Skip to main content
SpringerLink
Log in

Accurate solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for the case of neutral atoms and positive ions

  • Published:
Zeitschrift für Physik A Atoms and Nuclei

Abstract

The numerical solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for atomic many electron systems is discussed in terms of a spline representation. Accurate values for groundstate energies are obtained for the full range of the central charge and all degrees of ionisation.

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. Thomas, L.H.: Proc. Camb. Phil. Soc.23, 542 (1926)

    Google Scholar 

  2. Fermi, E.: Z. Phys.36, 902 (1926) and48, 73 (1928)

    Google Scholar 

  3. Dirac, P.A.M.: Proc. Camb. Phil. Soc.26, 376 (1930)

    Google Scholar 

  4. Weizsäcker, C.F. von: Z. Phys.96, 431 (1935)

    Google Scholar 

  5. Hohenberg, P., Kohn, W.: Phys. Rev.136, B 864 (1964)

    Google Scholar 

  6. Kirzhnits, D.A.: JETP5, 64 (1957); Field theoretical methods in many body systems. Oxford: Pergamon Press 1976

    Google Scholar 

  7. Tomishima, Y., Yonei, K.: J. Phys. Soc. Jpn.21, 142 (1966)

    Google Scholar 

  8. Gross, E.K.U., Dreizler, R.M.: Phys. Rev. A20, 1798 (1979)

    Google Scholar 

  9. Rechenberg, I.: Evolutionsstrategie. Problemata. Vol. 15. Stuttgart: Frommann-Holzboog 1973

    Google Scholar 

  10. Toepfer, A., Gross, E.K.U., Dreizler, R.M.: Phys. Rev. A20, 1808 (1979)

    Google Scholar 

  11. Boor, C. de: A practical guide to splines. Applied Math. Scienc. Vol. 27. Berlin, Heidelberg, New York: Springer-Verlag 1978

    Google Scholar 

  12. Clementi, E., Roetti, C.: At. Data Nucl. Data Tables14, 177 (1974)

    Google Scholar 

  13. Descleaux, J.P.: At. Data Nucl. Data Tables12, 321 (1973)

    Google Scholar 

  14. Yonei, K., Tomishima, Y.: J. Phys. Soc. Jpn.20, 1051 (1965)

    Google Scholar 

  15. Meyer, A., Wang, G., Young, W.H.: Z. Naturf.31 a, 898 (1976)

    Google Scholar 

  16. Ascher, U.: J. Comput. Phys.34, 401 (1980)

    Google Scholar 

  17. Ascher, U., Christiansen, J., Russel, R.D.: Tech. Rep. 77-13, Dept. Comp. Sci. Univ. B.C. Vancouver, Canada

  18. Ascher, U., Russel, R.D.: Tech. Rep. 77-14, Dept. Comp. Sci., Univ. B.C. Vancouver, Canada

  19. Csavinsky, P.: Phys. Rev. A8, 1688 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik der Universität, Frankfurt/Main, Federal Republic of Germany

    W. Stich, E. K. U. Gross, P. Malzacher & R. M. Dreizler

Authors
  1. W. Stich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. K. U. Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Malzacher
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. M. Dreizler
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We wish to thank the DFG for support of this project and the Rechenzentrum of the GSI use of its facilities.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stich, W., Gross, E.K.U., Malzacher, P. et al. Accurate solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for the case of neutral atoms and positive ions. Z Physik A 309, 5–11 (1982). https://doi.org/10.1007/BF01420144

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420144

Keywords

Search

Navigation