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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)

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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 j 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 rm is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations.

© 1976 Optical Society of America

Robert D. Cowan and Donald C. Griffin, "Approximate relativistic corrections to atomic radial wave functions," J. Opt. Soc. Am. 66, 1010-1014 (1976)

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  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.

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