  We consider the branching and annihilating random walk $A\to 2A$ and $2A\to
0$ with reaction rates $\sigma$ and $\lambda$, respectively, and hopping rate
$D$, and study the phase diagram in the $(\lambda/D,\sigma/D)$ plane. According
to standard mean-field theory, this system is in an active state for all
$\sigma/D>0$, and perturbative renormalization suggests that this mean-field
result is valid for $d >2$; however, nonperturbative renormalization predicts
that for all $d$ there is a phase transition line to an absorbing state in the
$(\lambda/D,\sigma/D)$ plane. We show here that a simple single-site
approximation reproduces with minimal effort the nonperturbative phase diagram
both qualitatively and quantitatively for all dimensions $d>2$. We expect the
approach to be useful for other reaction-diffusion processes involving
absorbing state transitions.
