Abstract

We have made precision measurements of the 4fng transitions (n = 5–11) of cesium observed in emission by using high-resolution Fourier spectroscopy. The 2G fine-structure intervals are found to have normal ordering and a slightly greater than hydrogenic splitting. Each of the 2F and 2G series of levels can be represented by a polarization formula, but the effective dipole and quadrupole polarizabilities derived from the two series differ widely. By a series of calculations using Hartree–Fock wave functions, we show that penetration and core–valence exchange effects, which are neglected in the polarization formula, contribute up to 20% of the departure from the hydrogenic nf term value. To a good approximation this explains the observed discrepancy in polarizabilities. The effective polarizabilities we obtained are compared with values measured by other experimental techniques. The role of nonadiabatic effects in limiting the accuracy and utility of polarizabilities derived from spectral data is discussed. Based on our 2G data and the best available values for the 2S and 2F levels, we find the Cs i ionization energy to be 31406.4556(20) cm−1.

© 1981 Optical Society of America

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References

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  1. K. Bockasten, “A study of C iv: term values, series formulae, and Stark effect,” Ark. Fys. 10, 567–582 (1956).
  2. P. Risberg, “A revision of the term systems for Na i and K i based on hollow cathode observations,” Ark. Fys. 10, 583–606 (1956).
  3. K. Bockasten, “Polarizability of Mg+2 derived from hydrogen-like terms of Mg ii,” Phys. Rev. 102, 729–730 (1956).
    [Crossref]
  4. K. Bockasten, “Polarization formula for the 2F-series of Cs i,” J. Opt. Soc. Am. 54, 1065 (1964).
    [Crossref]
  5. U. Litzén, “The 5g levels of the alkali metals,” Phys. Scr. 1, 253–255 (1970).
    [Crossref]
  6. C. B. Ross, D. R. Wood, and P. S. Scholl, “Series limit and hydrogen like series in Pb ii,” J. Opt. Soc. Am. 66, 36–39 (1976).
    [Crossref]
  7. C. H. H. Van Deurzen, “Analysis of 4-ionized vanadium (V v),” J. Opt. Soc. Am. 67, 476–480 (1977).
    [Crossref]
  8. B. Edlén, “Atomic spectra,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. XXVII.
  9. K. B. S. Eriksson and I. Wenåker, “New wavelength measurements in Cs i,” Phys. Scr. 1, 21–24 (1970).
    [Crossref]
  10. H. J. Kleiman, “Interferometric measurements of cesium i,” J. Opt. Soc. Am. 52, 441–447 (1961).
    [Crossref]
  11. R. W. Shorthill and G. R. Fowles, “Interferometric measurements of isotope shifts in mercury ii and mercury iii with enriched isotopes,” J. Opt. Soc. Am. 48, 459 (1958).
    [Crossref]
  12. C. J. Sansonetti and K. L. Andrew, “Improved determinations of the n2D and n2F fine-structure intervals in neutral cesium,” Phys. Rev. A 22, 1370–1374 (1980).
    [Crossref]
  13. M. Born and W. Heisenberg, “Über den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten,” Z. Phys. 23, 388–410 (1924).
    [Crossref]
  14. J. E. Mayer and M. G. Mayer, “The polarizabilities of ions from spectra,” Phys. Rev. 43, 605–611 (1933).
    [Crossref]
  15. We refer to the polarizabilities derived from spectral data as effective polarizabilities because they may differ from the static polarizabilities of the ion core because of nonadiabatic effects in the atom. This is discussed in greater detail in Section 5.
  16. K. Bockasten, “Mean values of powers of the radius for hydrogenic electron orbits,” Phys. Rev. A 9, 1087–1089 (1974).
    [Crossref]
  17. A. Fröman, J. Linderberg, and Y. Öhrn, “Penetration effect in the 2F-series of Cs i,” J. Opt. Soc. Am. 54, 1064–1065 (1964).
    [Crossref]
  18. H. Eissa and U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: I. A correction to the adiabatic approximation,” Proc. Phys. Soc. London 92, 556–565 (1967).
    [Crossref]
  19. E. J. Kelsey and L. Spruch, “Retardation effects on high Rydberg states: a retarded R−5 polarization potential,” Phys. Rev. A 18, 15–25 (1978).
    [Crossref]
  20. U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: II. Evaluation of the polarizabilities from observed spectra,” Proc. Phys. Soc. London 92, 566–576 (1967).
    [Crossref]
  21. D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
    [Crossref]
  22. R. D. Cowan and J. B. Mann, “Stabilization of solution of the Hartree–Fock equations,” J. Comput. Phys. 16, 160–166 (1974).
    [Crossref]
  23. R. D. Cowan and D. C. Griffin, “Approximate relativistic corrections to atomic radial wavefunctions,” J. Opt. Soc. Am. 66, 1010–1014 (1976).
    [Crossref]
  24. K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).
  25. J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
    [Crossref]
  26. H. Coker, “Empirical free-ion polarizabilities of the alkali metal, alkaline earth metal, and halide ions,” J. Phys. Chem. 80, 2078–2084 (1976).
    [Crossref]
  27. K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
    [Crossref]
  28. R. R. Freeman and D. Kleppner, “Core polarization and quantum defects in high-angular-momentum states of alkali atoms,” Phys. Rev. A 14, 1614–1619 (1976).
    [Crossref]

