Abstract

Data are presented from Hartree–Fock calculations and from empirical level fitting showing a linear decrease with energy in the various radial integrals which describe Coulomb repulsion and spin–orbit interaction of atomic electrons.

© 1969 Optical Society of America

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References

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  1. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), Ch. IV.
  2. J. C. Slater, Quantum Theory of Atomic Structure (McGraw–Hill Book Co., New York, 1960).
  3. C. Froese, J. Chem. Phys. 45, 1417 (1966).
    [Crossref]
  4. M. Blume and R. E. Watson, Proc. Roy. Soc. (London) A270, 127 (1962); M. Wilson, J. Opt. Soc. Am. 58, 855 (1968).
    [Crossref]
  5. B. G. Wybourne, Spectroscopic Properties of Rare Earths (John Wiley & Sons, Inc., New York, 1965), p. 82.
  6. M. G. Mayer, Phys. Rev. 60, 184 (1941). Cf. Ref. 2, Vol. I, p. 225 for the change of the d well in the transition elements.
    [Crossref]

1966 (1)

C. Froese, J. Chem. Phys. 45, 1417 (1966).
[Crossref]

1962 (1)

M. Blume and R. E. Watson, Proc. Roy. Soc. (London) A270, 127 (1962); M. Wilson, J. Opt. Soc. Am. 58, 855 (1968).
[Crossref]

1941 (1)

M. G. Mayer, Phys. Rev. 60, 184 (1941). Cf. Ref. 2, Vol. I, p. 225 for the change of the d well in the transition elements.
[Crossref]

Blume, M.

M. Blume and R. E. Watson, Proc. Roy. Soc. (London) A270, 127 (1962); M. Wilson, J. Opt. Soc. Am. 58, 855 (1968).
[Crossref]

Condon, E. U.

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), Ch. IV.

Froese, C.

C. Froese, J. Chem. Phys. 45, 1417 (1966).
[Crossref]

Mayer, M. G.

M. G. Mayer, Phys. Rev. 60, 184 (1941). Cf. Ref. 2, Vol. I, p. 225 for the change of the d well in the transition elements.
[Crossref]

Shortley, G. H.

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), Ch. IV.

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw–Hill Book Co., New York, 1960).

Watson, R. E.

M. Blume and R. E. Watson, Proc. Roy. Soc. (London) A270, 127 (1962); M. Wilson, J. Opt. Soc. Am. 58, 855 (1968).
[Crossref]

Wybourne, B. G.

B. G. Wybourne, Spectroscopic Properties of Rare Earths (John Wiley & Sons, Inc., New York, 1965), p. 82.

J. Chem. Phys. (1)

C. Froese, J. Chem. Phys. 45, 1417 (1966).
[Crossref]

Phys. Rev. (1)

M. G. Mayer, Phys. Rev. 60, 184 (1941). Cf. Ref. 2, Vol. I, p. 225 for the change of the d well in the transition elements.
[Crossref]

Proc. Roy. Soc. (London) (1)

M. Blume and R. E. Watson, Proc. Roy. Soc. (London) A270, 127 (1962); M. Wilson, J. Opt. Soc. Am. 58, 855 (1968).
[Crossref]

Other (3)

B. G. Wybourne, Spectroscopic Properties of Rare Earths (John Wiley & Sons, Inc., New York, 1965), p. 82.

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), Ch. IV.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw–Hill Book Co., New York, 1960).

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Figures (2)

Fig. 1
Fig. 1

Hartree–Fock–Slater integrals for the SL terms of Pr iv 4f2, plotted as a function of the term value of the SL-term center of gravity. Each integral is normalized to 1.00 for the lowest term and displaced vertically by successive increments of 0.02. Data in Table I.

Fig. 2
Fig. 2

Empirical least-squares fit of the observed levels of Pr iv 4f2 for various fixed values of η, defined in Eq. (2). The parabola is the residual, defined as the sum of the squares of the deviations between calculated eigenvalues and observed term values.

Tables (3)

Tables Icon

Table I Hartree–Fock radial integrals for terms of Pr iv 4f2.

Tables Icon

Table II Fractional changes of Hartree–Fock–Slater integrals from lowest to highest SL term of various configurations.

Tables Icon

Table III Least–squares fit for Pr iv 4f2, in cm−1.

Equations (2)

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P ( l 1 l 2 ) = [ 1 - η ] P ( l 1 l 2 ) ,
H m m = k c m m k [ 1 - η T - T min T max - T min ] P k ,