Integrals for Exponentially Correlated Four-Body Systems of General Angular Symmetry

  • Frank E. Harris
Chapter

Abstract

This contribution considers the spatial integrals arising for Coulomb four-body systems when the basis wavefunctions include exponentials in all six interparticle coordinates and are also eigenfunctions of the orbital angular momentum. Integration over the Euler angles describing the overall rotation of the system leads to polynomials in the interparticle distances which are explicitly presented for a range of angular quantum numbers. Completion of the integrals can then be carried out using the known closed analytical formulas for fully correlated exponential wavefunctions. The present approach leads to a complete separation of the angular part of the integrals and avoids the introduction of the series expansions normally used in Hylleraas-type methods for these systems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. A. Hylleraas, Z. Phys. 54, 347 (1929).CrossRefGoogle Scholar
  2. 2.
    J.-L. Calais and P.-O. Löwdin, J. Mol. Spectrosc. 8, 203 (1962).CrossRefGoogle Scholar
  3. 3.
    P.-O. Löwdin, Rev. Mod. Phys. 36, 966 (1964).CrossRefGoogle Scholar
  4. 4.
    G. W. F. Drake, Phys. Scr. T83, 83 (1999).CrossRefGoogle Scholar
  5. 5.
    F. W. King, J. Mol. Struct. (Theochem) 400, 7 (1997).Google Scholar
  6. 6.
    F. E. Harris, Adv. Quantum Chem. (to appear in Osvaldo Goscinski volume).Google Scholar
  7. 7.
    L. M. Delves and T. Kalotas, Aust. J. Phys. 21, 431 (1968).CrossRefGoogle Scholar
  8. 8.
    A. J. Thakkar and V. H. Smith Jr., Phys. Rev. A 15, 1 (1977).CrossRefGoogle Scholar
  9. 9.
    D. M. Fromm and R. N. Hill, Phys. Rev. A 36, 1013 (1987).CrossRefGoogle Scholar
  10. 10.
    F. E. Harris, Phys. Rev. A 55, 1820 (1997).CrossRefGoogle Scholar
  11. 11.
    F. E. Harris, A. M. Frolov, and V. H. Smith, Jr., J. Chem. Phys. 119, 8833 (2003).CrossRefGoogle Scholar
  12. 12.
    G. Breit, Phys. Rev. 35, 569 (1930).CrossRefGoogle Scholar
  13. 13.
    C. L. Schwartz, Phys. Rev. 123, 1700 (1961).CrossRefGoogle Scholar
  14. 14.
    A. K. Bhatia and A. Temkin, Rev. Mod. Phys. 36, 1050 (1964).CrossRefGoogle Scholar
  15. 15.
    A. M. Frolov and V. H. Smith Jr., Phys. Rev. A 53, 3853 (1996).CrossRefGoogle Scholar
  16. 16.
    Y. Öhrn and J. Linderberg, Mol. Phys. 49, 53 (1983).CrossRefGoogle Scholar
  17. 17.
    Z.-C. Yan and G. W. F. Drake, J. Phys. B 30, 4723 (1997).CrossRefGoogle Scholar
  18. 18.
    A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, NJ, 1960).Google Scholar
  19. 19.
    L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics: Theory and Application (Addison-Wesley, Reading MA, 1981), pp. 307ff.Google Scholar
  20. 20.
    D. M. Brink and G. R. Satchler, Angular Momentum, 3rd ed. (Clarendon Press, Oxford, 1993).Google Scholar
  21. 21.
    E. Remiddi, Phys. Rev. A 44, 5492 (1991). For errata, see Refs. [22] and [23].CrossRefGoogle Scholar
  22. 22.
    J. S. Sims and S. A. Hagstrom, Phys Rev. A 68, 016501 (2003); errata: 68, 059903(E).CrossRefGoogle Scholar
  23. 23.
    F. E. Harris, A. M. Frolov, and V. H. Smith Jr., Phys. Rev. A 00, 0000 (2004).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Frank E. Harris
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of UtahGainesvilleUSA
  2. 2.Quantum Theory ProjectUniversity of FloridaGainesvilleUSA

Personalised recommendations