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.
Similar content being viewed by others
References
Sigmund, P., Winterbon, K.B.: Nucl. Instrum. Methods119, 541 (1974)
Mayer, L.: Phys. Status Solidi44, 253 (1971)
Bothe, W.: Z. Phys.5, 63 (1921)
Lindhard, J., Nielsen, V., Scharff, M.: K. Dan. Vidensk. Selsk. Mat. Fys. Medd.36, no 10 (1968)
Roussopoulos, P.: C.R. Acad. Sci.236, 1858 (1953)
Williams, M.M.R.: Mathematical methods in particle transport theory. London: Butterworth et Co. Ltd. 1970
Duderstadt, J.J., Martin, N.R.: Transport theory. New York: John Wiley & Sons Inc. 1979
Moisewitsch, B.L.: Variational principles. London: John Wiley & Sons, Ltd. 1966
Demkov, Yu.N.: Sov. Phys. JETP11, 1351 (1960)
Kleber, M., Zweigel, J.: Phys. Rev. A19, 579 (1979)
Molière, G.: Z. Naturforsch.3a, 78 (1949)
Bethe, H.A.: Phys. Rev.89, 1256 (1953)
Bohr, N.: K. Dan. Vidensk. Selsk. Mat. Fys. Medd.18, no 8 (1948)
Hvelplund, P., Laegsgard, E., Olsen, J.ø., Pedersen, E.H.: Nucl. Instrum. Methods90, 315 (1970)
Wilson, W.D., Haggmark, L.G., Biersack, J.P.: Phys. Rev. B15, 2458 (1977)
Winterbon, K.B.: Radiat. Eff.13, 215 (1972)
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01436205