Abstract

<i>Ab initio</i> Hartree—Fock calculations in the single-configuration approximation predict that the 3<i>s</i> 3<i>p</i><sup>6 2</sup><i>S</i><sub>½</sub> level of Cl <sub>I</sub> lies far above the ionization limit, although this level is observed to be the lowest of all even <i>J</i> = 1/2 levels other than 3<i>s</i><sup>2</sup> 3<i>p</i><sup>4</sup> 4<i>s</i><sup>4</sup><i>P</i><sub>½</sub>, <sup>2</sup><i>P</i><sub>½</sub>. The solution of this anomaly lies in configuration interaction with the high-lying portion of the 3<i>s</i><sup>2</sup> 3<i>p</i><sup>4</sup> ∊<i>d</i><sup>2</sup><i>S</i><sub>½</sub> continuum, which is sufficiently strong to depress the computed <i>s p</i><sup>6</sup> level to its observed position. This interaction with the continuum is an extension of the well-known interaction of <i>sp</i><sup>ω + 1</sup> with the discrete <i>s</i><sup>2</sup><i>p</i><sup>ω - 1</sup><i>nd</i> 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 <sub>1</sub> and I <sub>1</sub> than in Cl <sub>1</sub>, with the result that there exists no bromine nor iodine level that is primarily <i>sp</i><sup>6</sup> in nature. The interactions produce large changes in computed transition probabilities and photoionization cross sections.

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  1. J. Reader, J. Opt. Soc. Am. 62, 1336A (1972); 64, 1017 (1974).
  2. L. J. Radziemski, Jr. and V. Kaufman, J. Opt. Soc. Am. 59, 424 (1969).
  3. R. D. Cowan, Phys. Rev. 163, 54 (1967).
  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 = ½ 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).
  8. U. Fano, Phys. Rev: 124, 1866 (1961).
  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).
  10. Corresponding values for the transitions from the perturbed and unperturbed 3d2S½ levels are A = 0.8·108 s-1 and 2.6·108 s-1, respectively.
  11. J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
  12. L. Minnhagen, Ark. Fys. 21, 415 (1962).
  13. Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s3p51P 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 sp51P 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, Jr. and V. Kaufman, J. Opt. Soc. Am. 64, 366 (1974).
  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 sp6 is 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).
  16. R. D. Cowan, unpublished calculations (1971).

Andrew, K. L.

Simpler cases, involving only two interacting levels, are discussed by R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

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.

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

Simpler cases, involving only two interacting levels, are discussed by R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

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

Fano, U.

U. Fano, Phys. Rev: 124, 1866 (1961).

Kaufman, V.

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

L. J. Radziemski, Jr. and V. Kaufman, J. Opt. Soc. Am. 64, 366 (1974).

Minnhagen, L.

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

Radziemski, Jr., L. J.

L. J. Radziemski, Jr. and V. Kaufman, J. Opt. Soc. Am. 64, 366 (1974).

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

Reader, J.

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

Toresson, Y. G.

Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s3p51P 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 sp51P 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 sp6 is 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).

Other (16)

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

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

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

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 = ½ 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.

Simpler cases, involving only two interacting levels, are discussed by R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

U. Fano, Phys. Rev: 124, 1866 (1961).

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).

Corresponding values for the transitions from the perturbed and unperturbed 3d2S½ levels are A = 0.8·108 s-1 and 2.6·108 s-1, respectively.

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

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

Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s3p51P 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 sp51P 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.

L. J. Radziemski, Jr. and V. Kaufman, J. Opt. Soc. Am. 64, 366 (1974).

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 sp6 is 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).

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

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