∆-Scaling in Spectator Fragmentation

Universal scaling-laws of fluctuations (the ∆-scaling laws) have been derived for equilibrium systems, and shown to apply also in certain out-of-equilibrium situations. [1]. Recently looking for signals of a phase transition in multifragmentation reactions the model-independent theory of universal fluctuation has been used [2]. The ∆-scaling is observed when two or more probability distributions PN [m] of the observable m for a system size N collapse onto a single scaling curve φ(z(∆)) independent of system size when plotted in terms of the scaling variables. The scaling law with ∆=1/2 is associated with low temperature (ordered) systems, or with observables which are not related to an order parameter. Scaling with ∆=1 is seen at high temperature (disordered system) and also for critical systems. For m to be an order parameter it must exhibit a corresponding change of ∆-scaling regime when some suitable control parameter (e.g. available energy, temperature, etc.) is varied. Using the data from the most recent ALADiN experiment [3], it has been investigated whether the Zmax distributions follow the ∆-scaling law. The multiplicity of charged particles measured in the Catania Hodoscope was used as impact parameter in oder to avoid possible autocorrelation with Zmax. An additional selection has, moreover, been applied to the data by defining two cuts on the asymmetry variable