ar X iv : c on d - m at / 9 20 70 15 v 1 1 5 Ju l 1 99 2 Fast - diffusion mean - field theory for k - body reactions in one dimension

We derive an improved mean-field approximation for k-body annihilation reactions kA → inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q ≤ 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hardcore particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values. Criteria for validity of the meanfield theory and its use in phenomenological data fits are derived. Numerical tests are reported for k = 3, 4, 5, 6.