1980 (2)

C. J. Sansonetti and K. L. Andrew, “Improved determinations of the n2D and n2F fine-structure intervals in neutral cesium,” Phys. Rev. A 22, 1370–1374 (1980).
[Crossref]

K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
[Crossref]

1978 (1)

E. J. Kelsey and L. Spruch, “Retardation effects on high Rydberg states: a retarded R−5 polarization potential,” Phys. Rev. A 18, 15–25 (1978).
[Crossref]

1977 (1)

1976 (4)

C. B. Ross, D. R. Wood, and P. S. Scholl, “Series limit and hydrogen like series in Pb ii,” J. Opt. Soc. Am. 66, 36–39 (1976).
[Crossref]

R. R. Freeman and D. Kleppner, “Core polarization and quantum defects in high-angular-momentum states of alkali atoms,” Phys. Rev. A 14, 1614–1619 (1976).
[Crossref]

H. Coker, “Empirical free-ion polarizabilities of the alkali metal, alkaline earth metal, and halide ions,” J. Phys. Chem. 80, 2078–2084 (1976).
[Crossref]

R. D. Cowan and D. C. Griffin, “Approximate relativistic corrections to atomic radial wavefunctions,” J. Opt. Soc. Am. 66, 1010–1014 (1976).
[Crossref]

1974 (2)

R. D. Cowan and J. B. Mann, “Stabilization of solution of the Hartree–Fock equations,” J. Comput. Phys. 16, 160–166 (1974).
[Crossref]

K. Bockasten, “Mean values of powers of the radius for hydrogenic electron orbits,” Phys. Rev. A 9, 1087–1089 (1974).
[Crossref]

1971 (1)

D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
[Crossref]

1970 (2)

K. B. S. Eriksson and I. Wenåker, “New wavelength measurements in Cs i,” Phys. Scr. 1, 21–24 (1970).
[Crossref]

U. Litzén, “The 5g levels of the alkali metals,” Phys. Scr. 1, 253–255 (1970).
[Crossref]

1967 (2)

U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: II. Evaluation of the polarizabilities from observed spectra,” Proc. Phys. Soc. London 92, 566–576 (1967).
[Crossref]

H. Eissa and U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: I. A correction to the adiabatic approximation,” Proc. Phys. Soc. London 92, 556–565 (1967).
[Crossref]

1964 (3)

K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).

