  The intrinsic contribution to the spin Hall effect in a 2DEG with
non-magnetic impurities is studied in a quantum Boltzmann approach. It is shown
that if the steady state response is perturbative in the spin-orbit coupling
parameter $\lambda$, then the precession term--vital for Dyakonov-Perel
relaxation and the key to the spin Hall effect in previous similar Boltzmann
studies--must be left out to first order in spin-orbit coupling. In such a case
one would have that to lowest order in the parameters electric field,
spin-orbit coupling, impurity strength and impurity concentration there is no
intrinsic contribution to the spin Hall effect, not only for a Rashba coupling
but for a general spin-orbit coupling. To cover all possible lowest order terms
we consider also electric field induced corrections to the collision integral
in the Keldysh formalism. However, these corrections turn out to be of second
order in $\lambda$. For comparison we derive some familiar results in the case
when the response is not assumed to be perturbative in $\lambda$. We also
include a detailed discussion of why a relaxation time approximation of the
collision integral fails. Finally we make a comment on pseudospin currents in
bilayer graphene.
