  We perform an analysis of recent experimental measurements and improve the
lithium interaction potentials. For $^6$Li a consistent description can be
given. We discuss theoretical uncertainties for the position of the wide $^6$Li
Feshbach resonance, and we present an analytic scattering model for this
resonance, based on the inclusion of a field-dependent virtual open-channel
state. We predict new Feshbach resonances for the $^6$Li-$^7$Li system, and
their importance for different types of crossover superfluidity models is
discussed.
