Skip to main content
SpringerLink
Log in

A semi-empirical approach to the calculation of absolute inner-shell electron impact ionization cross sections

  • Published:
Zeitschrift für Physik D Atoms, Molecules and Clusters

Abstract

Extending a recently developed semiclassical approach, we report the development of a formula which allows the satisfactory description and prediction of absolute electron impact ionization cross sections for K, L, and M inner-shell ionization in the energy range from threshold up to 109 eV for all elements. The present formulation also allows to derive and extend a previously noted scaling law for K-shell ionization. The present results are compared with previous theoretical and experimental determinations where available.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Powell, C.J.: Electron impact ionization. Märk, T.D., Dunn, G.H. (eds.), Chap. 6, pp. 198–231. Wien: Springer 1985

    Google Scholar 

  2. Hippler, R.: Progress in atomic spectroscopy. Part C. Beyer, H.G., Kleinpoppen, H. (eds.), pp. 511–575. New York: Plenum 1984

    Google Scholar 

  3. Powell, C.J.: Rev. Mod. Phys.48, 33 (1976)

    Google Scholar 

  4. Tawara, H., Harrison, K.G., de Heer, F.J.: Physica63, 351 (1973)

    Google Scholar 

  5. Garscadden, A.: Z. Phys. D24, 97 (1992)

    Google Scholar 

  6. Bethe, H.: Ann. Phys.5, 325 (1930)

    Google Scholar 

  7. Inokuti, M.: Rev. Mod. Phys.43, 297 (1971)

    Google Scholar 

  8. Scofield, J.H.: Phys. Rev. A18, 963 (1978)

    Google Scholar 

  9. Eschway, P., Manakos, P.: Z. Phys. A308, 199 (1982)

    Google Scholar 

  10. Gryzinski, M.: Phys. Rev. A138, 305 (1965)

    Google Scholar 

  11. Casnati, E., Tartari, A., Baraldi, C.: J. Phys. B15, 155 (1982); B16, 505 (1983)

    Google Scholar 

  12. Deutsch, H., Märk, T.D.: Int. J. Mass. Spectrom. Ion Proc.79, R1 (1987)

  13. Margreiter, D., Deutsch, H., Märk, T.D.: Contrib. Plasma Phys.30, 487 (1990)

    Google Scholar 

  14. Deutsch, H., Margreiter, D., Märk, T.D.: Proceedings of the Pentagonale Workshop on Elementary Processes in Clusters, Lasers and Plasmas, Kühtai. Märk, T.D., Schrittwieser, R.W. (eds.), pp. 28–40. STUDIA 1991

  15. Margreiter, D., Deutsch, H., Schmidt, M., Märk, T.D.: Int. J. Mass. Spectrom. Ion Proc.100, 157 (1990)

    Google Scholar 

  16. Deutsch, H., Cornelissen, C., Cespiva, L., Bonacic-Koutecky, V., Margreiter, D., Märk, T.D.: Int. J. Mass. Spectrom. Ion Proc. (in press) (1993)

  17. Gryzinski, M.: Phys. Rev.138, 322 (1965)

    Google Scholar 

  18. Thomson, J.J.: Philos. Mag.23, 449 (1912)

    Google Scholar 

  19. Märk, T.D.: Beitr. Plasma Phys.22, 257 (1982)

    Google Scholar 

  20. Younger, S.M., Märk, T.D.: Electron impact ionization. Märk, T.D., Dunn, G.H. (eds.), Chap. 2, pp. 35, 36. Wien: Springer 1985

