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We theoretically investigate a Rashba spin-orbit coupled Fermi gas nearFeshbach resonances, by using mean-field theory and a two-channel model thattakes into account explicitly Feshbach molecules in the close channel. In theabsence of spin-orbit coupling, when the channel coupling $g$ between theclosed and open channels is strong, it is widely accepted that the two-channelmodel is equivalent to a single-channel model that excludes Feshbach molecules.This is the so-called broad resonance limit, which is well-satisfied byultracold atomic Fermi gases of $^{6}$Li atoms and $^{40}$K atoms in currentexperiments. Here, with Rashba spin-orbit coupling we find that the conditionfor equivalence becomes much more stringent. As a result, the single-channelmodel may already be insufficient to describe properly an atomic Fermi gas of$^{40}$K atoms at a moderate spin-orbit coupling. We determine a characteristicchannel coupling strength $g_{c}$ as a function of the spin-orbit couplingstrength, above which the single-channel and two-channel models areapproximately equivalent. We also find that for narrow resonance with smallchannel coupling, the pairing gap and molecular fraction is strongly suppressedby SO coupling. Our results can be readily tested in $^{40}$K atoms by usingoptical molecular spectroscopy.

Validity of single-channel model for a spin-orbit coupled atomic Fermi gas near Feshbach resonances