Statistical Models of Heavy Ion Collisions and Their Parallels

Abstract

Collisions between heavy ions produce highly fragmented nuclei, and at very high energies many new particles are produced. One approach to understanding the outcome of such collisions is based on statistical thermodynamics. This article discusses a simple statistical framework and shows its connection to several other approaches and fields. In the collision of two heavy ions or, in general, any two objects, the distribution of products and fragments is of concern. For example, the EOS collaboration¹ reported a power law distribution of fragments with an exponent τ = 2.2. Namely, the number of clusters of size k falls as k ^−τ. This τ is related to the critical point properties of a nuclear liquid-gas phase transition, and using a percolative picture² other critical exponents were obtained. Data on basalt-basalt collisions³ has a similar behavior: The number of fragments dN in a mass interval dm falls as dN/dm ~ m ^−τ with τ = 1.68, and this behavior occurs over 16 orders of magnitude in m. This feature also appears in the fragmentation of a piece of gypsum⁴ with an exponent τ = 1.63, and this property is used as an example of a behavior known as self-organized criticality.⁵ Even in the shuffling of a deck of cards, a power law can be found. Some of the specific ideas to be discussed will be illustrated with this simple example.