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

Precise constraints on the equation of state (EoS) of dense matter can be obtained through comparison of data from heavy-ion (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 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.