A. Fröman, J. Linderberg, and Y. Öhrn, “Penetration effect in the 2F-series of Cs i,” J. Opt. Soc. Am. 54, 1064–1065 (1964).
[Crossref]

K. Bockasten, “Polarization formula for the 2F-series of Cs i,” J. Opt. Soc. Am. 54, 1065 (1964).
[Crossref]

1961 (1)

1958 (1)

1956 (3)

K. Bockasten, “A study of C iv: term values, series formulae, and Stark effect,” Ark. Fys. 10, 567–582 (1956).

P. Risberg, “A revision of the term systems for Na i and K i based on hollow cathode observations,” Ark. Fys. 10, 583–606 (1956).

K. Bockasten, “Polarizability of Mg+2 derived from hydrogen-like terms of Mg ii,” Phys. Rev. 102, 729–730 (1956).
[Crossref]

1953 (1)

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
[Crossref]

1933 (1)

J. E. Mayer and M. G. Mayer, “The polarizabilities of ions from spectra,” Phys. Rev. 43, 605–611 (1933).
[Crossref]

1924 (1)

M. Born and W. Heisenberg, “Über den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten,” Z. Phys. 23, 388–410 (1924).
[Crossref]

Andrew, K. L.

C. J. Sansonetti and K. L. Andrew, “Improved determinations of the n2D and n2F fine-structure intervals in neutral cesium,” Phys. Rev. A 22, 1370–1374 (1980).
[Crossref]

D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
[Crossref]

Bockasten, K.

K. Bockasten, “Mean values of powers of the radius for hydrogenic electron orbits,” Phys. Rev. A 9, 1087–1089 (1974).
[Crossref]

K. Bockasten, “Polarization formula for the 2F-series of Cs i,” J. Opt. Soc. Am. 54, 1065 (1964).
[Crossref]

K. Bockasten, “A study of C iv: term values, series formulae, and Stark effect,” Ark. Fys. 10, 567–582 (1956).

K. Bockasten, “Polarizability of Mg+2 derived from hydrogen-like terms of Mg ii,” Phys. Rev. 102, 729–730 (1956).
[Crossref]

Born, M.

M. Born and W. Heisenberg, “Über den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten,” Z. Phys. 23, 388–410 (1924).
[Crossref]

Coker, H.

H. Coker, “Empirical free-ion polarizabilities of the alkali metal, alkaline earth metal, and halide ions,” J. Phys. Chem. 80, 2078–2084 (1976).
[Crossref]

Cowan, R. D.

R. D. Cowan and D. C. Griffin, “Approximate relativistic corrections to atomic radial wavefunctions,” J. Opt. Soc. Am. 66, 1010–1014 (1976).
[Crossref]

R. D. Cowan and J. B. Mann, “Stabilization of solution of the Hartree–Fock equations,” J. Comput. Phys. 16, 160–166 (1974).
[Crossref]

D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
[Crossref]

Edlén, B.

B. Edlén, “Atomic spectra,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. XXVII.

Eissa, H.

H. Eissa and U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: I. A correction to the adiabatic approximation,” Proc. Phys. Soc. London 92, 556–565 (1967).
[Crossref]

Eriksson, K. B.

K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).

Eriksson, K. B. S.

K. B. S. Eriksson and I. Wenåker, “New wavelength measurements in Cs i,” Phys. Scr. 1, 21–24 (1970).
[Crossref]

Fowles, G. R.

Freeman, R. R.

R. R. Freeman and D. Kleppner, “Core polarization and quantum defects in high-angular-momentum states of alkali atoms,” Phys. Rev. A 14, 1614–1619 (1976).
[Crossref]

Fröman, A.

Gallagher, T. F.

K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
[Crossref]

Griffin, D. C.

R. D. Cowan and D. C. Griffin, “Approximate relativistic corrections to atomic radial wavefunctions,” J. Opt. Soc. Am. 66, 1010–1014 (1976).
[Crossref]

D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
[Crossref]

Heisenberg, W.

