Effect of continuum configuration interaction on the position of s p^{6} in neutral chlorine, other halogens
JOSA, Vol. 64, Issue 11, pp. 1474-1478 (1974)
http://dx.doi.org/10.1364/JOSA.64.001474
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Abstract
Ab initio Hartree—Fock calculations in the single-configuration approximation predict that the 3s 3p^{6 2}S_{½} 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 3s^{2} 3p^{4} 4s^{4}P_{½}, ^{2}P_{½}. The solution of this anomaly lies in configuration interaction with the high-lying portion of the 3s^{2} 3p^{4} ∊d^{2}S_{½} continuum, which is sufficiently strong to depress the computed s p^{6} level to its observed position. This interaction with the continuum is an extension of the well-known interaction of sp^{ω + 1} with the discrete s^{2}p^{ω - 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 _{1} and I _{1} than in Cl _{1}, with the result that there exists no bromine nor iodine level that is primarily sp^{6} in nature. The interactions produce large changes in computed transition probabilities and photoionization cross sections.
Citation
Robert D. Cowan, Leon J. Radziemski, Jr., and Victor Kaufman, "Effect of continuum configuration interaction on the position of s p^{6} in neutral chlorine, other halogens," J. Opt. Soc. Am. 64, 1474-1478 (1974)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-64-11-1474
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References
- 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 p^{4}d^{2}S terms, the configuration-interaction matrix elements between ^{2}S 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 p^{4}d configuration. Interactions with these ^{4}D, ^{4}P, and ^{2}P levels are appreciable only over very small ranges of the R^{k} 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.
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- Y. G. Toresson, Ark. Fys. 18, 417 (1960). We calculate the 3s3p^{5}^{1}P 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 sp^{5}^{1}P designation for a level at 81.437 kK is in error; the proper identification may be 3p^{3}(^{2}D)3d^{1}P, 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 3s^{2}nd configurations, this level having been pushed off the top of the Rydberg series in the same way that sp^{6} 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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