Equilibrium in nuclear multifragmentation and percolation, and the behaviour of the macroscopic entropy near the phase transition

Abstract

In this paper we attempt to explain the success of equilibrium statistical models in the analysis of products of small impact parameter heavy ion collisions. Our argument is based on an examination of restrictions on the space of microscopic states due to the dynamics of the collision process. We then proceed to consider the example of a simple cubic bond breaking percolation process. We show that slow convergence of certain physical observables near the phase transition is related to the fact that all partitions of the total number of sites have small probabilities (entropy maximum). We discuss the importance of similar behaviour for decay of highly excited nuclei.

Liquid–Gas phase transition in nuclei

“…Although transport models predict that nucleonnucleon collisions can rapidly thermalize nucleon momentum distributions at Fermi energies and above, the application of statistical equilibrium concepts seems counter-intuitive when dealing with highly-excited systems which disintegrate almost as soon as they are formed. Given that reaction products are produced on a timescale which is comparable with the time for the projectile to 'cross' the target, the success of equilibrium models could imply that the dynamical evolution of the system prior to multifragmentation is important only insofar as it determines the constraints which are required to characterize effective statistical ensembles in order to understand the data [45,46]. To end this section, we will further develop these points and explain the paradigm shift required in order to progress with the identification of a phase transition in hot nuclei.…”

“…To use classical equilibrium statistical mechanics requires an adequate definition of the relevant microstates i.e. just that information which ineluctably entails the production of a given macroscopic event [45]. For the multibody decay of hot nuclei, the microstates relevant to a statistical description correspond to the microscopic configuration of each reaction at the freeze-out instant: this is defined as the time after which the characteristics of the fragments and particles produced in the reaction will no longer significantly change, apart from the effects of secondary decay (evaporation of light particles due to residual excitation energy) and Coulombian acceleration due to mutual repulsion between charged fragments.…”

“…To quote the fathers of the first statistical model of composite fragment production in the 20-200 MeV per nucleon bombarding energy range, Randrup and Koonin, "it is not necessary to argue that equilibrium be reached in any given collision, since a statistical occupation of the phase space at the one-fragment inclusive level can occur as a result of averaging over many separate collision events, each of which can be far from equilibrium throughout" [73]. This approach has been called pseudo-equilibrium [45].…”

“…Early on in the development of statistical models for multifragmentation, Gross suggested that equilibrium might be achieved at the level of each reaction by "chaotic mixing" [74], a sufficiently intense period of nucleon and energy exchange between the strongly-interacting nascent fragments as the system expands towards freeze-out. However, as Cole has pointed out [45], this is a strong hypothesis which can in addition unnecessarily complicate the interpretation of results. Instead we concern ourselves only with the equilibrium of statistical ensembles composed of the systems at freeze-out; more precisely, as exact equilibrium is a theoretical abstraction which cannot be achieved in the real world, our statistical ensemble need only be sufficiently close to equilibrium for most observable properties to be consistent with a uniform population of the phase space.…”

Multifragmentation of atomic nuclei

“…A possible solution to the first of these difficulties, at least with respect to probabilities corresponding to given mass-charge partitions of the excited parent nucleus, has been given in [7] and is based on the ensemble approach to equilibrium statistical mechanics. Accelerator-based nuclear physics is one of the few areas where projectiletarget collisions produce isolated systems.…”