    Google Scholar 

  21. Rudge, M.R.H.: Rev. Mod. Phys.40, 564 (1968)

    Google Scholar 

  22. Burgess, A.: Atomic collision processes. McDowell, M.R.C. (ed.), p. 237. Amsterdam: North Holland 1963

    Google Scholar 

  23. Vriens, L.: Phys. Rev.141, 88 (1966)

    Google Scholar 

  24. Margreiter, D.: Master Thesis, Institut für Ionenphysik, Universität Innsbruck (1988)

  25. Deutsch, H., Scheier, P., Märk, T.D.: Int. J. Mass. Spectrom. Ion Proc.74, 81 (1986)

    Google Scholar 

  26. Mott, M.S., Massey, H.S.W.: The theory of atomic collisions, p. 243. Oxford: Oxford Press 1949

    Google Scholar 

  27. Otvos, J.W., Stevenson, D.P.: J. Am. Chem. Soc.78, 546 (1956)

    Google Scholar 

  28. Mann, J.B.: J. Chem. Phys.46, 1646 (1967)

    Google Scholar 

  29. Tiwari, P., Rai, D.K., Rustgi, M.L.: J. Chem. Phys.73, 3040 (1980)

    Google Scholar 

  30. Margreiter, D.: Ph.D. Thesis, Institut für Ionenphysik, Universität Innsbruck (1993)

  31. Syage, J.A.: J. Phys. B24, L527 (1991)

  32. Stephan, K., Helm, H., Märk, T.D.: J. Chem. Phys.73, 3763 (1980)

    Google Scholar 

  33. Stephan, K., Märk, T.D.: J. Chem. Phys.81, 3116 (1984)

    Google Scholar 

  34. Wetzel, R.C., Baiocchi, F.A., Hayes, T.R., Freund, R.B.: Phys. Rev. A35, 559 (1987)

    Google Scholar 

  35. Holle, J.C., Lo, H.H., Fite, W.L.: Phys. Rev. A23, 1708 (1981)

    Google Scholar 

  36. Desclaux, J.P.: At. Nucl. Data Tables12, 325–354 (1973)

    Google Scholar 

  37. It is interesting to note that our earlier calculation utilizing the DM formulation have been made using the quantum mechanically calculated radii by Fraga et al. [38]. These authors did not include relativistic effects. Replacing these radii by those given in Ref. 36 which include relativistic effects, improves the agreement of our calculations with the reliable data sets (see Ref. 30 and also examples given in the present paper)

  38. Fraga, S., Karwovski, J., Saxena, K.M.S.: Handbook of atomic data. Amsterdam: Elsevier 1976

    Google Scholar 

  39. Lotz, W.: J. Opt. Soc. Am.60, 206 (1970)

    Google Scholar 

  40. Deutsch, H., Märk, T.D.: Contr. Plasma Physics. (in press) (1993)

  41. Luyken, B.F.J., de Heer, F.J., Baas, R.C.: Physica61, 200 (1972)

    Google Scholar 

  42. Peach, G.: J. Phys. B3, 328 (1970); ibid.4, 1670 (1971)

    Google Scholar 

  43. Omidvar, K., Kyle, H.L.: VIIth ICPEAC, p. 890. Amsterdam: North Holland 1971

    Google Scholar 

  44. Vriens, L.: Proc. Phys. Soc.89, 13 (1966)

    Google Scholar 

  45. Lotz, W.: Z. Phys.206, 205 (1967)

    Google Scholar 

  46. McGuire, E.J.: Phys. Rev. A3, 267 (1971)

    Google Scholar 

  47. It is interesting to note that the Gryzinski formula (Eq. (1)), which quite accurately describes the cross section for example for carbon (see Fig. 1), fails considerably in the case of another simple atom such as neon (see Fig. 2). This is in accordance with earlier observations concerning valence electron ionization cross sections [24, 25]

