RENORMALIZATION-GROUP STUDY OF THE A+B-]PHI DIFFUSION-LIMITED REACTION

The A + B --> empty set diffusion-limited reaction, with equal initial densities a(0) = b(0) = n(0), is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension d > 2 an effective theory is derived, from which the density and correlation functions call be calculated. We find the density decays in time as a, b similar to C root Delta(Dt)(-d/4) for d < 4, with Delta = n(0) - C'n(0)(d/2) + ..., where C is a universal constant and C' is nonuniversal. The calculation is extended to the case of unequal diffusion constants D-A not equal D-B, resulting in a new amplitude but the same exponent. For d less than or equal to 2 a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an epsilon = 2 - d expansion. Finally, we address reaction zones formed in the steady state by opposing currents of A and B particles, and derive scaling properties.