RENORMALIZATION-GROUP CALCULATION FOR THE REACTION KA-]CIRCLE-DIVIDE

The diffusion-controlled reaction kA --> empty set is known to be stro ngly dependent on fluctuations in dimensions d less-than-or-equal-to d (c) = 2/(k - 1). We develop a field-theoretic renormalization group ap proach to this system which allows explicit calculation of the observa bles as expansions in epsilon(1/(k - 1)), Where epsilon = d(c) - d. Fo r the density it is found that, asymptotically, n approximately A(k)t( -d/2). The decay exponent is exact to all orders in epsilon, and the a mplitude A(k) is universal, and is calculated to second order in epsil on(1/(k - 1)) for k = 2,3. The correlation function is calculated to f irst order, along with a long-wavelength expansion for the second-orde r term. For d = d(c) we find n approximately A(k)(ln t/t)1/(k - 1) wit h an exact expression for A(k). The formalism can be immediately gener alized to the reaction kA --> lA, l < k, with the consequence that the density exponent is the same, but the amplitude is modified.