Skip to main content
Log in

Variational calculation of the angular width of the multiple scattering distribution in foil transmission

  • Published:
Zeitschrift für Physik A Atoms and Nuclei

Abstract

A simple formula is derived for calculating the angular width of multiple scattering distributions for atomic particles traversing thin foils. The universal result is obtained by applying the variational method on standard multiple scattering theory. This procedure can be carried through in a straight-forward way, thus saving lengthy series expansions and Fourier transforms. In the case of power cross sections exact analytical expressions can be obtained. A remarkably good agreement is found between our calculation and previous theories, as well as with results from our computer simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sigmund, P., Winterbon, K.B.: Nucl. Instrum. Methods119, 541 (1974)

    Google Scholar 

  2. Mayer, L.: Phys. Status Solidi44, 253 (1971)

    Google Scholar 

  3. Bothe, W.: Z. Phys.5, 63 (1921)

    Google Scholar 

  4. Lindhard, J., Nielsen, V., Scharff, M.: K. Dan. Vidensk. Selsk. Mat. Fys. Medd.36, no 10 (1968)

  5. Roussopoulos, P.: C.R. Acad. Sci.236, 1858 (1953)

    Google Scholar 

  6. Williams, M.M.R.: Mathematical methods in particle transport theory. London: Butterworth et Co. Ltd. 1970

    Google Scholar 

  7. Duderstadt, J.J., Martin, N.R.: Transport theory. New York: John Wiley & Sons Inc. 1979

    Google Scholar 

  8. Moisewitsch, B.L.: Variational principles. London: John Wiley & Sons, Ltd. 1966

    Google Scholar 

  9. Demkov, Yu.N.: Sov. Phys. JETP11, 1351 (1960)

    Google Scholar 

  10. Kleber, M., Zweigel, J.: Phys. Rev. A19, 579 (1979)

    Google Scholar 

  11. Molière, G.: Z. Naturforsch.3a, 78 (1949)

    Google Scholar 

  12. Bethe, H.A.: Phys. Rev.89, 1256 (1953)

    Google Scholar 

  13. Bohr, N.: K. Dan. Vidensk. Selsk. Mat. Fys. Medd.18, no 8 (1948)

  14. Hvelplund, P., Laegsgard, E., Olsen, J.ø., Pedersen, E.H.: Nucl. Instrum. Methods90, 315 (1970)

    Google Scholar 

  15. Wilson, W.D., Haggmark, L.G., Biersack, J.P.: Phys. Rev. B15, 2458 (1977)

    Google Scholar 

  16. Winterbon, K.B.: Radiat. Eff.13, 215 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We like to thank Mrs. Barbara Standke for typing the manuscript. One of us (M.M.J.) gratefully acknowledges the kind hospitality of the atomic collision group at the Hahn-Meitner-Institute, C-2, during his stay in Berlin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jakas, M.M., Biersack, J.P. Variational calculation of the angular width of the multiple scattering distribution in foil transmission. Z Physik A 315, 29–33 (1984). https://doi.org/10.1007/BF01436205

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01436205

Keywords

Navigation