Limiting charge for electrostatic point sources

  • P. Gärtner
  • U. Heinz
  • B. Müller
  • W. Greiner


We investigate the behaviour of the vacuum charge around a supercritical nucleus withZ>137 in dependence on the nuclear radius. The screening effects are considered in a quasiclassical approximation. We show that in the point nucleus limit the nuclear charge is screened by the vacuum charge up toZ=137. This means that the coupling strength of a point charge in QED cannot be larger than 1. The influence of the heavier leptons is also discussed.


Elementary Particle Point Source Coupling Strength Point Charge Nuclear Charge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Richtmyer, R.D.: Principles of Advanced Mathematical Physics. Vol. 1. New York, Heidelberg, Berlin: Springer 1978Google Scholar
  2. 2.
    Case, K.M.: Phys. Rev.80, 797 (1950)Google Scholar
  3. 3.
    Pomeranchuk, I., Smorodinsky, J.: J. Phys. Moscow9, 97 (1945)Google Scholar
  4. 4.
    Werner, F.G., Wheeler, J.A.: Phys. Rev.109, 126 (1958)Google Scholar
  5. 5.
    Pieper, W., Greiner, W.: Z. Phys.218, 327 (1969)Google Scholar
  6. 6.
    Müller, B., Rafelski, J., Greiner, W.: Z. Phys.257, 62 (1972)Google Scholar
  7. 7.
    Müller, B., Rafelski, J., Greiner, W.: Z. Phys.257, 183 (1972)Google Scholar
  8. 8.
    Zeldovich, Y.B., Popov, V.S.: Sov. Phys. Usp.14, 673 (1972)Google Scholar
  9. 9.
    Reinhardt, J., Greiner, W.: Rep. Prog. Phys.40, 219 (1977)Google Scholar
  10. 10.
    Rafelski, J., Fulcher, L.P., Klein, A.: Phys. Rep.38, 227 (1978)Google Scholar
  11. 11.
    Brodsky, S.J., Mohr, P.J.: In: Structure and Collisions of Ions and Atoms; Sellin, I.A. (ed.) Berlin-Heidelberg-New York: Springer 1978Google Scholar
  12. 12.
    Klaus, M.: Preprint, Dept. of Mathematics, University of Virginia, Charlottesville, USA, 1980Google Scholar
  13. 13.
    Lampert, M.A., Crandall, R.S.: Phys. Rev. A21, 362 (1980)Google Scholar
  14. 14.
    Rose, E.M.: Relativistic Electron Theory, New York: Wiley 1961Google Scholar
  15. 15.
    Müller, B., Rafelski, J., Greiner, W.: Nuovo Cimento18A, 551 (1973)Google Scholar
  16. 16.
    Reinhardt, J., Müller, B., Greiner, W.: In: Coherence and Correlation in Atomic Collisions, Kleinpoppen, H., Williams, J.F. (eds.) New York 1980Google Scholar
  17. 17.
    Reinhard, P.G.: Lett. Nuovo Cimento3, 313 (1970)Google Scholar
  18. 18.
    Reinhard, P.G., Greiner, W., Arenhövel, H.: Nucl. Phys. A166, 173 (1971)Google Scholar
  19. 19.
    Vallarta, M.S., Rosen, N.: Phys. Rev.41, 708 (1932)Google Scholar
  20. 20.
    Gärtner, P.: Diploma thesis, Frankfurt 1979Google Scholar
  21. 21.
    Rudkjøbing, M.: Dan. Mat. Fys. Medd.27, 5 (1952)Google Scholar
  22. 22.
    Migdal, A.B., Popov, V.S., Voskresenskij, D.N.: Sov. Phys. JETP45, 436 (1977)Google Scholar
  23. 23.
    Langer, R.E.: Phys. Rev.51, 669 (1937)Google Scholar
  24. 24.
    Fröman, N., Fröman, P.O.: JWKB Approximation, Amsterdam: North-Holland 1965Google Scholar
  25. 25.
    Mur, V.D., Popov, V.S., Voskresenskij, D.N.: JETP Lett.28, 129 (1978)Google Scholar
  26. 26.
    Migdal, A.B.: Sov. Phys. JETP43, 211 (1976)Google Scholar
  27. 27.
    Gross, E., Rafelski, J.: Phys. Rev. A20, 44 (1979)Google Scholar
  28. 28.
    Uehling, E.A.: Phys. Rev.48, 55 (1935)Google Scholar
  29. 29.
    Popov, V.S.: Sov. Phys. JETP33, 665 (1971)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • P. Gärtner
    • 1
  • U. Heinz
    • 1
  • B. Müller
    • 1
  • W. Greiner
    • 1
  1. 1.Institut für Theoretische Physik der Johann-Wolfgang-Goethe-UniversitätFrankfurt am MainFederal Republic of Germany

Personalised recommendations