Clusters of atoms coupled by long range interactions

Abstract

We present a study on cluster size distribution for atoms randomly distributed in a three-dimensional continuous medium. Statistical results are obtained by a Monte Carlo method. r0 being the range of interaction, it is found that the infinite cluster appears when the mean number of atoms, W, in a sphere of radius r0 reaches a value slightly higher than 2.6. Besides this, the statistical results are compared to the results deduced from branching process models : some essential features are then outlined and an approximate expression is proposed for the number of atoms belonging to clusters of small sizes, for a large range of concentration.