MAXIMUM-ENTROPY METHOD AND EQUILIBRIUM CHARGE-STATE DISTRIBUTIONS

The maximum entropy method is implemented in order to describe equilib rium distributions arising in beam-foil spectroscopy. Since there are very few charge states involved, the usual moment conditions, based on simple powers x(i), give rise to severe numerical difficulties alread y for three moments and cannot be applied in these systems. Earlier de vised methods, based on Lagrange interpolation polynomials Q(i)(x) wit h abscissae chosen as zeros of Chebyshev polynomials in the interval b eing studied, are adapted and implemented for the present problems of charge state distributions. A reduced variable x = (q - [q])/[q], wher e q is the charge and [q] the mean charge, is chosen. Using the method described above calculations of equilibrium charge state distribution s for copper ions (exit energy range 0.559-2.304 MeV u-1) colliding wi th carbon foils are carried out in order to exhibit the usability of t he method. The new moment conditions associated to the Q(i)(x) provide a framework for a systematic analysis of equilibrium distributions. I n future work the algorithm will be applied for systematic studies of charge state distributions, of approach to equilibrium, of deviations from Gaussian behaviour, of the shell effect etc. Applications to rela ted problems like fragmentation will also be possible.