  We develop the microscopic theory of the extrinsic spin Hall conductivity of
a two-dimensional electron gas, including skew-scattering, side-jump, and
Coulomb interaction effects. We find that while the spin-Hall conductivity
connected with the side-jump is independent of the strength of
electron-electron interactions, the skew-scattering term is reduced by the
spin-Coulomb drag, so the total spin current and the total spin-Hall
conductivity are reduced for typical experimental mobilities. Further, we
predict that in paramagnetic systems the spin-Coulomb drag reduces the spin
accumulations in two different ways: (i) directly through the reduction of the
skew-scattering contribution (ii) indirectly through the reduction of the spin
diffusion length. Explicit expressions for the various contributions to the
spin Hall conductivity are obtained using an exactly solvable model of the
skew-scattering.
