  Transverse spin diffusion in a polarized, interacting Fermi gas leads to the
Leggett-Rice effect, where the spin current precesses around the local
magnetization. With a spin-echo sequence both the transverse diffusivity and
the spin-rotation parameter $\gamma$ are obtained; the sign of $\gamma$ reveals
the repulsive or attractive character of the effective interaction. In a
trapped Fermi gas the spin diffusion equations become nonlinear, and their
numerical solution exhibits an inhomogeneous spin state even at the spin echo
time. While the microscopic diffusivity and $\gamma$ increase at weak coupling,
their apparent values inferred from the trap-averaged magnetization saturate in
agreement with a recent experiment for a dilute ultracold Fermi gas.