M. Born and W. Heisenberg, “Über den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten,” Z. Phys. 23, 388–410 (1924).
[Crossref]

Johansson, I.

K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).

Kahn, A. H.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
[Crossref]

Kelsey, E. J.

E. J. Kelsey and L. Spruch, “Retardation effects on high Rydberg states: a retarded R−5 polarization potential,” Phys. Rev. A 18, 15–25 (1978).
[Crossref]

Kleiman, H. J.

Kleppner, D.

R. R. Freeman and D. Kleppner, “Core polarization and quantum defects in high-angular-momentum states of alkali atoms,” Phys. Rev. A 14, 1614–1619 (1976).
[Crossref]

Linderberg, J.

Litzén, U.

U. Litzén, “The 5g levels of the alkali metals,” Phys. Scr. 1, 253–255 (1970).
[Crossref]

Mann, J. B.

R. D. Cowan and J. B. Mann, “Stabilization of solution of the Hartree–Fock equations,” J. Comput. Phys. 16, 160–166 (1974).
[Crossref]

Mayer, J. E.

J. E. Mayer and M. G. Mayer, “The polarizabilities of ions from spectra,” Phys. Rev. 43, 605–611 (1933).
[Crossref]

Mayer, M. G.

J. E. Mayer and M. G. Mayer, “The polarizabilities of ions from spectra,” Phys. Rev. 43, 605–611 (1933).
[Crossref]

Norlén, G.

K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).

Öhrn, Y.

Öpik, U.

U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: II. Evaluation of the polarizabilities from observed spectra,” Proc. Phys. Soc. London 92, 566–576 (1967).
[Crossref]

H. Eissa and U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: I. A correction to the adiabatic approximation,” Proc. Phys. Soc. London 92, 556–565 (1967).
[Crossref]

Risberg, P.

P. Risberg, “A revision of the term systems for Na i and K i based on hollow cathode observations,” Ark. Fys. 10, 583–606 (1956).

Ross, C. B.

Safinya, K. A.

K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
[Crossref]

Sandner, W.

K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
[Crossref]

Sansonetti, C. J.

C. J. Sansonetti and K. L. Andrew, “Improved determinations of the n2D and n2F fine-structure intervals in neutral cesium,” Phys. Rev. A 22, 1370–1374 (1980).
[Crossref]

Scholl, P. S.

Shockley, W.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
[Crossref]

Shorthill, R. W.

Spruch, L.

E. J. Kelsey and L. Spruch, “Retardation effects on high Rydberg states: a retarded R−5 polarization potential,” Phys. Rev. A 18, 15–25 (1978).
[Crossref]

Tessman, J. R.

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
[Crossref]

Van Deurzen, C. H. H.

Wenåker, I.

K. B. S. Eriksson and I. Wenåker, “New wavelength measurements in Cs i,” Phys. Scr. 1, 21–24 (1970).
[Crossref]

Wood, D. R.

Ark. Fys. (3)

K. Bockasten, “A study of C iv: term values, series formulae, and Stark effect,” Ark. Fys. 10, 567–582 (1956).

P. Risberg, “A revision of the term systems for Na i and K i based on hollow cathode observations,” Ark. Fys. 10, 583–606 (1956).

K. B. Eriksson, I. Johansson, and G. Norlén, “Precision wavelength measurements connecting the Cs i 6s, 6p, and 6d levels, with a study of the correction for phase change in infrared interferometry,” Ark. Fys. 28, 233–238 (1964).

