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The Landau Distribution For Charged Particles Traversing Thin Films

Author

Listed:
  • M. MARUCHO

    (Department of Chemistry, Univeristy of Houston, Houston, Texas, 77204-5003, USA)

  • C. A. GARCIA CANAL

    (Laboratorio de Física Teórica, Departamento de Física, Universidad Nacional de La Plata, C.C. 67 - 1900 La Plata, Argentina)

  • HUNER FANCHIOTTI

    (Laboratorio de Física Teórica, Departamento de Física, Universidad Nacional de La Plata, C.C. 67 - 1900 La Plata, Argentina)

Abstract

The Landau distribution as well as its first and second momenta are well suited for describing the energy loss of charged particles traversing a thin layer of matter. At present, just rational approximations and asymptotic expressions for these functions were obtained. In this paper we present a direct calculation of the integral representation of these functions obtaining perturbative and nonperturvative solutions expressed in terms of fast convergent series. We also provide a simple numerical algorithm which allows to control speed and precision of the results. The testing runs have provided, in reasonable computing times, correct results up to 13-14 significant digits on the density and distribution functions and 9-10 on the first and second momenta. If necessary, this accuracy could be improved by adding more coefficients to the algorithm.

Suggested Citation

  • M. Marucho & C. A. Garcia Canal & Huner Fanchiotti, 2006. "The Landau Distribution For Charged Particles Traversing Thin Films," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(10), pages 1461-1476.
    • Handle: RePEc:wsi:ijmpcx:v:17:y:2006:i:10:n:s0129183106009928
    DOI: 10.1142/S0129183106009928
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    Cited by:

    1. Letac, Gérard, 2022. "Duality for real and multivariate exponential families," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Shaul K. Bar-Lev, 2023. "The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments," Mathematics, MDPI, vol. 11(20), pages 1-23, October.

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