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 neighbours with probability 0 < q less-than-or-equal-to 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hard-core 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 mean-field theory and its use in phenomenological data fits are derived. Numerical tests are reported for k = 3, 4, 5, 6.