J. Comput. Phys. (1)

R. D. Cowan and J. B. Mann, “Stabilization of solution of the Hartree–Fock equations,” J. Comput. Phys. 16, 160–166 (1974).
[Crossref]

J. Opt. Soc. Am. (7)

J. Phys. Chem. (1)

H. Coker, “Empirical free-ion polarizabilities of the alkali metal, alkaline earth metal, and halide ions,” J. Phys. Chem. 80, 2078–2084 (1976).
[Crossref]

Phys. Rev. (3)

J. R. Tessman, A. H. Kahn, and W. Shockley, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890–895 (1953).
[Crossref]

J. E. Mayer and M. G. Mayer, “The polarizabilities of ions from spectra,” Phys. Rev. 43, 605–611 (1933).
[Crossref]

K. Bockasten, “Polarizability of Mg+2 derived from hydrogen-like terms of Mg ii,” Phys. Rev. 102, 729–730 (1956).
[Crossref]

Phys. Rev. A (6)

C. J. Sansonetti and K. L. Andrew, “Improved determinations of the n2D and n2F fine-structure intervals in neutral cesium,” Phys. Rev. A 22, 1370–1374 (1980).
[Crossref]

K. Bockasten, “Mean values of powers of the radius for hydrogenic electron orbits,” Phys. Rev. A 9, 1087–1089 (1974).
[Crossref]

K. A. Safinya, T. F. Gallagher, and W. Sandner, “Resonance measurements of f–h and f–i intervals in cesium using selective and delayed field ionization,” Phys. Rev. A 22, 2672–2678 (1980).
[Crossref]

R. R. Freeman and D. Kleppner, “Core polarization and quantum defects in high-angular-momentum states of alkali atoms,” Phys. Rev. A 14, 1614–1619 (1976).
[Crossref]

E. J. Kelsey and L. Spruch, “Retardation effects on high Rydberg states: a retarded R−5 polarization potential,” Phys. Rev. A 18, 15–25 (1978).
[Crossref]

D. C. Griffin, R. D. Cowan, and K. L. Andrew, “Instabilities in the iterative solution of the Hartree–Fock equations for excited electrons,” Phys. Rev. A 3, 1233–1242 (1971).
[Crossref]

Phys. Scr. (2)

K. B. S. Eriksson and I. Wenåker, “New wavelength measurements in Cs i,” Phys. Scr. 1, 21–24 (1970).
[Crossref]

U. Litzén, “The 5g levels of the alkali metals,” Phys. Scr. 1, 253–255 (1970).
[Crossref]

Proc. Phys. Soc. London (2)

H. Eissa and U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: I. A correction to the adiabatic approximation,” Proc. Phys. Soc. London 92, 556–565 (1967).
[Crossref]

U. Öpik, “The polarization of a closed-shell core of an atomic system by an outer electron: II. Evaluation of the polarizabilities from observed spectra,” Proc. Phys. Soc. London 92, 566–576 (1967).
[Crossref]

Z. Phys. (1)

M. Born and W. Heisenberg, “Über den Einfluss der Deformierbarkeit der Ionen auf optische und chemische Konstanten,” Z. Phys. 23, 388–410 (1924).
[Crossref]

Other (2)

We refer to the polarizabilities derived from spectral data as effective polarizabilities because they may differ from the static polarizabilities of the ion core because of nonadiabatic effects in the atom. This is discussed in greater detail in Section 5.

B. Edlén, “Atomic spectra,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. XXVII.

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Figures (3)

Fig. 1
Fig. 1

(a) The relative positions of the 4f 2F and ng 2G levels and their allowed transitions are illustrated. The 4f 2F fine structure is inverted, but the ng 2G levels have normal fine-structure ordering. (b) The 4fng multiplet has three lines whose positions and intensities are shown schematically. In our data the 4f 2F7/2ng 2G7/2,9/2 transitions (B and C) were not resolved. We have obtained an estimate of the 2G fine-structure intervals from the separation of the lines in the observed doublet.

Fig. 2
Fig. 2

The polarization formula can conveniently be plotted in the linearized form of Eq. (6). Here the solid line is the fitted formula, whereas the crosses represent the experimental levels. Both the 2G series (a) and the 2F series (b) can be described accurately by polarization formulas with approximately the same series limit, but the fitted ion polarizabilities are quite different. When the two series are fitted simultaneously (c), the fitted limit is much higher and the quality of the fit is poor. The rms deviation shown here refers only to the levels included in the fit.

