Abstract

Ab initio Hartree–Fock calculations in the single-configuration approximation predict that the 3s3p6 2S1/2 level of Cl i lies far above the ionization limit, although this level is observed to be the lowest of all even J = 1/2 levels other than 3s23p44s 4P1/2, 2P1/2. The solution of this anomaly lies in configuration interaction with the high-lying portion of the 3s23p4∊d 2S1/2 continuum, which is sufficiently strong to depress the computed sp6 level to its observed position. This interaction with the continuum is an extension of the well-known interaction of spw+1 with the discrete s2pw−1 nd Rydberg series, and is important in all neutral third-row elements Al to Cl, as well as in Br and I and probably other fourth- and fifth-row elements. The effect is, however, somewhat smaller in Br i and I i than in Cl i, with the result that there exists no bromine nor iodine level that is primarily sp6 in nature. The interactions produce large changes in computed transition probabilities and photoionization cross sections.

© 1974 Optical Society of America

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References

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  1. J. Reader, J. Opt. Soc. Am. 62, 1336A (1972); J. Opt. Soc. Am. 64, 1017 (1974).
  2. L. J. Radziemski and V. Kaufman, J. Opt. Soc. Am. 59, 424 (1969).
    [Crossref]
  3. R. D. Cowan, Phys. Rev. 163, 54 (1967).
    [Crossref]
  4. If radial wave functions had been computed for the p4d2S terms, the configuration-interaction matrix elements between 2S terms would have been zero (Brillouin’s theorem). However, we are using radial functions for the center of gravity of each configuration; hence only the average interaction is zero, and there are residual nonzero matrix elements for the individual LS terms.
  5. There are, of course, four additional J=12 levels in each p4d configuration. Interactions with these 4D, 4P, and 2P levels are appreciable only over very small ranges of the Rk scale factor, and for simplicity have been ignored in the figure.
  6. A case similar to the present one is discussed by E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), pp. 41 and 42.
  7. Simpler cases, involving only two interacting levels, are discussed by R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965)
    [Crossref]
  8. U. Fano, Phys. Rev. 124, 1866 (1961).
    [Crossref]
  9. The possibility of a Beutler–Fano profile appearing in a discrete Rydberg series as well as in a continuum was recognized by Fano (Ref. 8, end of Sec. 1, and Appendix B). An experimental instance of such a profile extending across the boundary between discrete and continuous spectrum appears in Ba i: W. R. S. Garton and K. Codling, Proc. Phys. Soc. Lond. 75, 87 (1960); W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 1219 (1969).
    [Crossref]
  10. Corresponding values for the transitions from the perturbed and unperturbed 3d2S1/2 levels are A= 0.8 · 108s−1and 2.6 · 108s−1, respectively.
  11. J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
    [Crossref]
  12. L. Minnhagen, Ark. Fys. 21, 415 (1962).
  13. Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s 3p5 1P level to interact comparatively weakly with the continuum, and to remain far above the ionization limit at ~125 kK. If this prediction is correct, it would indicate that Toresson’s sp5 1P designation for a level at 81.437 kK is in error; the proper identification may be 3p3(2D)3d1P, which we compute to lie at 81.6 kK.
  14. L. J. Radziemski and V. Kaufman, J. Opt. Soc. Am. 64, 366 (1974).
    [Crossref]
  15. A. W. Weiss, Phys. Rev. 178, 82 (1969); K. B. S. Eriksson, Ark. Fys. 39, 421 (1969); R. D. Cowan, J. Phys. Colloq. Suppl. 31, C4-191 (1970). The level computed in each of these investigations to lie just above the ionization limit is the nonphysical result of including only a finite number of 3s2nd configurations, this level having been pushed off the top of the Rydberg series in the same way that sp6is pushed off the bottom in Fig. 2; the Fano-profile phase relations are such that transitions from this level to the ground configuration acquire a very high strength, analogous to the strong continuum in Fig. 4. If continuum effects are included in the manner of the present Cl i calculation, this physically unrealistic level settles inconspicuously down among the other members of the Rydberg series (Ref. 16); cf. C. D. Lin, Astrophys. J. 187, 385 (1974) and A. W. Weiss, Phys. Rev. A 9, 1524 (1974).
    [Crossref]
  16. R. D. Cowan, unpublished calculations (1971).

