Abstract

Theoretical calculation of energy levels and spectra <i>ab nitio</i> are described forinitio transitions of the type p<sup>m</sup>-p<sup>m-1</sup><i>l</i>, especially 3<i>p<sup>m</sup></i>-3<i>p</i><sup>m-1</sup>3<i>d</i> transitions in the Ar I and Cl I isoelectronic sequences. Strong changes of wvavefunction composition occur in going from neutral atoms to ions as a result of collapse of the 3<i>d</i> wavefunction; for <i>m</i> = 2 and 6 these take the form of coupling changes, and for <i>m</i> = 3-5 they take the form of changes of parentage composition. Abnormally low Ti v 3<i>p</i><sup>6</sup>-3<i>p</i><sup>5</sup>4<i>d</i> intensities are explained as an interference effect in evaluation of the dipole radial integral.

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  1. R. D. Cowan, J. Opt. Soc. Am. 58, 808 (1968).
  2. R. D. Cowan, Phys. Rev. 163, 54 (1967).
  3. In this paper, most energies will be given in units of one kilo-Kayser = 1000 cm-1.
  4. In collaboration with M. Wilson, some (unpublished) calculations have been made for La II and Ce III, each of which has a large number of closely-spaced and overlapping two-electron configurations. It was found to be essential to include relativistic and correlation corrections to predict even the correct ordering of the centers of gravity of most of the configurations; in such complicated cases, the present computational methods give errors about fivefold greater than that quoted above.
  5. Cf. B. Edlén, "Atomic Spectra," in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1964), Vol. XXVII, p. 186, (Ref. 1).
  6. The author is indebted to K. Hallén, A. Borgström, and L. Minnhagen for providing values of the K II and Ca III 3p5nd energy levels in advance of publication.
  7. B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, Inc., New York, 1965), pp. 69-78.
  8. The existence of LS coupling conditions in Ca III has been pointed out by Y. Shadmi (quoted by C. E. Moore), J. Opt. Soc. Am. 53, 886 (1963).
  9. A. H. Gabriel, B. C. Fawcett, and C. Jordan, Nature 206, 390 (1965).
  10. A. H. Gabriel, B. C. Fawcett, and C. Jordan, Proc. Phys. Soc. (London) 87, 825 (1966).
  11. For Ca III, computed values are R1 (3d,4d) = 23.0, R1 (3d,5d) = 13.6, R1 (3d,6d) = 9.4, R1 (4d,5d) = 4.6, R1 (4d,6d) = 3.2, and R1 (5d,6d) = 2.0 kK. Corresponding values for Fe IX are 17.1, 4.6, 1.4, 5.8, 3.9, and 2.6 kK, respectively. (r1 = g1 = 4/3.)
  12. C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U. S.) Circ. No. 467, 3 vols. (U. S. Government Printing Office, Washington, 1949, 1952, 1958).
  13. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), Vol. II, pp. 287, 290 f.
  14. The parentage changes from one limit to the other are entirely analogous to the coupling changes in two-electron spectra discussed byR. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965) [see especially Fig. 4].
  15. Even viewing parentage notation as a serial-numbering device, the highest 3p43d2D in K III to Ni XII has been mis-identified9 as (1D) 2D. This is the result of mis-extrapolation to the (1D) 2D of Ar II at 172 kK as listed in AEL [where (1S) 2D is erroneously given at 186 kK] instead of to the correct (1S) 2D at 179 kK [L. Minnhagen, Arkiv Fysik 14, 123 (1958)].
  16. The low reliability of theoretical dipole integrals when interference effects are large is well known; see, for example, D. R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) A242, 117 (1949).
  17. Though at first glance it would appear to be a strong co-incidence that destructive interference should occur at a physically detectable integral value of Z, observations show only that intensities in Ti are no more than 10-2 of those in neighboring elements [B. Edlén, private communication]; since intensities are proportional to P2, this implies only that P = 0 occurs within ±0.1 of an integral value of Z so that there is a 20% chance of intensities being down by a factor of 10-2 in some element. Much greater coincidences have been observed—for example, a line in the spectrum of Pb I has been found [D. R. Wood, K. L. Andrew, A. Giacchetti, and R. D. Cowan, J. Opt. Soc. Am. 58, 830 (1968)] to suffer a purely fortuitous intensity loss by a factor smaller than 10-6!
  18. L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).
  19. In an earlier published version of, Fig. 12 [R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966)], the ordinates (values of S αgfλ) were computed by hand on the assumption of pure LS coupling and 100% pure parentage. Comparison of the two figures gives an indication of the importance of parentage and LS mixing of the wavefunctions. (Wavelengths are somewhat different in the two figures because hfs wavefunctions were employed for the old calculations.)
  20. G. Racah, Phys. Rev. 63, 367 (1943), Eq. (19); or C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (The MIT Press, Cambridge, Mass., 1963), pp. viii and 4.

Andrew, K. L.

The parentage changes from one limit to the other are entirely analogous to the coupling changes in two-electron spectra discussed byR. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965) [see especially Fig. 4].

Bates, D. R.

The low reliability of theoretical dipole integrals when interference effects are large is well known; see, for example, D. R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) A242, 117 (1949).

Borgström, A.

The author is indebted to K. Hallén, A. Borgström, and L. Minnhagen for providing values of the K II and Ca III 3p5nd energy levels in advance of publication.

Cowan, R. D.

The parentage changes from one limit to the other are entirely analogous to the coupling changes in two-electron spectra discussed byR. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965) [see especially Fig. 4].

R. D. Cowan, Phys. Rev. 163, 54 (1967).

R. D. Cowan, J. Opt. Soc. Am. 58, 808 (1968).

Damgaard, A.

