Advertisement

Hyperspherical Coordinates for Electron Correlations

  • A. R. P. Rau
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 2)

Abstract

The use of hyperspherical coordinates for the study of strongly correlated phenomena in atoms is reviewed. These collective coordinates prove natural for describing the few-electron system and have been introduced independently at times in the history of the subject when it was necessary to describe strong correlations between electrons at small, intermediate and large distances.

Keywords

Wave Function Excited State Schrodinger Equation Double Ionization Ionization Limit 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    See, for instance, Smirnov, Yu.F., and Shitikova, K.V., Sov. J. Nucl. Phys. 8, 344 (1977).Google Scholar
  2. 2.
    Fano, U., Rep. Prog. Phys. 46 97 (1983).ADSCrossRefGoogle Scholar
  3. 3.
    Lin, C.D., Adv. Atom. Mol. Phys. 22, 77 (1986).CrossRefGoogle Scholar
  4. 4.
    Fano, U., and Rau, A.R.P., Atomic Collisions and Spectra. Orlando: Academic 1986, chapters 10 and 11.Google Scholar
  5. 5.
    Fischer, C.F., The Hartree-Fock Method for Atoms. New York: Wiley 1977.Google Scholar
  6. 6.
    Bartlett, J.H., Phys. Rev. 51, 661 (1937); Bartlett, J.H., Gibbons, J.J., and Dunn, C.G., Phys. Rev. 47, 679 (1935).ADSMATHCrossRefGoogle Scholar
  7. 7.
    Fock, V.A., Izv. Akad. Nauk SSR, Ser. Fiz. 161 (1954) [Engl, trans!.: K. Norsk Vidensk. Selsk. Forh. 31, 138 (1948)].Google Scholar
  8. 8.
    Frankowski, K., and Pekeris, C.L., Phys. Rev. 146, 46 (1966); Freund, D.E., Huxtable, B-D., and Morgan, J.D., Phys. Rev. A 29, 980 (1984).ADSCrossRefGoogle Scholar
  9. 9.
    Macek, J., Phys. Rev. 160, 170 (1967); Feagin, J.M., Macek, J., and Starace, A.F., Phys. Rev. A 32, 3219 (1985).ADSCrossRefGoogle Scholar
  10. 10.
    Morgan, J.D., Theor. Chim. Acta 69, 181 (1986).CrossRefGoogle Scholar
  11. 11.
    Demkov, Yu.N., and Ermolaev, A.M., Sov. Phys. JETP 36, 633 (1959).MathSciNetGoogle Scholar
  12. 12.
    Cavagnero, M., Phys. Rev. A 30, 1169 (1984).ADSCrossRefGoogle Scholar
  13. 13.
    Fano, U., and Cooper, J.W., Rev. Mod. Phys. 40, 441 (1968).ADSCrossRefGoogle Scholar
  14. 14.
    Lipsky, L., and Russek, A., Phys. Rev. 142, 59 (1966); Lipsky, L. Anania, R., and Conneely, M.J., At. Data Nucl. Data Tables 20, 727 (1977).ADSCrossRefGoogle Scholar
  15. 15.
    Madden, R.P., and Codling, K., Phys. Rev. Lett. 10, 516 (1963); Astrophys. J. 141, 364 (1965).ADSCrossRefGoogle Scholar
  16. 16.
    Cooper, J.W., Fano, U., and Prats, F., Phys. Rev. Lett. 10, 518 (1963).ADSCrossRefGoogle Scholar
  17. 17.
    Lin. C.D., Phys. Rev. A 25, 76 (1982); 26, 2305 (1982); 27, 22Google Scholar
  18. 18.
    Feagin, J.M., J.Phys. B17, 2433 (1984).ADSGoogle Scholar
  19. 19.
    Vilenkin, N.J., Special Functions and the Theory of Group Representations, Translations of Mathematical Monographs., Vol. 22. Providence: American Mathematical Society 1968.Google Scholar
  20. 20.
    Knirk, D.L., J. Chem. Phys. 60, 66 and 760 (1974).ADSGoogle Scholar
  21. 21.
    Avery, J., and Wen, Z.Y., Int. J. Quantum Chem. 22, 717 (1982).CrossRefGoogle Scholar
  22. 22.
    Koyama, N., Fukuda, H., Motoyama, T., and Matsuzawa, M., J. Phys. B 19, L331 (1986).ADSCrossRefGoogle Scholar
  23. 23.
    Christensen-Dalsgaard, B.L., Phys. Rev. A 29, 2242 (1984).ADSCrossRefGoogle Scholar
  24. 24.
    Herrick, D.R., Phys. Rev. A 12, 413 (1975); Adv. Chem Phys. 52, 1, (1983).Google Scholar
  25. 25.
    Wannier, G.H., Phys. Rev. 90, 817 (1953).ADSMATHCrossRefGoogle Scholar
  26. 26.
    Rau, A.R.P., Phys Rev. A 4, 207 (1971); Phys. Rep. 110, 369ADSCrossRefGoogle Scholar
  27. 27.
    Peterkop, R., J. Phys. B 4, 513 (1971); 16, L587 (1983).ADSCrossRefGoogle Scholar
  28. 28.
    Greene, C.H., and Rau, A.R.P., Phys. Rev. Lett. 48, 533 (1982); J. Phys. B 16, 99 U982 ).ADSCrossRefGoogle Scholar
  29. 29.
    Macek, J., and Feagin, J.M., J. Phys. B. 18, 2161 (1985).ADSCrossRefGoogle Scholar
  30. 30.
    Wong, H.Y., and Rail, A.R.P., to be published.Google Scholar
  31. 31.
    Rau, A.R.P., in Van Dyck, R.S., and Fortson, E.N., Atomic Physics, Vol.9. Singapore: World Scientific 1984, p. 491; in Briand, J.P., Atoms in Unusual Situations, NATO ASI Series, Vol. 143. New York: Plenum 1986, p. 383.Google Scholar
  32. 32.
    Rau, A.R.P., J. Phys. B9, L283 (1976); 17, L75 (1984); Pramana 23, 297 (1984).ADSCrossRefGoogle Scholar
  33. 33.
    Read, F.H., in Dunn, G.H. and Mark, T., Electron Impact Ionization. Wien-New York: Springer 1984, p 42.Google Scholar
  34. 34.
    Fournier-Lagarde, P., Mazeau, J., and Huetz, A., J. Phys. B 17, L591 (1984); Selles, P., Mazeau, J., and Huetz, A., J.Phys. B, to be published (1987).ADSCrossRefGoogle Scholar
  35. 35.
    Buckman, S.J., Hammond, P., Read, F. H., and King, G. C., J. Phys. B 16, 4039 (1983); Buckman, S.J. and Newman, D.S., to be published.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. R. P. Rau
    • 1
  1. 1.Department of Physics and AstronomyLouisiana State UniversityBaton RougeUSA

Personalised recommendations