Fluctuations of fragment observables

This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak and the occurrence of a phase transition or a critical phenomenon is critically analyzed. Many different phenomena can lead both to the creation and to the suppression of a fluctuation peak. In particular, the role of constraints due to conservation laws and to data sorting is shown to be essential. From the experimental point of view, a comparison of the available fragmentation data reveals that there is a good agreement between different data sets of basic fluctuation observables, if the fragmenting source is of comparable size. This compatibility suggests that the fragmentation process is largely independent of the reaction mechanism (central versus peripheral collisions, symmetric versus asymmetric systems, light ions versus heavy ion induced reactions). Configurational energy fluctuations, that may give important information on the heat capacity of the fragmenting system at the freeze out stage, are not fully compatible among different data sets and require further analysis to properly account for Coulomb effects and secondary decays. Some basic theoretical questions, concerning the interplay between the dynamics of the collision and the fragmentation process, and the cluster definition in dense and hot media, are still open and are addressed at the end of the paper. A comparison with realistic models and/or a quantitative analysis of the fluctuation properties will be needed to clarify in the next future the nature of the transition observed from compound nucleus evaporation to multi-fragment production.Comment: Contribution to WCI (World Consensus Initiative) Book " "Dynamics and Thermodynamics with Nuclear Degrees of Freedom", to appear on Euorpean Physics Journal A as part of the Topical Volume. 9 pages, 12 figure

Tracking energy fluctuations from fragment partitions in the Lattice Gas model

Partial energy fluctuations are known tools to reconstruct microcanonical heat capacities. For experimental applications, approximations have been developed to infer fluctuations at freeze out from the observed fragment partitions. The accuracy of this procedure as well as the underlying independent fragment approximation is under debate already at the level of equilibrated systems. Using a well controlled computer experiment, the Lattice Gas model, we critically discuss the thermodynamic conditions under which fragment partitions can be used to reconstruct the thermodynamics of an equilibrated system.Comment: version accepted for publication in Phys.Rev.

Comment on "Partial energies fluctuations and negative heat capacities" by X. Campi et al

Studying the energy partioning published in nucl-th/0406056v2 we show that the presented results do not fulfill the sum rule due to energy conservation. The observed fluctuations of the energy conservation test point to a numerical problem. Moreover, analysis of the binding energies show that the fragment recognition algorithm adopted by Campi et al. leads with a sizeable probability to fragments containing up to the total mass even for excitation energies as large as 3/4 of the total binding. This surprising result points to another problem since the published inter-fragment energy is not zero while a unique fragment is present. This problem may be due to either the fragment recognition algorithm or to the definition of the inter and intra-fragment energy. These numerical inconsistencies should be settled before any conclusion on the physics can be drawn

Experimental Signals of Phase Transition

The connection between the thermodynamics of charged finite nuclear systems and the asymptotically measured partitions is presented. Some open questions, concerning in particular equilibrium partitions are discussed. We show a detailed comparison of the decay patterns in Au+ C,Cu,Au central collisions and in Au quasi-projectile events. Observation of abnormally large fluctuations in carefully selected samples of data is reported as an indication of a first order phase transition (negative heat capacity) in the nuclear equation of state.Comment: 8 pages, 8th International Conference on Nucleus-Nucleus Collisions, Moscow 200