  We study the linear response spin Hall conductivity of a two-dimensional
electron gas (2DEG) in the presence of the Rashba spin orbit interaction in the
diffusive transport regime. When defect scattering is modeled by isotropic
short-range potential scatterers the spin Hall conductivity vanishes due to the
vertex correction. A non-vanishing spin Hall effect may be recovered for
dominantly forward defect scattering.
