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Maximum Entropy and Equilibrium Charge State Distributions
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
1993 (English)In: Journal of Physics B, ISSN 0953-4075, Vol. 26, no 15, 2345-2358 p.Article in journal (Refereed) Published
Abstract [en]

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-)/, where q is the charge and the mean charge, is chosen. Using the method described above calculations of equilibrium charge state distributions for copper ions (exit energy range 0.599-2.304 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. In 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 related problems like fragmentation will also be possible.

Place, publisher, year, edition, pages
1993. Vol. 26, no 15, 2345-2358 p.
Keyword [en]
maximum entropy method
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:miun:diva-1482Local ID: 160OAI: oai:DiVA.org:miun-1482DiVA: diva2:26514
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-01-10Bibliographically approved

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