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Abundance of Nanoclusters in a Molecular Beam: The Magic Numbers

We review the theory behind abundance of experimentally observed nanoclusters produced in beams, aiming to understand their magic number behavior. It is shown how use of statistical physics, with certain assumptions, reduces the calculation of equilibrium abundance to that of partition functions of single clusters. Methods to practically calculate these partition functions are introduced. As an illustration, we compute the abundance of Lennard-Jones clusters at low temperatures, which reveals their experimentally observed magic number behavior. We then briefly review kinetic approach to the problem and comment on the interplay between chemical, mechanical and thermodynamic stability of the clusters in more generality.