Density effect in relativistic K-shell ionization


Using a grazing emission method, we have made measurements of 22.6-GeV electron impact ionization cross sections at the front and back faces of ∼ 70-µm thick Al and Cu foils. These give, respectively, the cross sections without and with a density effect predicted by Fermi. For Cu, the back cross section ratio at 22.6 and 5.1 GeV (previously measured) is 1.00±0.04, confirming the predicted energy independence of this cross section. The absolute cross sections agree overall with theoretical calculations.

This is a preview of subscription content, access via your institution.


  1. 1.

    Williams, E.J.: K. Dan. Vidensk. Selsk. Mat. Fys. Medd.13, 4 (1935)

    Google Scholar 

  2. 2.

    Jauch, J.M., Rohrlich, F.: The theory of photons and electrons, Chapt. 12. Reading, Mass.: Addison Wesley 1955

    Google Scholar 

  3. 3.

    Sorensen, A.H.: Phys. Rev. A36, 3125 (1987)

    Google Scholar 

  4. 4.

    Chechin, V.A., Ermilova, V.K.: Z. Phys. D13, 33 (1989)

    Google Scholar 

  5. 5.

    Nuclear Physics, a course given by Enrico Fermi at the University of Chicago, compiled by Orear, J., Rosenfeld, A.H., Schluter, R., Sect. II.A, Chicago: University of Chicago 1950

    Google Scholar 

  6. 6.

    Fermi, E.: Phys. Rev.37, 485 (1940)

    Google Scholar 

  7. 7.

    Kamiya, M., Kuwako, A., Ishii, K., Morita, S., Oyamada, M.: Phys. Rev. A22, 413 (1980). Because few-µm thick targets were used, these measurements are expected to lie between the saturated and unsaturated cross sections

    Google Scholar 

  8. 8.

    Bak, J.F., Meyer, F.E., Petersen, J.B.B., Uggerhoj, E., Ostergaard, K., Moller, S.P., Sorensen, A.H., Siffert, P.: Phys. Rev. Lett.51, 1163 (1983); Bak, J.F., Petersen, J.B.B., Uggerhoj, E., Ostergaard, K., Moller, S.P., Sorensen, A.H.: Phys. Scri.33, 147 (1986). Because of the particular detection geometry used, these measurements lie between the saturated and unsaturated cross sections

    Google Scholar 

  9. 9.

    Sorensen, A.H., Uggerhoj, E.: Comments At. Mol. Phys.17, 285 (1986); Bak, J.F. et al.: Phys. Rev. Lett.51, 1163 (1983)

    Google Scholar 

  10. 10.

    Hayward, E.: Phys. Rev.72, 937 (1947); Kepler, R.G., d'Andlau, C.A., Fretter, W.B., Hansen, L.F.: Nuovo Cimento7, 71 (1958)

    Google Scholar 

  11. 11.

    Meyerhof, W.E., Jensen, D.G., Kawall, D.M., Kuhn, S.E., Spooner, D.W., Meziani, Z.-E., Faust, D.N.: Phys. Rev. Lett.68, 2293 (1992)

    Google Scholar 

  12. 12.

    In this energy range, the bremsstrahlung and knock-on electron induced X-ray yields are independent of energy, so that the calculated values at 5.1 GeV could be used, which had been shown to be accurate [11]. For synchrotron radiation, special calculations were made by M. Sullivan, taking into account the bending dipole and focusing quadrupole magnets in the SLAC beamline

  13. 13.

    Krause, M.O.: J. Phys. Chem. Ref. Data8, 307 (1979); Bambynek, W., Crasemann, B., Fink, R.W., Freund, H.-U., Mark, H., Swift, C.D., Price, R.E., Rao, P.V.: Rev. Mod. Phys.44, 716 (1972)

    Google Scholar 

  14. 14.

    Saloman, E.B., Hubbell, J.H., Scofield, J.M.: At. Data Nucl. Data Tables38, 1 (1988)

    Google Scholar 

  15. 15.

    Lapicki, G.: J. Phys. Chem. Ref. Data18, 111 (1989). Figures 6 and 9 of this reference show that for A1, in the velocity range used by us, the experimentalK-X-ray production cross section is 0.8 times the value predicted by the ECPSSR theory (with ω k =0.039). This semiempirical value, giving 34,300 and 86,250b for 1.5- and 2.2-MeV α-particles, respectively, was used in determining ε

    Google Scholar 

  16. 16.

    Genz, H., Brendel, C., Eshway, P., Kuhn, U., Löw, W., Richter, A., Seserko, P., Sauerwein, R.: Z. Phys. A305, 9 (1982). See also footnote [10] of Bak, J.F. et al.: Phys. Rev. Lett.51, 1163 (1983)

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Spooner, D.W., Meyerhof, W.E., Kuffner, J.J. et al. Density effect in relativistic K-shell ionization. Z Phys D - Atoms, Molecules and Clusters 29, 265–268 (1994).

Download citation


  • 34.80.Dp