Perturbative approach to anA+B→C reaction-diffusion system

The hierarchy of kinetic equations for diffusion-reaction processes are rederived using a Fock space formalism for the Master equation. In the diffusion dominated case the reactive part can be analyzed perturbationally. In according to the experimental situation the behaviour of the system is governed by one space dimension. The summation of a whole class of terms in a perturbative serie yields the scaling behaviour of the production rate of the C particle. The solution depends on the ratio of the diffusion constantsD=D_A/D_B and the ratio of the characteristic time scales for reaction and diffusion, respectively. Various special cases and approximations are discussed in terms ofD. The analytical results can be supported by numerical simulations.