  48. Dijkkamp, D., de Heer, F.J.: J. Phys. B14, 1327 (1981)

    Google Scholar 

  49. Jessenberger, J., Hink, W.: Z. Phys. A275, 331 (1975)

    Google Scholar 

  50. Burhop, E.H.S.: Proc. Cambr. Philos. Soc.36, 43 (1940)

    Google Scholar 

  51. Arthurs, A.M., Moiseiwitsch, B.L.: Proc. R. Soc. A London247, 550 (1958)

    Google Scholar 

  52. Rudge, M.R.H., Schwartz, S.B.: Proc. Phys. Soc.88, 563 (1966)

    Article  Google Scholar 

  53. McGuire, E.J.: J. Phys.32 (Suppl.), C4-C7 (1971)

    Google Scholar 

  54. Aydinol, M.: J. Phys. B14, 741 (1981)

    Google Scholar 

  55. Hippler, R., McGregor, I., Aydinol, M., Kleinpoppen, H.: Phys. Rev. A23, 1730 (1981)

    Google Scholar 

  56. McGuire, E.J.: Phys. Rev. A16, 62 (1977)

    Google Scholar 

  57. Motz, J.W., Placious, R.C.: Phys. Rev.136, A662 (1964)

  58. Rester, D.H., Dance, W.E.: Phys. Rev.152, 1 (1966)

    Google Scholar 

  59. Hansen, H., Flammersfeld, A.: Nucl. Phys.79, 135 (1966)

    Google Scholar 

  60. Middleman, L.M., Ford, R.L., Hofstadter, R.: Phys. Rev. A2, 1429 (1970)

    Google Scholar 

  61. Berkner, K.H., Kaplan, S.N., Pyle, R.V.: Bull. Am. Phys. Soc.15, 786 (1970)

    Google Scholar 

  62. Davis, D.V., Mistry, V.D., Quarles, C.A.: Phys. Lett. A38, 169 (1972)

    Google Scholar 

  63. Dangerfield, G.R., Spicer, B.M.: J. Phys. B8, 1744 (1975)

    Google Scholar 

  64. Ishii, K., Kamiya, M., Sera, K., Morita, S., Tawara, H., Oyamad, M., Chu, T.C.: Phys. Rev. A15, 906 (1977)

    Google Scholar 

  65. Hoffmann, D.D.H., Genz, H., Löw, W., Richter, A.: Phys. Lett. A65, 304 (1978)

    Google Scholar 

  66. Pessa, W.M., Newell, W.R.: Phys. Scr.3, 175 (1971)

    Google Scholar 

  67. Quarles, C.A.: Phys. Rev. A13, 1278 (1976)

    Google Scholar 

  68. Khare, S.P., Prakash, S.: Phys. Lett. A140, 238 (1989)

    Google Scholar 

  69. Shima, K.: Phys. Lett.77A, 237 (1980)

    Google Scholar 

  70. Hübner, H., Ilgen, K., Hoffmann, K.W.: Z. Phys.255, 269 (1972)

    Google Scholar 

  71. Scholz, W., Li-Scholz, A., Colle, R., Preiss, I.L.: Phys. Rev. Lett.29, 761 (1971)

    Google Scholar 

  72. Hoffmann, D.D.H., Brendel, C., Genz, G., Löw, W., Müller, S., Richter, A.: Z. Phys. A293, 187 (1979)

    Google Scholar 

  73. Palinkas, J., Schlenk, B.: Z. Phys. A297, 297 (1980)

    Google Scholar 

  74. Reusch, S., Genz, H., Löw, W., Richter, A.: Z. Phys. D3, 379 (1986)

    Google Scholar 

  75. The accuracy of the present theoretical approach is difficult to asses due to the fact that the accuracy of the available previous theoretical and experimental data is not very certain in some of the cases

Download references

Author information

Author notes

  1. H. Deutsch

    Present address: Fachbereich Physik, Ernst Moritz Arndt Universität, Greifswald, Germany

Authors and Affiliations

  1. Institut für Ionenphysik, Leopold Franzens Universität, Technikerstrasse 25, A-6020, Innsbruck, Austria

    H. Deutsch, D. Margreiter & T. D. Märk

Authors
  1. H. Deutsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Margreiter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. D. Märk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Guest Professor at the Institut für Ionenphysik, Universität Innsbruck

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deutsch, H., Margreiter, D. & Märk, T.D. A semi-empirical approach to the calculation of absolute inner-shell electron impact ionization cross sections. Z Phys D - Atoms, Molecules and Clusters 29, 31–37 (1994). https://doi.org/10.1007/BF01437161

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01437161

PACS

Search

Navigation