The low reliability of theoretical dipole integrals when interference effects are large is well known; see, for example, D. R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) A242, 117 (1949).

Edlén, B.

Cf. B. Edlén, "Atomic Spectra," in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1964), Vol. XXVII, p. 186, (Ref. 1).

Ekberg, J. O.

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

Fawcett, B. C.

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Proc. Phys. Soc. (London) 87, 825 (1966).

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Nature 206, 390 (1965).

Gabriel, A. H.

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Nature 206, 390 (1965).

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Proc. Phys. Soc. (London) 87, 825 (1966).

Hallén, K.

The author is indebted to K. Hallén, A. Borgström, and L. Minnhagen for providing values of the K II and Ca III 3p5nd energy levels in advance of publication.

Jordan, C.

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Proc. Phys. Soc. (London) 87, 825 (1966).

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Nature 206, 390 (1965).

Minnhagen, L.

The author is indebted to K. Hallén, A. Borgström, and L. Minnhagen for providing values of the K II and Ca III 3p5nd energy levels in advance of publication.

Moore, C. E.

C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U. S.) Circ. No. 467, 3 vols. (U. S. Government Printing Office, Washington, 1949, 1952, 1958).

Racah, G.

G. Racah, Phys. Rev. 63, 367 (1943), Eq. (19); or C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (The MIT Press, Cambridge, Mass., 1963), pp. viii and 4.

Shadmi, Y.

The existence of LS coupling conditions in Ca III has been pointed out by Y. Shadmi (quoted by C. E. Moore), J. Opt. Soc. Am. 53, 886 (1963).

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), Vol. II, pp. 287, 290 f.

Svensson, L. Å

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

Wybourne, B. G.

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, Inc., New York, 1965), pp. 69-78.

Other (20)

R. D. Cowan, J. Opt. Soc. Am. 58, 808 (1968).

R. D. Cowan, Phys. Rev. 163, 54 (1967).

In this paper, most energies will be given in units of one kilo-Kayser = 1000 cm-1.

In collaboration with M. Wilson, some (unpublished) calculations have been made for La II and Ce III, each of which has a large number of closely-spaced and overlapping two-electron configurations. It was found to be essential to include relativistic and correlation corrections to predict even the correct ordering of the centers of gravity of most of the configurations; in such complicated cases, the present computational methods give errors about fivefold greater than that quoted above.

Cf. B. Edlén, "Atomic Spectra," in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1964), Vol. XXVII, p. 186, (Ref. 1).

The author is indebted to K. Hallén, A. Borgström, and L. Minnhagen for providing values of the K II and Ca III 3p5nd energy levels in advance of publication.

B. G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience Publishers, John Wiley & Sons, Inc., New York, 1965), pp. 69-78.

The existence of LS coupling conditions in Ca III has been pointed out by Y. Shadmi (quoted by C. E. Moore), J. Opt. Soc. Am. 53, 886 (1963).

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Nature 206, 390 (1965).

A. H. Gabriel, B. C. Fawcett, and C. Jordan, Proc. Phys. Soc. (London) 87, 825 (1966).

For Ca III, computed values are R1 (3d,4d) = 23.0, R1 (3d,5d) = 13.6, R1 (3d,6d) = 9.4, R1 (4d,5d) = 4.6, R1 (4d,6d) = 3.2, and R1 (5d,6d) = 2.0 kK. Corresponding values for Fe IX are 17.1, 4.6, 1.4, 5.8, 3.9, and 2.6 kK, respectively. (r1 = g1 = 4/3.)

C. E. Moore, Atomic Energy Levels, Natl. Bur. Std. (U. S.) Circ. No. 467, 3 vols. (U. S. Government Printing Office, Washington, 1949, 1952, 1958).

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), Vol. II, pp. 287, 290 f.

The parentage changes from one limit to the other are entirely analogous to the coupling changes in two-electron spectra discussed byR. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965) [see especially Fig. 4].

Even viewing parentage notation as a serial-numbering device, the highest 3p43d2D in K III to Ni XII has been mis-identified9 as (1D) 2D. This is the result of mis-extrapolation to the (1D) 2D of Ar II at 172 kK as listed in AEL [where (1S) 2D is erroneously given at 186 kK] instead of to the correct (1S) 2D at 179 kK [L. Minnhagen, Arkiv Fysik 14, 123 (1958)].

The low reliability of theoretical dipole integrals when interference effects are large is well known; see, for example, D. R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) A242, 117 (1949).

Though at first glance it would appear to be a strong co-incidence that destructive interference should occur at a physically detectable integral value of Z, observations show only that intensities in Ti are no more than 10-2 of those in neighboring elements [B. Edlén, private communication]; since intensities are proportional to P2, this implies only that P = 0 occurs within ±0.1 of an integral value of Z so that there is a 20% chance of intensities being down by a factor of 10-2 in some element. Much greater coincidences have been observed—for example, a line in the spectrum of Pb I has been found [D. R. Wood, K. L. Andrew, A. Giacchetti, and R. D. Cowan, J. Opt. Soc. Am. 58, 830 (1968)] to suffer a purely fortuitous intensity loss by a factor smaller than 10-6!

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

In an earlier published version of, Fig. 12 [R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966)], the ordinates (values of S αgfλ) were computed by hand on the assumption of pure LS coupling and 100% pure parentage. Comparison of the two figures gives an indication of the importance of parentage and LS mixing of the wavefunctions. (Wavelengths are somewhat different in the two figures because hfs wavefunctions were employed for the old calculations.)

G. Racah, Phys. Rev. 63, 367 (1943), Eq. (19); or C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (The MIT Press, Cambridge, Mass., 1963), pp. viii and 4.

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