Nuclear multifragmentation along the liquid–vapor univariant equilibrium line and beyond

Abstract

J.B. Elliott, L. Phair, G.J. Wozniak “Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Reducibility (stochasticity in multiplicity distributions) and thermal scaling (one frag- ment emission probabilities are Boltsmann factors) are empirical features of nuclear mul- tifragmentation shared by the Fisher Droplet Model and by percolation. A new scaling feature (l/Z scaling) of the mz parameter of the binomial distribution shows that the fragmentation space is uniformly explored and leads to a determination of the source size. 1. INTRODUCTION The Fisher Droplet Model (FDM) [l] and p ercolation models [2] have been employed in attempts to understand multifragmentation. The FDM enjoyed early success in predicting power-law distributions in fragment masses at the critical point in a liquid-vapor diagram [3]. Percolation models also predicted a power-law distribution in fragment sizes near the critical point [4]. Both models still enjoy great popularity and have been employed in the analysis of Au multifragmentation data obtained by the EOS Collaboration [5-91. Extensive analyses of nuclear multifragmentation data have shown two empirical prop- erties of the fragment multiplicities which have been named reducibility and thermal scal- ing [lo-121. Reducibility refers to the observation that for each energy bin, E, the fragment multiplicities, n, are distributed according to a binomial or Poissonian law. As such, their multiplicity distributions, P,,, can be reduced to a one-fragment production probability p, according to the binomial or Poissonian law: where m is the total number of trials in the binomial distribution. The experimental ob- servation that P,, could be constructed in terms of p was considered evidence for stochastic fragment production, i.e. fragments are produced independently of each other. Thermal scaling refers to the feature that p behaves with temperature T as a Boltzmann factor: p o( exp(-B/T). Th us a plot of lnp vs. l/T, an Arrhenius plot, should be linear if p is a Boltzmann factor. The slope B is the one-fragment production barrier. Analyses of multifragmentation distributions along these lines have demonstrated the presence of these features [lo] and have led to the extraction of barriers [ll]. Is it possible to understand the success of these different models and are they both consistent with the empirical findings of reducibility and thermal scaling? 037.S9474/01/S - see front matter 0 2001 Elsevier Science