  Dynamical mean-field approximations are performed to study the phase
transition of a pair contact process with diffusion in different spatial
dimensions. The level of approximation is extended up to 18-site clusters for
the one-dimensional model. The application of coherent anomaly method shows
that the critical $\beta$ exponent does not depend on the strength of diffusion
rate. The extension of the mean-field approximation to higher dimensions also
suggests that the critical behavior may be described by a unique set of
exponents.
