Nuclear multifragmentation critical exponents.

In a recent Letter [1] the EoS collaboration presented data of fragmentation of 1 A GeV gold nuclei incident on carbon. By analyzing moments of the fragment charge distribution, the authors claim to determine the values of the critical exponents γ, β, and τ for finite nuclei. These data represent a crucial step forward in our understanding of the physics of nuclear fragmentation. However, as we will show in the following, the analysis presented in [1] is not sufficient to support the claim that the critical exponents for nuclear fragmentation have been unambiguously determined. The main difficulty in observing critical behavior in nuclear fragmentation is that nuclei cannot be prepared and held near the temperature and density associated with the critical point. Instead, complicated nuclear reactions must be used to excite the nuclei, which may then expand to conditions sufficiently close to the critical point. The time spent at these conditions during the reaction is an open question. However, even if one assumes that conditions sufficiently close to critical are explored in some of the observed reactions, there remain at least two problems with interpreting the subsequent experimental signals. One is to identify which of the resulting particles have participated in the equilibrated system near the critical conditions, and which have resulted from the " pre-equilibrium " stage of the reaction. The other problem is to measure the " temperature " of the decaying system. These two problems are interrelated in the procedure used in Ref. [1], where the authors assume that the observed multiplicity can be used as an indicator of temperature. In this comment, we use the percolation model of nuclear fragmentation [2] to demonstrate the nature of these problems in determining critical exponents. In percolation models one uses a bond breaking parameter p with values between 0 and 1, including p c , the " critical value ". In this model, near the critical point, the charge of the largest fragment is Z max ∝ (p − p c) β , and the second moment of the mass distribution is M 2 ∝ |p − p c | −γ , with β = 0.41 and γ = 1.8. We follow the analysis of [1] and use m c = 26, in accordance with the cut employed in [1]. It is worth noting that we also find roughly identical values of γ and γ ′ for the liquid …