  We present some exact results for branching and annihilating random walks. We
compute the nonuniversal threshold value of the annihilation rate for having a
phase transition in the simplest reaction-diffusion system belonging to the
directed percolation universality class. Also, we show that the accepted
scenario for the appearance of a phase transition in the parity conserving
universality class must be improved. In order to obtain these results we
perform an expansion in the branching rate around pure annihilation, a theory
without branching. This expansion is possible because we manage to solve pure
annihilation exactly in any dimension.
