive tool to probe molecular energy structure as well as
atomic scattering properties. An analytic expression of the rf excitation
lineshape is derived, which in general contains a bound-free component and a
bound-bound component. In particular, we show that the bound-free process
strongly depends on the sign of the scattering length in the outgoing channel
and acquires a Fano-type profile near a Feshbach resonance. The derived
lineshapes provide an excellent fit to both the numerical calculation and the
experimental measurements.
