Renormalization group calculation for the reaction kA + 0

The diffusion-controlled reaction kA + M is known IO be strongly dependent on Ruchlations in dimensions d < d. = 2 / ( k 1). We develop a field-theoretic renormalization group approach to this system which allows explicit calculation of the observables as expansions in c I / ( ~ I ) , where f = d, d . For the density it is found that, asymptotically, n Akr-d/Z. The decay exponent is emcl to all orders in 6, and the amplitude Ax is universal, and is calculated to second order in 6'/('-') for k = 2.3. The correlation function is dculated to first order, along with a long-wavelengJh expansion for the second-order term. For d = d, we find n A k ( l n t / t ) l / ( k l ) with an exact expression for A X , The formalism can be immediately generalized to the reaction k A + t A . e c k. with the consequence that the density exponent is the same, but the amplitude is modified,