  We show that two types of spin-orbit coupling in the 2 dimensional hole gas
(2DHG), with and without inversion symmetry breaking, contribute to the
intrinsic spin Hall effect\cite{murakami2003,sinova2003}. Furthermore, the
vertex correction due to impurity scattering vanishes in both cases, in sharp
contrast to the case of usual Rashba coupling in the electron band. Recently,
the spin Hall effect in a hole doped $GaAs$ semiconductor has been observed
experimentally by Wunderlich \emph{et al}\cite{wunderlich2004}. From the fact
that the life time broadening is smaller than the spin splitting, and the fact
impurity vertex corrections vanish in this system, we argue that the observed
spin Hall effect should be in the intrinsic regime.
