Collision statistics of clusters: from Poisson model to Poisson mixtures

Clusters traverse a gas and collide with gas particles. The gas particles are absorbed, and the clusters become hosts. If the clusters are size-selected, the number of guests will be Poisson distributed. We review this by showcasing four laboratory procedures that all rely on the validity of the Poisson model. The effects of a statistical distribution of the clusters' sizes in a beam of clusters are discussed. We derive the average collision rates. Additionally, we present Poisson mixture models that also involve standard deviations. We derive the collision statistics for common size distributions of hosts and also for some generalizations thereof. The models can be applied to large noble gas clusters traversing doping gas. While outlining how to fit a generalized Poisson to the statistics, we still find even these Poisson models to be often insufficient.