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Maximum entropy method and equilibrium charge state distributions

The maximum entropy method is implemented in order to describe equilibrium distributions arising in beam-foil spectroscopy. Since there are very few charge states involved, the usual moment conditions, based on simple powers xi, give rise to severe numerical difficulties already for three moments and cannot be applied in these systems. Earlier devised methods, based on Lagrange interpolation polynomials Qi(x) with abscissae chosen as zeros of Chebyshev polynomials in the interval being studied, are adapted and implemented for the present problems of charge state distributions. A reduced variable x=(q-(q))/(q), where q is the charge and (q) the mean charge, is chosen. Using the method described above calculations of equilibrium charge state distributions for copper ions (exit energy range 0.559-2.304 MeV u-1) colliding with carbon foils are carried out in order to exhibit the usability of the method. The new moment conditions associated to the Qi(x) provide a framework for a systematic analysis of equilibrium distributions.