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A mean-field theory for the diffusion-controlled cluster formation is presented by considering the competition among the different portions of a growing cluster for the incoming diffusive particles. This competition is shown to introduce a screening length which depends inversely on the density of the cluster. The Hausdorff dimensionality D of these clusters is shown to be (d^{2+1) } (d+1) where d is the Euclidean dimensionality. This result is in excellent agreement with that of the computer simulations of Witten and Sander and of Meakin.
M. Muthukumar (Mon,) studied this question.
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