OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 10 — Oct. 1, 1976
  • pp: 1010–1014

Approximate relativistic corrections to atomic radial wave functions

Robert D. Cowan and Donald C. Griffin  »View Author Affiliations


JOSA, Vol. 66, Issue 10, pp. 1010-1014 (1976)
http://dx.doi.org/10.1364/JOSA.66.001010


View Full Text Article

Acrobat PDF (587 KB) Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number <i>j</i> is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of <i>r<sup>m</sup></i> is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations.

© 1976 Optical Society of America

Citation
Robert D. Cowan and Donald C. Griffin, "Approximate relativistic corrections to atomic radial wave functions," J. Opt. Soc. Am. 66, 1010-1014 (1976)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-66-10-1010


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill, New York, 1960); E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. P., Cambridge, England, 1935).
  2. I. P. Grant, "Relativistic calculation of atomic structures," Adv. Phys. 19, 747–811 (1970).
  3. J. B. Mann and J. T. Waber, "SCF relativistic Hartree-Fock calculations on the superheavy elements 118–131," J. Chem. Phys. 53, 2397–2406 (1970); "Self-consistent relativistic Dirac-Hartree-Fock calculations of lanthanide atoms," Atomic Data 5, 201–229 (1973).
  4. J. P. Desclaux, D. F. Mayers, and F. O'Brien, "Relativistic atomic wave functions," J. Phys. B 4, 631–642 (1971); J. P. Desclaux, "A multiconfiguration relativistic Dirac-Fock program," Computer Phys. Commun. 9, 31–45 (1975).
  5. D. A. Liberman, J. T. Waber, and D. T. Cromer, "Self-consistent-field Dirac-Slater wave functions for atoms and ions. I. Comparison with previous calculations," Phys. Rev. 137, A27–A34 (1965); D. A. Liberman and D. T. Cromer, "Relativistic self-consistent field program for atoms and ions," Computer Phys. Commun. 2, 107–113 (1971).
  6. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Elcctron Atoms (Springer-Verlag, Berlin, 1957), Sec. 13, especially Eq. (13. 6) and the paragraph following Eq. (13. 11).
  7. R. D. Cowan, "Atomic self-consistent-field calculations using statistical approximations for exchange and correlation," Phys. Rev. 163, 54–61 (1967). The HX potential consists of the Hartree potential plus a modification of Slater's ρ1/3 exchange potential. The originally suggested value k1 = 0. 7 in the exchange portion has been decreased to 0. 65 on the basis of subsequent experience.
  8. We used an extensively modified early version of the program developed by C. Froese Fischer, "A multi-configuration Hartree-Fock program with improved stability," Computer Phys. Commun. 4, 107–116 (1972); 7, 236 (1974).
  9. D. F. Mayers, "Relativistic self-consistent field calculation for mercury," Proc. R. Soc. Lond. A 241, 93–109 (1957); R. G. Boyd, A. C. Larson, and J. T. Waber, "Indirect relativistic effect on the 5ƒ electrons in uranium," Phys. Rev. 129, 1629–1630 (1963).
  10. D. C. Griffin, K. L. Andrew, and R. D. Cowan, "Theoretical calculations of the d-, f-, and g-electron transition series," Phys. Rev. 177, 62–71 (1969); "Instabilities in the iterative solution of the Hartree-Fock equations for excited electrons," Phys. Rev. A 3, 1233–1242 (1971).
  11. R. D. Cowan and J. B. Mann, "The atomic structure of super-heavy elements," in Atomic Physics, 2, Proceedings of the Second International Conference on Atomic Physics (Plenum, London, 1971), pp. 215–226.
  12. R. Zalubas, "Present state of analysis of the first spectrum of thorium (ThI)," J. Opt. Soc. Am. 58, 1195–1199 (1968); W. C. Martin, L. Hagan, J. Reader, and J. Sugar, "Ground levels and ionization potentials for lanthanide and actinide atoms and ions," J. Phys. Chem. Ref. I)ata 3, 771–779 (1974); R. Zalubas and C. H. Corliss, "Energy levels and classifiedlines in the second spectrumof thorium (ThII)," J. Res. Natl. Bur. Stand. (U.S.) 78A, 163–246 (1974).
  13. C. E. Moore, Atomic Energy Levels, Natl. Bur. Stds. Circe. No. 467 (U. S. GPO, Washington, D. C., 1958), Vol. III.
  14. V. Kaufman and J. Sugar, "Spectrum and energy levels of five-times ionized tantalum (Ta vi)," J. Opt. Soc. Am. 65, 302–309 (1975).
  15. Yong-Ki Kim and J. P. Desclaux, "Relativistic ƒ values for the resonance transitions of Li- and Be-like ions," Phys. Rev. Lett. 36, 139–141 (1976).
  16. L. Armstrong, Jr., W. R. Fielder, and Dong L. Lin, "Relativistic effects on transition probabilities in the Li and Be isoelectronic sequences," Phys. Rev, A 14, 1114–1128 (1976)
  17. On the basis of a variety of trial calculations, we have found it suitable to evaluate d at r equal to one-quarter of the largest radius for which the series expansion is to be employed.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited