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 cI/(~-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 - Ak(lnt/t)l/(k-l) with an exact expression for AX, The formalism can be immediately generalized to the reaction kA + tA. e c k. with the consequence that the density exponent is the same, but the amplitude is modified,

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