1974 (1)

1972 (1)

J. Reader, J. Opt. Soc. Am. 62, 1336A (1972); J. Opt. Soc. Am. 64, 1017 (1974).

1969 (2)

L. J. Radziemski and V. Kaufman, J. Opt. Soc. Am. 59, 424 (1969).
[Crossref]

A. W. Weiss, Phys. Rev. 178, 82 (1969); K. B. S. Eriksson, Ark. Fys. 39, 421 (1969); R. D. Cowan, J. Phys. Colloq. Suppl. 31, C4-191 (1970). The level computed in each of these investigations to lie just above the ionization limit is the nonphysical result of including only a finite number of 3s2nd configurations, this level having been pushed off the top of the Rydberg series in the same way that sp6is pushed off the bottom in Fig. 2; the Fano-profile phase relations are such that transitions from this level to the ground configuration acquire a very high strength, analogous to the strong continuum in Fig. 4. If continuum effects are included in the manner of the present Cl i calculation, this physically unrealistic level settles inconspicuously down among the other members of the Rydberg series (Ref. 16); cf. C. D. Lin, Astrophys. J. 187, 385 (1974) and A. W. Weiss, Phys. Rev. A 9, 1524 (1974).
[Crossref]

1967 (1)

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

1965 (1)

1963 (1)

J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
[Crossref]

1962 (1)

L. Minnhagen, Ark. Fys. 21, 415 (1962).

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

1960 (2)

The possibility of a Beutler–Fano profile appearing in a discrete Rydberg series as well as in a continuum was recognized by Fano (Ref. 8, end of Sec. 1, and Appendix B). An experimental instance of such a profile extending across the boundary between discrete and continuous spectrum appears in Ba i: W. R. S. Garton and K. Codling, Proc. Phys. Soc. Lond. 75, 87 (1960); W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 1219 (1969).
[Crossref]

Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s 3p5 1P level to interact comparatively weakly with the continuum, and to remain far above the ionization limit at ~125 kK. If this prediction is correct, it would indicate that Toresson’s sp5 1P designation for a level at 81.437 kK is in error; the proper identification may be 3p3(2D)3d1P, which we compute to lie at 81.6 kK.

Andrew, K. L.

Codling, K.

The possibility of a Beutler–Fano profile appearing in a discrete Rydberg series as well as in a continuum was recognized by Fano (Ref. 8, end of Sec. 1, and Appendix B). An experimental instance of such a profile extending across the boundary between discrete and continuous spectrum appears in Ba i: W. R. S. Garton and K. Codling, Proc. Phys. Soc. Lond. 75, 87 (1960); W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 1219 (1969).
[Crossref]

Condon, E. U.

A case similar to the present one is discussed by E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), pp. 41 and 42.

Cowan, R. D.

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

Garton, W. R. S.

The possibility of a Beutler–Fano profile appearing in a discrete Rydberg series as well as in a continuum was recognized by Fano (Ref. 8, end of Sec. 1, and Appendix B). An experimental instance of such a profile extending across the boundary between discrete and continuous spectrum appears in Ba i: W. R. S. Garton and K. Codling, Proc. Phys. Soc. Lond. 75, 87 (1960); W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 1219 (1969).
[Crossref]

Kaufman, V.

Minnhagen, L.

L. Minnhagen, Ark. Fys. 21, 415 (1962).

Radziemski, L. J.

Reader, J.

J. Reader, J. Opt. Soc. Am. 62, 1336A (1972); J. Opt. Soc. Am. 64, 1017 (1974).

Shortley, G. H.

A case similar to the present one is discussed by E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), pp. 41 and 42.

Tech, J. L.

J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
[Crossref]

Toresson, Y. G.

Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s 3p5 1P level to interact comparatively weakly with the continuum, and to remain far above the ionization limit at ~125 kK. If this prediction is correct, it would indicate that Toresson’s sp5 1P designation for a level at 81.437 kK is in error; the proper identification may be 3p3(2D)3d1P, which we compute to lie at 81.6 kK.

Weiss, A. W.

A. W. Weiss, Phys. Rev. 178, 82 (1969); K. B. S. Eriksson, Ark. Fys. 39, 421 (1969); R. D. Cowan, J. Phys. Colloq. Suppl. 31, C4-191 (1970). The level computed in each of these investigations to lie just above the ionization limit is the nonphysical result of including only a finite number of 3s2nd configurations, this level having been pushed off the top of the Rydberg series in the same way that sp6is pushed off the bottom in Fig. 2; the Fano-profile phase relations are such that transitions from this level to the ground configuration acquire a very high strength, analogous to the strong continuum in Fig. 4. If continuum effects are included in the manner of the present Cl i calculation, this physically unrealistic level settles inconspicuously down among the other members of the Rydberg series (Ref. 16); cf. C. D. Lin, Astrophys. J. 187, 385 (1974) and A. W. Weiss, Phys. Rev. A 9, 1524 (1974).
[Crossref]

Ark. Fys. (2)

L. Minnhagen, Ark. Fys. 21, 415 (1962).

Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s 3p5 1P level to interact comparatively weakly with the continuum, and to remain far above the ionization limit at ~125 kK. If this prediction is correct, it would indicate that Toresson’s sp5 1P designation for a level at 81.437 kK is in error; the proper identification may be 3p3(2D)3d1P, which we compute to lie at 81.6 kK.

