Collision statistics of clusters: From Poisson model to Poisson mixtures

TL;DR

This paper reviews the Poisson model for cluster-gas collisions, introduces Poisson mixture models accounting for size distribution variability, and discusses their applications and limitations in analyzing collision statistics.

Contribution

It extends traditional Poisson models by incorporating mixture models and size distribution effects, providing a more comprehensive framework for collision statistics analysis.

Findings

Poisson models are often insufficient for complex size distributions

Poisson mixture models can incorporate variability in cluster sizes

Derived collision rates for common and generalized size distributions

Abstract

Clusters traverse a gas and collide with gas particles. The gas particles are adsorbed 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 cluster sizes in a beam of clusters are discussed. We derive the average collision rates. Additionally, we present Poisson mixture models that involve also 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.