  We consider spin transport in a two-component ultracold Fermi gas with
attractive interspecies interactions close to the BCS pairing transition. In
particular, we consider the spin-transport relaxation rate and the
spin-diffusion constant. Upon approaching the transition, the scattering
amplitude is enhanced by pairing fluctuations. However, as the system
approaches the transition, the spectral weight for excitations close to the
Fermi level is decreased by the formation of a pseudogap. To study the
consequence of these two competing effects, we determine the spin-transport
relaxation rate and the spin-diffusion constant using both a Boltzmann approach
and a diagrammatic approach. The former ignores pseudogap physics and finite
lifetime effects. In the latter, we incorporate the full pseudogap physics and
lifetime effects, but we ignore vertex corrections, so that we effectively
calculate single-particle relaxation rates instead of transport relaxation
rates. We find that there is qualitative agreement between these two approaches
although the results for the transport coefficients differ quantitatively.
