Reconstructing the impact parameter dependence of experimental observables from intermediate energy heavy-ion collision data

Abstract

22 pages, 15 figures. Submitted to Physical Review CPrecise constraints on the equation of state (EoS) of dense matter can be obtained through comparison of data from heavy-ion collisions (HIC) with transport models employing different effective interactions. An essential input for such comparisons is a reliable estimate of the impact parameter distributions P(b) which are representative of the data. For HIC in the intermediate energy range (20-150 MeV/A), there was no way up to now to extract such distributions from data in a model-independent way and it is well known that the only existing method for experimental impact parameter estimation underestimates those of the most central collisions, but not by how much. We adopt a method first developed for ultra-relativistic HIC in which a monotonic relationship is assumed between the mean value of a given observable X and b, whose parameters are adjusted in order to reproduce the b-integrated inclusive distribution P(X), taking into account fluctuations of X around . Using Bayes' theorem, the resulting conditional probability distribution P(X|b) can then be used to deduce both the impact parameter dependence of the observable X and the impact parameter distributions P(b|S) of any subset of events S represented by the corresponding experimental distribution P(X|S). We perform a survey of the bombarding energy, total mass and mass asymmetry dependence of the deduced impact parameter dependence for the most common observables used for centrality estimation and/or selections. A consistent picture of the evolution of reaction mechanisms in this energy range towards the participant-spectator regime emerges. Evaluating the effective centrality of commonly-used selections of "central collisions" we show that it is largely independent of the colliding system, decreasing in a very similar way with the available energy in the center of mass frame