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.
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HF plus first-order relativistic energy corrections, the latter evaluated as expectation values of the mass-velocity and Darwin operators [omitting the factor in large parentheses ( )−1 in the latter] using nonrelativistic HX wave functions (Ref. 7).
J. B. Mann (private communication); see also Ref. 3.
TABLE II
Expectation values of rm for U i 5f36d7s2 (atomic units).a
The exponents indicate the powers of ten by which the associated numbers are to be multiplied.
J. B. Mann (private communication). The DHF calculation is for the configuration
, except that 5f+ is for
and 6d+ is for
.
TABLE III
One-electron eigenvalues ∊nl or ∊nlj and experimental binding energiesa for U i 5f36d7s2 (Ry).
Comparison of eigenvalues with experimental binding energies on the basis of Koopmans’ theorem is only approximately valid.
See footnote a of Table I.
J. B. Mann (private communication); see footnote b of Table II. The (2j + 1)–weighted DHF values for 2p, 3p, 3d, 5f, and 6d are −1365, −342.5, −270.1, −0.641, and −0.373, respectively.
K. Siegbahn et al., ESCA-Atomic, Molecular, and Solid State Structure Studied by Means of Electron Spectroscopy (Almqvist and Wiksells, Uppsala, 1967).
TABLE IV
Spin-orbit parameter values ζnl (Ry) for U i 5f36d7s2.
Values computed via the method of M. Blume and R. E. Watson, Proc. R. Soc. Lond. A 270, 127 (1962).
J. B. Mann (private communication). Values computed from the relation ζnl ≅ 2(∊nlj+ − ∊nji−)/(2l + 1).
K. Siegbahn et al., ESCA-Atomic, Molecular, and Solid State Structure Studied by Means of Electron Spectroscopy (Almqvist and Wiksells, Uppsala, 1967), calculated as for DHF; except ζ5f and ζ6d obtained by least-squares fitting of experimental energy levels, F. Guyon, J. Blaise, and J-F. Wyart, J. Phys. (Paris) 35, 929–933 (1974).
See footnote a of Table IV.
C. E. Moore, Atomic Energy Levels, Natl. Bur. Stds. Circ. No. 467 (U.S. GPO, Washington, D.C., 1947–1958), 3 volumes, except Ta vi values from V. Kaufman and J. Sugar (Ref. 14).
Tables (5)
TABLE I
Total binding energies (in rydbergs) of neutral closed-shell atoms by nonrelativistic (HF), semirelativistic (HFR), and relativistic (DHF) methods.
HF plus first-order relativistic energy corrections, the latter evaluated as expectation values of the mass-velocity and Darwin operators [omitting the factor in large parentheses ( )−1 in the latter] using nonrelativistic HX wave functions (Ref. 7).
J. B. Mann (private communication); see also Ref. 3.
TABLE II
Expectation values of rm for U i 5f36d7s2 (atomic units).a
The exponents indicate the powers of ten by which the associated numbers are to be multiplied.
J. B. Mann (private communication). The DHF calculation is for the configuration
, except that 5f+ is for
and 6d+ is for
.
TABLE III
One-electron eigenvalues ∊nl or ∊nlj and experimental binding energiesa for U i 5f36d7s2 (Ry).
Comparison of eigenvalues with experimental binding energies on the basis of Koopmans’ theorem is only approximately valid.
See footnote a of Table I.
J. B. Mann (private communication); see footnote b of Table II. The (2j + 1)–weighted DHF values for 2p, 3p, 3d, 5f, and 6d are −1365, −342.5, −270.1, −0.641, and −0.373, respectively.
K. Siegbahn et al., ESCA-Atomic, Molecular, and Solid State Structure Studied by Means of Electron Spectroscopy (Almqvist and Wiksells, Uppsala, 1967).
TABLE IV
Spin-orbit parameter values ζnl (Ry) for U i 5f36d7s2.
Values computed via the method of M. Blume and R. E. Watson, Proc. R. Soc. Lond. A 270, 127 (1962).
J. B. Mann (private communication). Values computed from the relation ζnl ≅ 2(∊nlj+ − ∊nji−)/(2l + 1).
K. Siegbahn et al., ESCA-Atomic, Molecular, and Solid State Structure Studied by Means of Electron Spectroscopy (Almqvist and Wiksells, Uppsala, 1967), calculated as for DHF; except ζ5f and ζ6d obtained by least-squares fitting of experimental energy levels, F. Guyon, J. Blaise, and J-F. Wyart, J. Phys. (Paris) 35, 929–933 (1974).
See footnote a of Table IV.
C. E. Moore, Atomic Energy Levels, Natl. Bur. Stds. Circ. No. 467 (U.S. GPO, Washington, D.C., 1947–1958), 3 volumes, except Ta vi values from V. Kaufman and J. Sugar (Ref. 14).
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