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We study the critical behavior of the pair annihilation model (PAM) with diffusion in one, two and three dimensions, using the pair approximation (PA) and Monte Carlo simulation. Of principal interest is the dependence of the critical creation rate, lambda_c, on the diffusion probability D, in particular, whether survival is possible at arbitrarily small creation rates, for sufficiently rapid diffusion. Whilst the PA predicts that in any spatial dimension d ≥ 1, lambda_c -> 0 at some diffusiondoi:10.1088/1742-5468/2010/05/p05009 fatcat:wrqz273mxvdzvictahxghngz2e