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Std. (1)

J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
[Crossref]

Phys. Rev. (3)

A. W. Weiss, Phys. Rev. 178, 82 (1969); K. B. S. Eriksson, Ark. Fys. 39, 421 (1969); R. D. Cowan, J. Phys. Colloq. Suppl. 31, C4-191 (1970). The level computed in each of these investigations to lie just above the ionization limit is the nonphysical result of including only a finite number of 3s2nd configurations, this level having been pushed off the top of the Rydberg series in the same way that sp6is pushed off the bottom in Fig. 2; the Fano-profile phase relations are such that transitions from this level to the ground configuration acquire a very high strength, analogous to the strong continuum in Fig. 4. If continuum effects are included in the manner of the present Cl i calculation, this physically unrealistic level settles inconspicuously down among the other members of the Rydberg series (Ref. 16); cf. C. D. Lin, Astrophys. J. 187, 385 (1974) and A. W. Weiss, Phys. Rev. A 9, 1524 (1974).
[Crossref]

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

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

Proc. Phys. Soc. Lond. (1)

The possibility of a Beutler–Fano profile appearing in a discrete Rydberg series as well as in a continuum was recognized by Fano (Ref. 8, end of Sec. 1, and Appendix B). An experimental instance of such a profile extending across the boundary between discrete and continuous spectrum appears in Ba i: W. R. S. Garton and K. Codling, Proc. Phys. Soc. Lond. 75, 87 (1960); W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 1219 (1969).
[Crossref]

Other (5)

Corresponding values for the transitions from the perturbed and unperturbed 3d2S1/2 levels are A= 0.8 · 108s−1and 2.6 · 108s−1, respectively.

If radial wave functions had been computed for the p4d2S terms, the configuration-interaction matrix elements between 2S terms would have been zero (Brillouin’s theorem). However, we are using radial functions for the center of gravity of each configuration; hence only the average interaction is zero, and there are residual nonzero matrix elements for the individual LS terms.

There are, of course, four additional J=12 levels in each p4d configuration. Interactions with these 4D, 4P, and 2P levels are appreciable only over very small ranges of the Rk scale factor, and for simplicity have been ignored in the figure.

A case similar to the present one is discussed by E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1935), pp. 41 and 42.

R. D. Cowan, unpublished calculations (1971).

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Figures (4)

Fig. 1
Fig. 1

The observed and calculated positions of the sp6 2S1/2 and 3s23p43d 2S1/2 levels in the Cl i isoelectronic sequence (ζ = 1 is Cl i, ζ = 2 is Ar ii, etc.; 1 kK = 1000 cm−1). ●, unperturbed positions; ○, positions including interactions of sp6 with 3d and 4d; ×, experimentally observed positions.

Fig. 2
Fig. 2

Ab initio computed energies of the 17 lowest discrete and pseudodiscrete sp6 + p4d 2S1/2 levels of Cl i, as all configuration-interaction parameters are scaled from zero up to 75% of the theoretical values. The dashed line indicates that the asymptotic portion of the lowest-level curve extrapolates back to the unperturbed 3s3p6 2S1/2 level.

Fig. 3
Fig. 3

Computed variation in the magnitudes of the 3s3p6, 3d, 4d, and 5d components of the eigenvectors for the three lowest-energy sp6 + p4d 2S1/2 levels of Cl i, as the configuration interactions are turned on; the bottom section of the figure corresponds to the lowest level. (The eigenvectors for the corresponding levels of Br i, calculated with a scale factor of 0.75, correspond roughly to those given in the figure for scale factors of 0.55, 0.50, and 0.45 from bottom to top, except with all principal quantum numbers increased by unity. Eigenvectors for I i correspond to slightly smaller scale factors than for Br i.)

Fig. 4
Fig. 4

Computed photoabsorption cross sections for the transition Cl i 3p5 2P1/2–3p4d 2S1/2, for configuration-interaction parameters equal to 0, 0.1, 0.3, 0.5, and 0.75 times the ab initio values. The curves are only semiquantitative and somewhat schematic for λ > 750 Å because of the limited resolution provided by the calculation.

Tables (1)

Tables Icon

Table I Interaction parameters (kK) and dipole matrix elements (atomic units) for Cl i.

Equations (4)

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R Δ E 1 = ( Δ E ) 1 2 R ryd 1 ,
Δ E = 2 / ( n * ) 3 ,
E E av ( n d ) - E av ( d ) = - 1 / ( n * ) 2
σ = π e 2 m c 2 R d f d E = 8.067 · 10 - 18 d f d E cm 2 ;