Fig. 3
Fig. 3

Comparison of the inferred and calculated nonpolarization contribution to the nf term values. The inferred values plotted are the average of columns A and B in Table 4. The calculated contribution includes penetration, exchange, and relativistic effects. Determination of the inferred and calculated contributions is discussed in detail of Section 3. The calculated values give a good representation of both the magnitude and the n dependence of nonpolarization effects except for the lowest values of n.

Tables (7)

Tables Icon

Table 1 Observed 4fng Transitions of Cs i

Tables Icon

Table 2 ng 2G Levels and Fine-Structure Intervals

Tables Icon

Table 3 Comparison of Polarization Fits to the n–12f 2F levels (n = 4–6)

Tables Icon

Table 4 Calculated and Inferred Corrections to the Polarization Term Values

Tables Icon

Table 5 Cs i Ionization Limit

Tables Icon

Table 6 History of the Cs i Ionization Limit

Tables Icon

Table 7 Theoretical and Empirical Values of the Cs+ Dipole and Quadrupole Polarizabilities

Equations (23)

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Δ ( n g G 2 ) = 36 [ - 0.1814 - Δ ( 4 f F 2 ) ] / 35 cm - 1 ,
T ( n , l ) = T H ( n , l ) + Δ T pol ( n , l ) ,
T H ( n , l ) = Z 2 R n 2 [ 1 + α 2 Z 2 n 2 ( n l + 1 2 - 3 4 ) ] ,
Δ T pol ( n , l ) = R a 0 [ α d r - 4 ( n , l ) + α q r - 6 ( n , l ) ] ,
E ( n , l ) = E - T H ( n , l ) - R a 0 [ α d r - 4 ( n , l ) + α q r - 6 ( n , l ) ] .
[ E - E ( n , l ) - T H ( n , l ) ] / R a 0 r - 4 ( n , l ) = α d + α q r - 6 ( n , l ) / r - 4 ( n , l ) .
H = H c + H v + H c - v = H c + ( p v 2 2 m - 2 z r v ) + k 2 r v - r k ,
H = H c + [ p v 2 2 m - 2 ( z - k 1 ) r v ] + 2 k { r v · r k r v 3 + 1 2 [ 3 ( r v · r k ) 2 r v 5 - r k 2 r v 3 ] } .
ψ ( p , q ) = ψ c ( p ) ψ H ( q ) ,
V pen ( r ) = V ( r ) - V H ( r ) ,
V H ( r ) = - 2 Z r
V ( r ) = - 2 r Z ( r ) r 2 d r
Z ( r ) = A - 0 r k q k ψ k 2 ( r ) d r .
Δ T pen = - 1 2 0 ψ v 2 ( r ) V pen ( r ) d r = - 1 2 V pen ,
E xch i j = - 1 2 k ( l i k l j 0 0 0 ) 2 G k ( i j ) ,
G k ( i j ) = 0 0 2 r < k r > k + 1 × ψ i ( r 1 ) ψ j ( r 2 ) ψ j ( r 1 ) ψ i ( r 2 ) d r 1 d r 2 .
Δ T xch = - 1 2 k q k E xch k v ,
Δ T rel = α 2 4 0 [ v - V ( r ) ] ψ v 2 ( r ) d r ,
Δ T rel = Δ T rel - R α 2 Z 4 n 4 ( n l + 1 2 - 3 4 ) .
E n = E - R / ( n - a - b t n - c t n 2 - ) 2 ,
t n = ( E - E n ) / R .
Δ T pol = R a 0 [ α d ( y 0 d r - 4 + y 2 d r - 6 ) + α q y 0 q r - 6 ] .
α d = y 0 d α d and α q = α d y 2 d + α q y 0 q .